CA2142501A1

CA2142501A1 - System and method for scheduling resource requests

Info

Publication number: CA2142501A1
Application number: CA002142501A
Authority: CA
Inventors: John E. Collins; Elizabeth M. Sisley
Original assignee: Minnesota Mining and Manufacturing Co
Current assignee: 3M Co
Priority date: 1994-03-18
Filing date: 1995-02-14
Publication date: 1995-09-19
Also published as: IL112552A; EP0672990A3; EP0672990A2; IL112552A0; JPH0830694A; US5623404A

Abstract

A system and method for scheduling resource requests for a resource provider generate a first schedule, based on expected durations of each resourcerequest, and a second schedule, based on longer, pessimistic durations of each resource request. A user interface simultaneously displays the first and second schedules to a system user. The first schedule provides the system user with a guide to good overall management of the resource performance. The second schedule provides the system user with a guide for making time commitments to customers with a greater degree of confidence. The system and method employ a variety of techniques including statistic probability calculations to determine expected and pessimistic durations for each resource request, and incorporate features for updating the first and second schedules in response to dynamic changes in the resource environment.

Description

SYSTEM AND METHOD FOR SCHEDULING
S RESOURCE REQUESTS

Field of the Invention The present invention relates to resource m~ag~ pnt~ and, more particularly, to techniques for s~hçd~ ng resoulc.; requests ~c~i~ned to a resource provider.

Discussion of Related Art Resource sched~ ne problems are a conce~l~ in many G,~,~ni~l;ons in which a plurality of resource requests are assigned to an individual resource provider. If the individual resource provider cannot handle all resource requests ~iml-lt~neously, a schedule must be generated. The s~hedule must define a time-ordered sequence of the resource requests ~signed to the individual resource provider, and specify particular times at which the resource provider is to serve each resource request.
Techniques for generating a sçhedl-le consider time-related factors such as the priorities and durations of the resource requests, and transition times between consecutively scheduled resource reqllest~
The durations of the resource requests, in particular, greatly affect the efficient schedl.ling of future resource requests, as well as the ability to make time commitmçnts to the entities requçstine resources. The duration of a ,eso- rce request refers to the amount of time that a resource provider requires to serve the request, and a time con,.,-i~",c,-l refers to a promised time at which the resource provider is to start to serve the request. In a cG~Iplete schedule, the resourcerequests are each ~signed start and cG",pletion times based on the eYpected durations of preceding resource requests and transition times. However, the durations of resource requests inevitably vary with the type of resources requested, and even vary for resource requests involving the same types of resources.
Variation in the duration of a resource request will introduce variability into its , comyletion time, and that variability will propagate to the start times of subsequent resource reque~s. This variation makes reliable sehed~ling very difficult.
Fxi.cting s~-h~-ling systems employ two basic appr~^hes to the uncellain~y problem. The first appr~^h simply A~sum~s a fixed duration for resource requests5 involving the same types of resou~ces, based on past ~Ape,ience. This appl.~ehaddresses the variation in the durations of resource requests involving diLrel~
types of resources, but ignores the potential unc~l lainly in the durations of resource requests of the same type. Thus, confid~nce in the ability to make time CG~ I e "ains low. The second approach attempts to accommod~te the ul~cel lainl~ by incorporating a degree of slack into the sched~ le based on predicted maximums for the durations of particular types of resource requests. This marginof error enables more confident time co.. ;l.. ç~ but results in an inefficient use of the resource provider's time.
One example of the foregoing sched~lling problem arises in the context of a 15 field service envirol""enl. A field service environment exists in many or~Pni~l;ons, characterized by a group of field service technicians dedicated to the repair and ..\Ai~ n~ce of a variet~v of industrial machines, office equipment, and the like. The field service technicians travel to a customer's location to pclrc."~, routine m~int~nonce of the cu~lo~e~'s equipment and to provide repair services pursuant to 20 customer service calls sçhe~ ed by a service call ~ispatçher Thus, in the field service environmenl, the technicians act as resource providers, pe,ru""n~g m~;..len~llce and repair services in response to resource requests in the form of routine m~intçn~nce appoinl",enls and customer service calls.
The duration of the service calls may vary according to the type of service involved. For eAalllple, a service call requesting a major repair may require much more time than a service call requesting routine m~intçnonce~ In addition, two service calls requestin~ the same type of repair may nevertheless vary in duration due to a col"bination of ul~reseen factors such as, for eA~"ple, misdio~osis of the problem by the customer, the pr~3ence of additional necessA~ y repairs noticed by the technician upon arrival, uneA~ e~iled delay in access to the equipment at the customer's location, and even variations in the pace of the technician's work. If the 2142SOl .
service call ~licpatrher generates a srhed~le based on the as;,u,-")tion of fLxed durations for certain types of service calls, the ability to make time CG~ to customers clearly is ,n-pairod. Alternatively, if the service call ~licp~tçhPr il~col~Jolales slack into the schP,dule by allotting a margin of unc~ y to each of 5 the service calls, time co~ ei~lc to cllstomers can be made with a higher degree of confidence. However, the srhed~lle will include a cienificsnt amount of nneceSC~.~ slack that causes incr~ed idle time for the service technician and overly pes~ cl;c ~n~ -f-~1s to CUSlGIll~ i, reslllting in general inefficiency.

SummarY of the Invention In view of the shortcG.~ .gs of eYisting resource scheduling techn;qll~c the present invention is directed to a system and method for schp~duling resource requests having uncertain durations with increased reliability.
Additional features and advantages of the invention will be set forth in part in the description that follows, and in part will be appal e"l from the description, or may be learned by practice of the invention. The advantages of the invention will be realized and a~ ed by the system and method particularly pointed out in the written description and claims hereof, as well as in the appended dl~wings.
To achieve the ~regoing advantages, as broadly embodied and described herein, the present invention provides, in one aspect, a system and method for scheduline a plurality of resource requests for a resource provider, whereill each of the resource requests has an uncertain duration. To sçhedule the resource requests, the system and method determine first potential durations for the resource requests, determine second potential durations for the resource requests, generate a sequence ofthe resource request~, gene.ale a first sçh~ e ofthe resource requests by ~Ccigning a first start time to each ofthe resource requests following a first one of the resource requests in the sequence based on a sum of the first potential durations dete""med for the preceding resource requests in the sequence, and gene, ~le a second schedule of the resource requests by ~c.ci~ a second start time to each of the resource requests following the first one ofthe resource requests in the 2142SOl -sequçnce based on a sum of the second potential durations dete. .nined for the plece~ih,g, resource requests in the se~uence In another aspect, the present invention provides a system and method for sç~edl-ling a plurality of resource requests for a ~source provider, wherein each of the resource requests has an uncc;l li~n duration, and each of the resource requests is associated with one of a plurality of ~liQ`ere lt types of activities. To sçhedllle the resource requestc, the system and method match each ofthe resource requests withone of a plurality of probaL 'ity distributions for a pote.ltial duration ofthe respective resource request based on the type of activity associated with the lespec~i~e resource request, generate a sequence ofthe lesol~rce requests, gener~le a first combined pl ob7~--lity distribution for each of the resource requests, the first combined probability distribution combhullg the probability distributions m~tshed with each of the preceding resource requests in the sequence, select a probability level, compute, for each of the resource requests, a duration in the first cG--,bined probability distribution for the respective resource request based on the probability level, and generate a s~ edule ofthe resource requests by ~Csignin~ a start time to each of the resource requests following the first one of the resource requests in the sequ~nce based on the duration in the first cG~I.billed probability distributioncomputed for the respective resource request.
It is to be understood that both the fo,egoing general desc-il,Lion and the following detailed description are e~e..-~,la"r and explanatory only, and not restrictive of the invention, as cl~imed The accG.Ilp~l~ing drawings are in~l~lded to provide a further undt;l~ n.1ing of the invention and are illCOIlJOl ated in and constitute a part of this specification.
The drawings illustrate e ~e . ~lq~ ~ embo~ Pnt~ of the invention and together with the description serve to explain the pli.lc;ples ofthe invention.

Brief D~ s ~ ;~lion of the Dl .... i Fig. 1 is a block diagram of a computer- r.plçmPnted software process 30 structure incorporating a system and method for sçhedllling resource requests in accordance with the present invention;

Fig. 2 is an example of a user interface displaying a representation of a set ofschedules in accordance with the present invention;
Fig. 3 is a flow diagram illustrating a technique for ge~c,aling an expected schedule and a pessimistic schedule of resource req~lest~, in accordance with the present invention;
Fig. 4 is an example of a probability distribution for the potential duration ofa resource request;
Fig. 5 is a flow diagram illustrating another technique for generating an expected schedule and a pçssimistic schedule of resource requests, in accordancewith the present invention;
Fig. 6 is an example of a user interface simultaneously displaying a repl esenlalion of an expected schedule and a pessimi~tic schedule of resource requests generated as in Fig. 3 or Fig. 5;
Fig. 7 is a flow diagram illustrating the generation of a warning indication in response to excessive variability in the expected and pessimistic schedules, in accordance with the present invention;
Fig. 8 is a flow diagram illustrating a technique for generating an optimistic schedule of resource requests, in accordance with the present invention;
Fig. 9 is an example of a user interface simlllt~neously displaying an expected schedule, a pes~imi~tic schedule, and an optimistic schedule of resource requests generated as in Figs. 3 or 5, and Fig. 8;
Fig. 10 is a flow diagram illustrating another technique for generating a pessimi~tic schedule of resource requests based on a combination of probability distributions for the durations of consecutively scheduled resource requests, inaccordance with the present invention;
Fig. 11 is an example of a combined probability distribution for the durations of consecutively scheduled resource requests;
Fig. 12 is a flow diagram illustrating the recalculation of a combined probability distribution in response to the actual duration of a completed resource request or the actual running duration of an active resource request, in accordance with the present invention;

Fig. 13 is an example of a schedule having a resource request with a duration extçntling beyond a sçhed~ling boundary;
Fig. 14 is an example of a terhniq~le for modifying the schedule shown in Fig. 13 to accommodate the portion ofthe resource request çYtçnfling beyond the sched~.ling boundary, in accordance with the present invention; and Fig. 15 is an example of a second technique for modifying the schedule shown in Fig. 13 to accommodate the portion of the resource request rYtçnding beyond the srhecll.ling boundary, in accordance with the present invention.

Detailed D~ )lion of the Preferred Embodiments One skilled in the art, given the description herein, will recognize the utilityof the system and method of the present invention in a variety of diverse resource environments in which scheduling problems exist. For example, it is conceivable that the system and method of the present invention may be adapted for ~ccignmrnt and scheduling problems existent in telecommunications systems, transportation disp~tçhing organizations, and emergency services dispatching or~ni7~tions.
However, for ease of description, as well as for purposes of example, the present invention will be described in the context of a field service emdl on.,lel.l. The system and method of the present invention will also be described together herein, with the method contemplated as being implemented as a series of operations performed by the system.
Fig. 1 is a block diagram of a computer-implemented software process structure 10 configured for application in a field service environment. The software process structure 10 incorporates a system 12 for ~csi~ning and schedllling service calls, a service m~n~g~n çn~ system (SMS) interface 14, and at least one interactive user interface 16. The ~csigning and schedllling (A/S) system 12 is a software system realized, for example, by a software process running on a standard UnixTMwolksla~ion. The A/S system 12 combines optil- i~alion, artificial intçllig~ r,e, and constraint-processing techniques to arrive at near-optimal ~ccignm~nt and schednlin~ solutions.

21~250 1 The SMS interface 16 provides communication between A/S system 12 and a service management system (SMS) (not shown), which IllA~ ;n.c a record of new service calls and changes to the attributes of pending service calls, as received from customers. The user interface 16 enables a system user, such as a service call lispAtch~r, to communicate with the A/S system 12, and provides a graphical epresel.lalion of leco....~ ed accignm~nt and sehçdl~ling solutions generated byA/S system 12. Via user interface 16, the system user can enter çhAnges to both the attributes of pending service calls and the attributes of teçhn;-i~nc ope- ali-~g in the field service environment, and may request reevaluation of previous Accignment and schedl-lin~ recommen~Ations by AJS system 12.
In response to new service calls, call cancellations, call attribute changes, technician attribute changes, and requests for reevaluation, as received from SMS
interface 14 or user interface 16, the A/S system 12 activates two software process modules that cooperate to reach an acsignment and sched~llin~ solution.
Specifically, as shown in Fig. 1, A/S system 12 comprises an assigner module 20,responsible for Acsjgning new and pending service calls among the technicians, and a scheduler module 22, invoked by the accigner module 20 to generate a schedule of the calls assigned to each individual technician. The system and method of the present invention are directed specifically to the sched.lling operation of scheduler module 22, and to the graphical display operation of user interface 16.
The assigner module 20 searches for potential assignments of service calls among the service technicians, and evaluates a portion of an objective function relating to the desirability of particular associations of calls and technicians. The assigner module 20 invokes scheduler module 22 to search for potential schedulesof the calls ~c.ci~ned to a particular technician, and then to evaluate a portion of the objective function relating to time. Each ofthe potential sçhedl.les searched byscheduler module 22 repl ese,lls a sequence of the service calls in finite time intervals. Thus, a complete accignment of a service call involves both an association of the call with a technician, as determined by assigner module 20, and a sçhed~-ling of the call at a particular time, as determined by the scheduler module 22.

For each invocation of scheduler module 22, the q-~ignçr module 20 passes to scheduler module 22 a set of service calls a~.~igned to a particular technician, as well as a set of call attributes identifying the type of service activity associated with each ofthe calls. In response, the sched~-ler module 22 p~rc,l,.,s a recursive depth-first search that explores potential schedules of the service calls ~igned to the technician to determine the most efficient sçllecl-.le. The sçhedlllçr module 22recursively generates each potential schedule by building a sequence of the service calls qc~igned to a technician one-call-at-a-time, and determines the efficiency, or "stress" value, of each schedule based on a variety of time-related factors.
The scheduler module 22 typically assigns a start time to the first call in the sequence based on the begi~ il-g ofthe work day plus an initial travel time from the technician's starting location. Because the actual duration of a service call isuncertain, however, scheduler module 22 assigns a completion time to the first call based on an estimated duration of the call. The estim-q-ted duration of a call may be specified by the system user and stored in a call duration file (not shown) referenced by the scheduler module 22. For example, the system user may estim~te durations for several types of calls based on an average of the durations of past calls involving the same service activities.
The scheduler module 22 assigns a start time to the next call by adding an estimated travel time to the completion time of the preceding call in the sequence.
The estimqted travel time eplesenls the time necessqry for the technician to travel between the customer locations associated with the preceding call and the next call.
Thus, scheduler module 22 determines the start time for the next call based on both the estimqted duration of the preceding call and an estimqted travel time between the preceding call and the next call. The travel time may be based on an average of past travel times between the locations associated with the calls, or may be estimqted based on the actual tli~tqncec between locations. For example, scheduler module 22 may ascertain the locations associated with particular service calls by referring to postal zip code centroid information. The scheduler module 22 assigns a completion time to the next call by adding the estimqted duration ofthe next call to the start time. In this manner, scheduler module 22 determines the completion time for the next call based on the estimqted duration ofthe plecedil~g call, the es~im~ted travel time between the pl eceding call and the next call, and the estim~ted duration of the next call. The schPAulrr module 22 recursively builds the rçm~inder ofthe sequence in the same manner by contin--ing to place one ofthe le~.~Ai~ g calls next in the sequence until none ofthe calls remains lln~çhed~lled.
Fig. 2 is an eY~mrle of a glaph-c~l replese..lalion of a set of srhedllles generated by the schedlller module 22, as displayed by user interface 16. The user interface 16 may be il~plcmen~erl, for example, using X-Windows, and preferably displays an interactive scheduler window 30 co..~ g a represenlalion of the sçhedllles for selected technicians. The scheduler window 30 incl~ldes a technician field 32 cont~inin~ a representation of a particular group of technicians under evaluation by the system user, a schedule field 34 co~ g a replesenlalion of thecalls assigned to each of the technicians and the particular times for which the calls are scheduled, and a command bar 36 co.~ -g eplesenlations of standard window control comm~nds.
In Fig. 2, the technician field 32 displays a group of technicians A, B, C, D, and E operating in the field service environmenl. The schedule field 34 represents the existing schedules of the technicians, as generated by the scheduler module 22, subject to approval or modification by the system user. The schedule field 34 inFig. 2 indicates that technician A has been ~c~igned first, second, and third scheduled calls rep-ese"led by call blocks 38, 40, and 42. The call blocks 38, 40, and 42 represent schedlllin.f~ ofthe calls between 9:00 and 15:00 on Monday, May17. Specifically, call blocks 38, 40, and 42 indicate assigned start times for the first, second, and third calls of app-ox~".ately 9:00, 11: 15, and 1: 15, respectively. The completion times indicated by call blocks 38, 40, and 42, respectively, are approximately 10:45, 12:45, and 2:45.
The schedule field 34 also inrl~ldes time blocks 44, 46, 48 represç~ -g travel times. Time block 44 indicates the initial travel time, from the beginning of the day, required for the technician to travel from headquarters, or from a location associated with an other~vise unavailable time, to the customer location associated with the first call. Travel times 46 and 48 separate the start and completion times of the consecutively scheduled calls in-lic~ted by call blocks 38 and 40, and call blocks 40 and 42, 1 espe.iLi~ely. The time blocks 46, 48 represent the time required by the technician to travel from a customer location associated with the preceding call to a customer location associated with the next call.
S Although the sçhedllles generated by s~hed~.ler module 22, as shown in Fig.

2, are useful for m~n~ng and predicting technician pe.ro,.-,al-ce, the start andcompletion times of each call nevertheless are based only on estimstions of uncertain durations. The uncel~inly ofthe durations makes the reliable schedl.lin~
of future service calls difficult, and results in a questionable degree of confidence in time co-~,-.. ;l~-.ents made to customers.
In accordance with the present invention, to increase the confidence of time co""nill.lents, the scheduler module 22 is configured to generate both a first schedule based on expected durations of the service calls, and a second schedulebased on pessimistic durations of the service calls. The expected durations may represent average durations, whereas the pçssimictic durations leplese"~ longer than average durations. By srhedl-lin~ according to average durations, the first, "expected" schedule enables good overall management oftechnician pelro~l,ance.
By scheduling according to longer durations, the second, 'lpessimicticll schedule enables the user to make time commitments to customers with a greater degree of confidence. Thus, after the scheduler module 22 has selected a call to be placednext in the sequence of calls of a potential schedule, the scheduler module 22 must assign expected and pescimictic start times and expected and pessimictic completion times to the call, in accordance with the present invention.
If the subject call is the first call in the sequence, the expected and pescimictic start times assigned by the sr.heduler module 22 are simply the beginning of the work day plus the initial travel time between the location of the technician's headquarters, or a location associated with an otherwise unavailable time, and the location associated with the first call. In contrast, if the call is a subsequent call in the sequence, the expected and pessimistic start times ac.si~ned by the scheduler module 22 are based, respectively, on the sums ofthe expected and pescimistic durations of the preceding calls in the sequence, the initial travel time, and the travel 21~2501 times between locations associated with consecutive preceding calls. The scheduler module 22 further assigns expected and pescimistic co-,-pl~tion times to the first call in the sequence based, respectively, on only the expected and pçscimictic durations of the first call and the initial travel time. If the call is a subsequent call in the sequence, however, the expected and peSsimictic completion times acsignpA by thescheduler module 22 are based on the sums of the expected and pescimictic durations, lespeclively, ofthe pleceding calls in the sequence and the call to which the completion time is assigned, the initial travel time, and the travel times between locations associated with consecutive pr~ceding calls.
The flow diagram of Fig. 3 illustrates the operation of the scheduler module 22 in assigning expected and pçs~ cl ;c start and completion times to an individual call, in accordance with the present invention. As indicated by block 50, the scheduler module 22 first determines the type of service activity associated with the call based on the call attributes passed by the assigner module 20. The scheduler module 22 then re~elences a call duration file (not shown) to determine expectedand pessimictic durations for service calls associated with the same type of activity.
The call duration file may contain a plurality of statistical probability distributions providing duration variability information for each type of activity. The call duration file alternatively way contain fixed expected and pessimi.ctic duration pairs for the particular type of activity, as entered by the system user. The system user may enter the fixed durations in the event that variability information is either unavailable or not yet developed for the particular field service environment. If the call duration file contains neither variability information nor fixed durations for the subject activity, the scheduler module 22 simply substitutes a default value for both the expected and peScimictic durations.
If the call duration file contains fixed expected and pessimistic duration pairs, the scheduler module 22 accepts them for use in ~cci~ninF~ expected and pescimistic start and co-"pl~,lion times. However, if the call duration file contains variability i~""a~ion, the scheduler module 22 m~tçi~çs the call with one of thestatistical probability distributions, as indicated by block 52 of Fig. 3, based on the type of activity associated with the call. The duration file may contain probability 2142~01 distributions di~erç..l;~ted by both the type of service activity and the particular technician involved. The duration file thereby incllldes variability i,~"..alion that considers the dirre, ~.~t durations attributed to individual technicians. In this case, scheduler module 22 m~tches the call with an app1op,;ale probability distribution based on the type of service activity involved and the identity of the particular technician, as determined by the call attributes.
An example of a st~tisti~l probability distribution is shown in the graph of Fig. 4, in which the curve 80 is a probability density function represe.~ g the probability p that a particular call will have a duration x, in mimltes A probability distribution can he constructed by monitoring the actual durations of calls of the same type as they are completed over a period of time. If variance in individualtechnician performance is a consideration, probability distributions can be constructed by monitoring durations of calls of the same type that involve the same technician.
l 5 Once the call has been matched with the approp. iate probability distribution, the scheduler module 22 selects a first probability level for the expected schedule and a second probability level for the pessimi~tic schedule, as indic~ted by blocks 54 and 56, respectively. The levels of probability represent relative degrees of certainty, or "confidence" in the call durations in the respective schedules. For example, a probability level of 0.5 affords a fifty percent degree of confidence in the expected schedule, which may be sufficient for m~n~ing technician pe,ro""ance.
A probability level of 0.5 corresponds to is the median of the distribution, andmeans that the actual duration of the call will be less than or equal to the expected duration fifty percent of the time. A much higher degree of confidence may be required for the pessimietic schedule to ensure that most of the time co.~.. ;l.. ~nts promised to customers are satisfied. Thus, if a probability level of 0.9 is selected, the system user can be ninety percent confident that the actual durations of the calls will be less than or equal to the pes~imi~tic durations determined by the scheduler module 22. With a probability level of 0.9, the system user can be ninety percent certain that a time co"-" il,.,ent to a customer will not be broken.

214250~

As indicated in blocks 58 and 60, re~,ecli~/ely, the scheduler module 22 computes durations in the probability distribution m~tched with the re~l~ecli~/e call based on the expected and pessimi~tic probability levels to determine the expected and pes~imi~tic durations. With rer~ ce to the graph shown in Fig. 4, a durationcan be computed based on the probability level by integrating along the density curve 80. For example, the duration T for a probability level of 0.9 can be ascertained according to the cA~ression:

o.s¦ ~i(x), (1) where ~(x) is the density function represenled by curve 80 of Fig. 4.
For s~led~ling the duration computed based on the expected probability level then serves as the expected duration of the call, and the duration computed based on the pe~.~imi~tic probability level serves as the pes~imi.stic duration ofthe call. The expected completion times are determined for each of the calls as they are placed in the sequence based on the expected durations. As a result, scheduler module 22 can assign an expected start time to a new call by adding the estim~ted travel time to the expected completion time for the immediately preceding call. The expected start time of the new call is then based on the expected durations computed for the preceding calls in the sequence plus travel times, as indicated by block 62. The scheduler module 22 assigns the expected completion time to the new call by adding the expected duration for the new call to the expected start time for the new call. Thus, the expected completion time is based on the expected durations computed for the preceding calls, the expected duration computed for the new call to which the completion time is ~csigned, and the travel times, as in~lic~ted by block 64.
Similarly, scheduler module 22 assigns the pes~imistic start time to a new call by adding the estim~ted travel time to the pes~imistic completion time for the immerli~tely preceding call. In this manner, the pessimi~tic start time for the new call is based on the pe.~simictic durations computed for the pleceding calls in the sequence plus travel times, as indicated by block 66. The scheduler module 22 assigns the pes~imictic completion time to the new call by adding the pessimi~tic duration for the new call to the pes~imistic start time for the new call, such that the pes~imictic completion time is then based on the pessimi~tic durations computed for the preceding calls, the pes~imistic duration computed for the call to which thecompletion time is ~si~ne~l~ and the travel times, as in-liçated by block 68. For the first call in the sequence, of course, the expected and pessimi~tic start times both correspond to the first available time on the schedule plus the initial travel time, and the expected and pes~imictic completion times are then based only on the expected and pessimi~tic durations, respectively, computed for the first call.
The travel times between locations associated with consecutively scheduled calls may also vary. Thercrol e, the scheduler module 22 may also r~rere,-ce a travel time file (not shown) similar to the call duration file when h1col 1l~ ~th~g travel time into the 0 schedule. A travel time file may provide, for example, expected and pes~imi~tic travel times for travel between the same two locations. As in the call duration file, the expected and pes~imi~tic travel times may be provided in the form of statistical probability distributions for travel time or fixed expected and pçssimi~tic travel time pairs. Thus, by determining the locations associated with consecutively sçhedl.led calls, based on the call attributes passed by assigner module 20, the scheduler module 22 can match a particular travel interval with a set ofexpected and pessimi~tic travel times in the travel time file.
As an alternative to selecting a first probability level for the expected schedule, scheduler module 22 may simply determine the mean duration in the probability distribution m~tçhed with the call. The scheduler module 22 then accepts the mean duration as the expected duration of the call. In most real-world probability distributions, the mean duration does not correspond to a probability level of 0. 5, but may be selected because it gives the best overall estim~te for the schedule. The operation ofthe schecll~lçr module 22 in generating an expected schedule based on mean durations and a pessimistic schedule based on probabilitylevels is illustrated in the flow diagram sho~vn in Fig. 5.
The scheduler module 22 first determines the type of service activity associated with each oil the service calls, as inflic~ted by block 82, and m~tçhes the respective call with a corresponding probability distribution, as indicated by block 84. Again, the probability distributions may be further dirrere~ ted according to 21~2501 the particular technician h~n~lin~ the call. For the expected sched~-le, the scheduler module 22 calculates a mean value for the durations in the probability distribution, as indicated by block 86. The mean value serves as the expected duration for thelespec~ e call. The scheduler module 22 then selects a pescimictic probability level, as indicated by block 88, based on a preset value or user input. As indicated byblock 90, the sched..ler module 22 computes a duration in the probability distribution m~tçhed with the lespecli~re call based on the pecsimictic probability level to determine the pescimistic duration.
The expected start time is then ~csiened by adding an estim~ted travel time to the expected completion time of the preceding call, such that the expected start time is based on the mean durations calculated for the preceding calls in the sequence plus travel times, as indicated by block 92. The scheduler module 22 assigns the expected completion time by adding the mean duration calculated for the call to the expected start time for the call. As a result, the expected completion time is based on both the mean durations calculated for the preceding calls in the sequence and the mean duration of the call to which the expected completion time is assigned, as indicated by block 94, plus travel times. The scheduler module 22 then assigns the pessimictic start time based on the durations computed for the pleceding calls in the sequence, as indicated by block 96, by adding the estim~ted travel time to the pescimistic completion time of the immedi~tely preceding call. As indicated by block 98, the pessimictic completion time assigned by scheduler module 22, which represents the addition of the pessimistic duration of the call to the pessimistic start time, is then based on the pescimictic durations computed for the preceding calls, the pessimistic duration computed for the call to which the completion time is ~ccigne~1, and the travel times.
In summary, the scheduler module 22 may be configured to query the system user via user interface 16 for both the expected and pessimi~tiC probability levels, may refer to expected and pes.cimictic probability levels previously set by the system user, or may query the user for only pçssimictic probability levels, determining the expected durations based on mean values. In all cases, however, the system user reserves the ability to manage technician performance and time 21~2501 commitments according to individual p,ererellce, or organizational policy, providing added flexibility.
After the scheduler module 22 has a~si~ed both expected and pes.cimistic start and completion times to each call in the recursively-generated sequçnce~ the user interface 16 simultaneously displays ~eprese"l~lions ofthe res-lltin~ expected and pessimictic schedules in the srhed~le field 34 of scheduler window 30, as indicated by block 70 of Fig. 3 and block 100 of Fig. 5. As shown in Fig. 6, forexample, the expected schedule for technician A is intlic~ted by the display of call blocks 38, 40, and 42. The call blocks 38, 40, 42 leprese~l, respectively, the expected durations of the service activities associated with the first, second, and third calls assigned to technician A. The user interface 16 provides a representation of the pes~imistic schedule for technician A by displaying time bars 100, 102, and 104 under the expected schedule. The time bars 100, 102, 104 represent, respectively, the pessimi~tic durations ofthe first, second, and third calls assigned to technician A. The representation ofthe pes~imistic schedule also includes time blocks 106, 108, and 110, corresponding to the travel times indicated by time blocks 44, 46, and 48 in the expected schedule. Alternatively, pes~imistic travel times may be displayed, as determined by reference to the travel time file. The user interface 16 may provide a toggle button for the system user to turn the display of the pes~imi~tic schedule on and off. Although in many cases the system user may be able to identify the time bar 100, 102, 104 that corresponds to a particular call block 38, 40, 42 by horizontal ~ nment~ the propagation of pessimictic durationsthroughout the pessimistic schedule may result in significant horizontal skew.
Therefore, the user interface 16 may display corresponding call blocks 38, 40, and 42 and time bars 100, 102, and 104 with m~tçhing colors to aid in identification.
In addition to displaying the expected and pessimi~tic schedules, the user interface 16 may display a warning indication, possibly acco.,.pal~ied by an audible signal, when the difference between the expected and pes~imi~tic start times for a particular call exceeds a predetermined threshold. As indicated by block 114 of Fig.
7, the scheduler module 22 calculates the difference between the expected and pes~imi~tic start times for each call in the sequence. The scheduler module 22 co~ )~ es the difference to the threshold, as inriic~ted by block 116, and, if the difference exceeds the threshold, llanSllliL~ a warning signal dheclil~g the user interface 16 to display the warning indication, as intli~qted by block 118. The warning indication serves to advise the system user that a time com",il,.,enl should not be made for the particular call due to an excessive degree of variation bclween the expected and pe~imi~tic start times of the call. One t,.~"ple of a warning indication is the display of a call block and a col,~i;,ponding time bar in a fl~chin~
manner.
As indicated by the flow diagram of Fig. 8, the scheduler module 22 may also generate an optimistic sçhed~le of the calls ~signed to a service technician.
Whereas the expected schedule enables good overall management of technician pe,ro".,ance, and the pessimi~tic schedule enables the user to make time commitments to customers with a greater degree of confidence, the optimistic schedule conceivably may be used as a pacing tool to motivate technicians to adhere to a better than expected schedule. To generate the optimistic schedule, the scheduler module 22 first selects an optimistic probability level, as in~ic~ted by block 120. Because the optimistic schedule is interlded to represent durations better than the expected durations, the system user should set the optimistic probability level lower than the expected probability level. Based on the optimistic probability level, scheduler module 22 then computes a duration in the same probability distribution previously matched with the call during generation of the expected and pec~imistic schedules, as indicated by block 122. The scheduler module 22 assigns an optimistic start time to the call, as indicated by block 124, based on the optimistic durations computed for the preceding calls in the sequence and the travel times between the precedillg calls, by adding the es~im~ted travel time to the optimistic completion time of the immediately precedi"g call. As in-lic~ted by block 126, the optimistic completion time a~si~ned to the call by the scheduler module 22 is then based on the optimistic durations computed for the preceding calls, the optimistic duration computed for the call to which the completion time is assigned, and the preceding travel times.

After the scheduler module 22 has ~csi~ed optimistic start and completion times to all of the calls in the sequence, the user interface 16 simultaneously displays to the system user r~rese.,lalions ofthe expected, pess;...;~ , and optimistic sçhedllles in the sçhed~le field 34 of scheduler window 30, as in-lic~q,ted by block 128 of Fig. 8. As shown in Fig. 9, for t~UIlpl~, the user interface 16 displays the Opli...iSIiC schedule of the calls acci~ed to techn;ciqn A in the form of time bars 130, 132, and 134 below the expected and pes~;...iCI;c schedules. The time bars 130, 132, and 134 represent, respectively, the optimistic durations computed for the first, second, and third calls lep-t;se..led by call blocks 38, 40, and 42. The representation ofthe optimistic schedule also incllldes time blocks 136, 138, and 140, corresponding to the travel times indicated by time blocks 44, 46, and 48 in the expected schedule. As in the case ofthe peSsimictic schedule, the user interface 16 may provide a toggle button for the system user to turn the display of the optimistic schedule on and off, and may display corresponding call blocks 38, 40, and 42, time bars 100, 100, and 104, and time bars 130, 132, and 134 with matching colors to aid in identification.
In accordance with the present invention, the scheduler module 22 alternatively may be configured to generate the pessimictic schedule based on combined probability distributions for the durations of the service calls in a sequence. As will be described, the use of combined probability distributions increases the efficiency of the peSsimictic schedule, enabling the system user to make earlier time commitments with an equivalent degree of confidence. The operation of the scheduler module 22 in generating a pecsimi~tic schedule based on combined probability distributions is illustrated in the flow diagram of Fig. 10.
The scheduler module 22 m~q,tçhec each of the service calls assigned to a particular technician with one of a plurality of statistical probability distributions stored in the call duration file based on the type of service activity qcso~i~ted with the respe.;li~e call, as indis~q,ted by block 142, and possibly based on the particular technician h~ndling the call. The sçhedlller module 22 assigns a pecsimistic start time for a particular call by adding an estim~ted travel time to the pessimisticcompletion time of the immediately preceding call. However, the determination of the pçesimistic start time by scheduler module 22 relies directly on the genelalion of a first co,llbined probability distribution that combines the probability distributions of the precedin~, calls in the sequencç~ as in~lic~ted by block 144. Specifically, scheduler module 22 selects a pe~eimi~tic probability level entered or preset by a S system user, as indic~te~ by block 146, and computes a duration in the first co"lbined probability distribution based on the probability level, as indicated by block 148.
The pes~ l;c completion time of the immedi~tely preceding call is the computed duration plus travel times, relative to the start of the schedule. Thus, the pçc~imistic start time ofthe next call is based on the corrupted duration in the first combined probability distribution, as indicated by block 150, plus intervening travel times. To determine the pessimistic completion time for the next call, schedulermodule 22 combines the probability distribution matched with the particular callwith the first combined probability distribution generated for the preceding calls to produce a second combined probability distribution, as indicated by block 152. The scheduler module 22 computes a duration in the second combined probability distribution based on the selected probability level, as indicated by block 154. The scheduler module 22 then assigns the pes.simi~tic completion time to the next call based on the computed duration and the intervening travel times, as indicated byblock 156. Because the computed duration represents the aggregate duration of the preceding service calls and the next call, the scheduler module 22 assigns the pessimistic completion time relative to the beginning of the schedule, with travel times included.
The scheduler module 22 col,lbines probability distributions by convolution, effectively multiplying them such that the conlbined probability distribution is the product of the probability distributions m~tched with the preceding calls and the probability distribution matched with the call to which the completion time is to be assigned. A combined probability distribution is generated to determine the pess;.,.;sl;c completion time for each preceding call in the sequence. Therefore, the probability distribution for a later call can be combined with the previous combined probability distribution instead of recombil ing all probability distributions on an individual basis. The calculation of the combil-ed probability distributions by scheduler module 22 may be either exact or appl o~,mate. For k independent exponential variables in sequence, for e~,.ple, the conlbil-alion of probabilitydistributions is represented by a k-erlang variable. Thus, the probability distribution S p(x) for the co-.-bh~ed durations of k service calls having eAponel.~ial distributions in sequence, as dete....ined by the sçhed..ler module 22, can be given by:
p(x) = 1- e~X~, 1/ j!(x 1~ (2) where x is the duration of a particular service call and p is a scale parameter equal to r~, where r is the mean duration in the probability distribution. For the start time of a call m + 1 in the sequence, the scheduler module 22 computes the combined durations of the p. eceding calls 1 through m where the combined density function of calls 1 through m is a k-erlang variable by Newton's method with the following iteration function:

x = x _ k!(/3) [e-x~ --p)--~ !(Xn /~)i ] (3) The scheduler module 22 effectively reduces the variability of service calls scheduled farther in the future by scheduling service calls according to a totalduration derived from a combined probability distribution. Specifically, as the number of service calls on the schedule increases, the total duration of all service calls approaches the sum of the average durations of the calls. Therefore, if the same probability level is applied both to the combined probability distribution for all calls in a sequence and in isolation to each individual probability distribution, the total pessimi~tic duration derived from the combined probability distribution clearly will be less than the-sum ofthe p~imi~tic durations derived from the individual probability distributions.
Fig. 11 is an example of a density curve 80 representing a probability distribution for the duration of an individual call, and a density curve 160 representing a combined probability distribution for the durations of two consecutively scheduled calls. For the example shown in Fig. 11, it is assumed that the consecutively scheduled calls are associated with the same service activities and are therefore matched with identical probability distributions. The density curve 80 rel)lesenls a 2-erlang probability distribution for the duration of each of the calls in the sequence. A 2-erlang probability distribution has been found to be typical for a field service environ.,le,ll. The density curve 160 reples~nls a cG",l,~lalion oftwo identical 2-erlang probability distributions by convolution, and thus represents a 4-erlang probability distribution.
The curve 80 has a "tail" 82 that extends to the maximum duration for an individual service call, whereas the "tail" 162 of curve 160 extends to the m~cimum aggregate duration of the two consecutively scheduled calls. In the example of Fig.
11, the individual curve 80 asymptotically approaches a probability leve~ of 0. The combined curve 160 theoretically will approach a corresponding probability level of 0 at exactly twice the maximum duration of the individual curve 80. However, thetail 162 of the combined curve 160 will tend toward the probability level much more quickly than tail 82, such that longer aggregate durations are less probable than longer individual durations.
~s~min~ that the system user has selected a probability level of 0.9, and that there are two consecutive service calls in a sequence, the pes~imictic durations derived from the individual probability distributions each carry a confidence level of 0.9. The sum ofthe individual pessimictic durations similarly carries a confidence level of 0.9. However, if the individual probability distributions are combined, the aggregate pessimistic duration now corresponds to a probability level in the combined probability distribution of:
pc=l.O-[(l-pl)x(l-p2)], (4) where pc is the combined probability level, pl is the probability level for the first call, and P2 is the probabiiity level for the second call. If pl and P2 are bothequivalent to 0.9, equation (4) will yield a combined probability level pc of:
1.0 - [(1.0 - 0.9) x (1.0 - 0.9)] = 0.99.
This higher probability level reflects the reduced variation in the combined probability distribution. The scheduler module 22 takes advantage of the reducedvariation by using the probability level specified by the system user not with the 214250~

individual probability distributions, but with the overall combined probability distribution. As a result, the aggregate pe~c.cimictic duration for the calls in the sequence is less than the sum of the individual pes~ cl ;c durations, enabling the system user to make earlier time co.~ ...f..~l s with the same level of confidence.
In accordance with the present invention, the scheduler module 22 also may be configured to modify the schedule as service calls are completed by a technician, or as the actual running duration of an active service call progresses, thereby providing an updating feature. A service call is "active" if a technician is p, esenlly serving the call. The SMS interface 14 and user interface 16 enable the s~lled.ller module 22 to monitor the actual durations of the service calls, in order to update the expected, pescimistic, and optimistic schedules. Specifically, the assigner module 20 receives notification of the start and completion times of preceding service calls from either the SMS via SMS interface 14 or the system user via user interface 16. The assigner module 20 references a real-time clock (not shown) upon receipt of such notification to determine start and completion times for the call, and "time-stamps" the call. In addition, as the running duration of an active call progresses without notification of a completion time, the assigner module 20 periodically time-stamps the call with the present time. Thus, the running duration is the minim~lm completion time possible for the call. At periodic intervals during the active duration of a call, and upon completion of the call, the assigner module 20 passes the time-stamped call and the other calls assigned to the same technician to thescheduler module 22 for a schedule update.
With respect to the expected and optimistic schedules, the scheduler module 22 assigns earlier start and completion times to the re~--Ai~ing service calls on the schedule if the pl eceding call is completed ahead of its scheduled completion time.
If either the actual completion time of the pl eceding call is later than its scheduled completion time, or the actual running duration of an active call extends beyond the scheduled completion time, the scheduler module 22 assigns later start and completion times to the rç~-~Ainil-g calls. Thus, the scheduler module 22 updates the schedule to reflect the actual situation in the field by moving calls forward or pushing them back on the sclledl.les The new start and co-l.pletion times assigned to the calls on the expected and optimistic schedules essçntiAlly represent the difference belween the s-~hed-lled completion times ofthe p.~ceding calls and the actual con-?letion times.
The scheduler module 22 modifies the pes.~imistic scl~edllle di~erelllly. The scheduler module 22 assigns the pes.cimi~tic start time for a later call by adding an estim~ted travel time to the pessimi~tic completion time of the immetliAtely precedih~g call. However, as a service call is cGmpl~led by a technician, or as the duration of an active service call progresses, the srt ~d~ler module 22 rec.~lcl.lqtes the aggregate duration for the r~mqining calls to reduce the variation in the Ainin~ schedule. Because a completed call has a known, fixed duration, any variation in the overall schedule due to that particular call is çliminAted. Similarly, the running duration of an active call effectively provides a minim~lm actual duration for the call upon completion. Thus, the combined probability distributions for the lelllAinil)g calls in the sequence can be recalculated to generate earlier or later start and completion times, as dictAted by the actual durations of the preceding completed calls and the actual running durations of the active preceding calls.
The operation of the scheduler module 22 in recalculAting the aggregate duration up to each ofthe uncompleted service calls is illustrated in Fig. 12. As indicated by block 170, the scheduler module 22 is able to monitor the actual durations of service calls by communication with the assigner module 20. After determining the actual duration of a completed call or the actual running duration of an active call based on the time-stamp il~oll"alion passed by the assigner module 20, the scheduler module 22 generates a combined probability distribution for each ofthe le~llAil~io~ service calls in the sequence that is neither completed nor active.
As indicated by block 172, the first new combined probability distribution for aservice call co.~.bh~es the probability tistributions m~tclled with each of the preceding calls in the sequence that are not completed and not active.
The scheduler module 22 computes a duration in the new first col-,bil ed probability distribution for the respective service call based on the pessimi~tic probability level, as indicated by block 174 of Fig. 12. With the actual duration of a 21~2501 preceding completed call known, the sc.hed~-ler module 22 assigns the pes~imi~tic completion time for a later call relative to the point on the schedule corresponding to the known completion time of the pl ecedh~g call. Similarly, with the runningduration of a preceding active call known, the sr.hed~ler module 22 assigns the pessimi~tic completion time for a later call relative to the point on the schedule corresponding to the minim..rn possible completion time ofthe precedil-g call, as indicated by the running duration. The pess; .~ ;c completion time for a call therefore can be assigned by adding the aggregate computed duration, plus traveltimes, to this known point on the schedule. The srhed..ler module 22 assigns a pes~imi~tic start time for the next call by adding the estim~ted travel time to the pes~imistic completion time of the pleceding call. Thus, as in~ic~ted by block 176, the pessimi.~tic start time for the next call is based on the computed duration in the new first probability distribution, plus intervening travel times, relative to the known point on the schedule.
To determine the pessimistic completion time for the next call, scheduler module 22 combines the probability distribution for the next call with the new first combined probability distribution generated for the immediately preceding call to produce a new second combined probability distribution, as indicated by block 178.
The scheduler module 22 then computes a duration in the new second probability distribution based on the probability level, as indicated by block 180, and assigns a pes.~imistic completion time to the next call based on the computed duration and the intervening travel times, as indicated by block 182. The computed duration represe"ls the aggregate duration of the uncompleted, nonactive preceding service calls and the next call. Consequently, scheduler module 22 also assigns the pessimi~tic completion time relative to the known point on the schedule, with travel times included.
As best represented by the scheduler window 30 shown in Fig. 2, the schedule of service calls assigned to a service technician is not continuous, but instead is divided into a plurality of discrete time segments. In Fig. 2, the time segments correspond to the length of an entire work day. For example, the schedule field 34 includes a time segment corresponding to the work day of 21~250~

Monday, May 17, and a following time seP.ment COll esponding to the work day of Tuesday, May 18. If a time segmç~l is large enough to accommodate both the expected and pesc;~ l;c durations of a service call, the system user can confidently make time co~ nc that fall within the se~..çnl boundaries. When the pessimictic cGmpletion time for a service call extends beyond an end of one of the time seg.n~llls, however, it may be desirable to distribute the call so that the service technician does not run into overtime.
The situation in which the pessimictic duration of a service call extends beyond a segm~nt boundary is illustrated in Fig. 13. The eYpecte~ s~hedl.le shown in Fig. 13 incl~ldec a time seg~ 188 having a first call with an expected duration represented by call block 190, and a second call with an expected duration represented by call block 194. The pessimistic schedule similarly includes the first call with a pessimictic duration represented by call block 200, and the second call with a pescimistic duration lepresellled by call block 204. Blocks 192 and 202 represent the travel times between the first and second calls. The expected completion of the second call, as l epl esenled by call block 194, rims to approxi...ately 16:30 ofthe time segm~nt 188, with 17:00 representing the end ofthe segrnçnt, as well as the end ofthe work day. However, the pessimictic completion time of the second call, as represented by call block 204, runs well beyond the end oftime segm~nt 188.
When the pes.cimistic completion time of a service call runs beyond the end of a time segment, the scheduler module 22 effectively overrides the previously assigned pessimictic completion time. The scheduler module 22 distributes the service call in one of two ways, depending on the policy of the particular system user or service organization. First, as shown in Fig. 14, the scheduler module may divide the call duration into a first component 212 and a second co-.lponenl 214.
The first component 212 fits within the time se~nent 188, and the second conll)onent 214 does not. Thus, the scheduler module 22 simply m~int~in~ the original pessimistic start time for the first component 212, and assigns a new pescimistic start time to the second co.. pone--l 214 at the be~inning ofthe next time segment 210. Although this first technique achieves an efficient use oftime, many 21~2501 field service technicians disfavor splitting an activity across a segmçnt boundary. In other words, technicians generally prefer to finish the entire job in one visit, if possible. Therefore, the scheduler module 22 alternatively may assign a new pessimi~tic start time to the entire service call at the be~nning ofthe next time segmçnt 210, as shown in Fig. 15. This second technique has the effect of movingthe entire call block 204 to the next work day.
Having described the invention, additional advantages and modifications will readily occur to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. Therefore, the specification and examples should be considered exemplary only, with the true scope and spirit of the invention being indicated by the following claims.

Claims

1. A computer-implemented method for scheduling a plurality of resource requests for a resource provider, wherein each of said resource requests has an uncertain duration, said method comprising the steps of:
determining first potential durations for said resource requests;
determining second potential durations for said resource requests;
generating a sequence of said resource requests; generating a first schedule of said resource requests by assigning a first start time to each of said resource requests following a first one of said resource requests in said sequence based on a sum of the first potential durations determined for the preceding resource requests in said sequence; and generating a second schedule of said resource requests by assigning a second start time to each of said resource requests following said first one of said resource requests in said sequence based on a sum of the second potential durations determined for the preceding resource requests in said sequence

2. The method of claim 1, wherein said step of generating said first schedule includes assigning a first completion time to said first one of said resource requests in said sequence based on the first potential duration determined for said first one of said resource requests in said sequence, and assigning a first completion time to each of said resource requests following said first one of said resourcerequests in said sequence based on a sum of said first potential durations determined for said preceding resource requests in said sequence and the first potential duration determined for the respective resource request to which said first completion time is assigned, wherein said step of generating said second schedule includes assigning a second completion time to said first one of said resource requests in said sequence based on the second potential duration determined for said first one of said resource requests in said sequence, and assigning a second completion time to each of said resource requests following said first one of said resource requests in said sequence based on a sum of said second potential durations determined for said preceding resource requests in said sequence and the second potential duration determined for the respective resource request to which said second completion time is assigned, and wherein said first potential duration for each of said resource requests is an expected duration of the respective resource request, and said second potential duration for each of said resource requests is a pessimistic duration of the respective resource request, said pessimistic duration being greater than said expected duration, and said method further comprising the step of simultaneously displaying representations of said first schedule and said second schedule on a display device.

3. The method of claim 1, further comprising the steps of:
determining third potential durations for each of said resource requests; and generating a third schedule of said resource requests by assigning a third start time to each of said resource requests following said first one of said resource requests in said sequence based on a sum of the third potential durations determined for the preceding resource requests in said third sequence, wherein said first potential duration for each of said resource requests is an expected duration of the respective resource request, said second potential duration for each of said resource requests is a pessimistic duration of the respective resource request, said pessimistic duration being greater than said expected duration, and said third potential duration for each of said resource requests is an optimistic duration of the respective resource request, said optimistic duration being less than said expected duration, and said method further comprising the step of simultaneously displaying representations of at least two of said first schedule, said second schedule, and said third schedule on a display device.

4. The method of claim 1, wherein each of said resource requests is associated with one of a plurality of different types of activities, said method further comprising the steps of:
matching each of said resource requests with one of a plurality of probability distributions for a potential duration of the respective resource request based on the type of activity associated with said respective resource request;

selecting a first probability level, wherein said step of determining said firstpotential duration for each of said resource requests includes computing a duration in the probability distribution matched with the respective resource request based on said first probability level, the duration computed based on said first probability level being the first potential duration for the respective resource request; and selecting a second probability level, wherein said step of determining said second potential duration for each of said resource requests includes computing a duration in the probability distribution matched with the respective resource request based on said second probability level, the duration computed based on said second probability level being the second potential duration for the respective resource request.

5. The method of claim 1, wherein each of said resource requests is associated with one of a plurality of different types of activities, said method further comprising the steps of:
matching each of said resource requests with one of a plurality of probability distributions for a potential duration of the respective resource request based on the type of activity associated with said respective resource request, wherein said step of determining said first potential duration includes the step of determining, for each of said resource requests, a mean duration in the probability distribution matched with the respective resource request, said meanduration being the first potential duration for the respective resource request; and selecting a probability level, wherein said step of determining said second potential duration for each of said resource requests includes computing a duration in the probability distribution matched with the respective resource request based on said probability level, the duration computed based on said probability level being the second potential duration for the respective resource request.

6. A computer-implemented method for scheduling a plurality of resource requests for a resource provider, wherein each of said resource requests has an uncertain duration, and each of said resource requests is associated with one of a plurality of different types of activities, said method comprising the steps of:
matching each of said resource requests with one of a plurality of probability distributions for a potential duration of the respective resource request based on the type of activity associated with said respective resource request;
generating a sequence of said resource requests;
generating, for each of said resource requests, a first combined probability distribution, said first combined probability distribution combining the probability distributions matched with each of the preceding resource requests in said sequence;
selecting a probability level;
computing, for each of said resource requests, a duration in the first combined probability distribution for the respective resource request based on said probability level; and generating a schedule of said resource requests by assigning a start time to each of said resource requests following said first one of said resource requests in said sequence based on the duration in said first combined probability distribution computed for the respective resource request based on said probability level.

7. The method of claim 6, further comprising the steps of:
generating, for each of said resource requests, a second combined probability distribution, said second combined probability distribution combining the probability distribution matched with the respective resource request and the probability distributions matched with each of the preceding resource requests in said sequence; and computing a duration in the second combined probability distribution for the respective resource request based on said probability level, wherein said step of generating said schedule includes assigning a completion time to each of said resource requests following said first one of said resource requests in said sequence based on the duration in said second combinedprobability distribution computed for the respective resource request based on said probability level.

8. The method of claim 6, further comprising the steps of:
monitoring actual durations of each of said preceding resource requests completed by said resource provider;
monitoring actual running durations of said preceding resource requests actively served by said resource provider;
generating, for each of said resource requests not completed and not actively served by said resource provider, a new first combined probability distribution, said new first combined probability distribution combining the probability distributions matched with each of the preceding resource requests in said sequence not completed and not actively served by said resource provider;
computing, for each of said resource requests not completed and not actively served by said resource provider, a duration in the new first combined probability distribution for the respective resource request based on said probability level; and modifying said schedule by assigning a start time to each of said resource requests not completed and not actively served by said resource provider based on the duration in said new first combined probability distribution computed for the respective resource request based on said probability level.

9. The method of claim 6, said method further comprising the steps of:
selecting a second probability level;
computing, for each of said resource requests, a second duration in the probability distribution matched with the respective resource request based on said second probability level; and generating a second schedule of said resource requests by assigning a start time to each of said resource requests following a first one of said resource requests in said sequence based on a sum of the second durations computed for the preceding resource requests in said sequence.

10. The method of claim 6, further comprising the steps of:
determining, for each of said resource requests, a mean duration in the probability distribution matched with the respective resource request; and generating a second schedule of said resource requests by assigning a start time to each of said resource requests following a first one of said resource requests in said sequence based on a sum of the mean durations determined for the preceding resource requests in said sequence.