user`s guide - Recherche : Service web
Contents
1. Listing 2 Example of the cutting plane parameter file 12 5 Parameter Files 5 4 Randomized Search Parameters This parameter file is only read by the randomized search program It contains the parameters that control the heuristic e ni integer element is the minimum number of skill groups with at least q ran domly generated number agents to activate the remove algorithm of size q We suggest to set it to 1 e n2 integer element is the maximum test size desired Which means that some test candidates may not be evaluated A test candidate is a skill group that can reduce the staffing cost by changing its staffing We suggest to set higher or equal to the number of agent groups It is preferable to evaluate every candidate e delta real element is the ratio of the number of test candidates over n2 that is added to the serie of tests If it is set to 1 0 then it will test every candidates This value must be between 0 and 1 inclusively e findInitialStaffing boolean element if set to true will generate automati cally the initial staffing with the parameters rootL and lowerCostRatio If set to false then the program will use the staffing defined in the Call Center parameter file as the initial solution We suggest to set to true e opGlobalTargetServiceLevel boolean element is the global target service level used for the approximated values feasibility test if useLDOTargetServiceLevel is set2. To set a parameter put the parameter name before and after the value 5 1 Call Center Parameter File 7 Example lt verbose gt true lt verbose gt For an array the values are separeted by a comma Example lt arrivalRates gt 10 9 10 lt arrivalRates gt To put comments in the XML file surround the comments like this lt comments gt Example to put the changeHeuristicCut parameter in comment lt lt changeHeuristicCut gt true lt changeHeuristicCut gt gt 5 1 Call Center Parameter File Both the optimizers and the simulation use the call center parameter file A fully detailed documentation on the available parameters can be found in the ContactCenters simu lation library and XML user s guide However for the optimizer to work not every parameter field is required to be filled The documentation is available in the PDF file guidemsk pdf of the ContactCenters simulation library 5 2 Simulator Parameter File The Java call center simulator also needs a parameter file to configure the simulation The parameters are described in the simulation and XML parameters user guide in the section batchSimParams and common simulation parameters These informations are read only by the simulator and are never used by the optimizer It would be important to understand the function of some variables The quality of the approximation by simulation is dependent of the length of the time simulated Ho
3. library for simulating contact centers 3 devel oped in the same laboratory by Eric Buist the simulation library SSJ 7 the scientific library colt and also implementation to support libraries for linear optimization li braries OR Objects 1 2 4 8 and Cplex 6 The linear optimization library OR Objects 1 2 4 8 is freely available This guide contains informations for the installation under the Windows and Linux operating system and for the usage of the staffing optimization programs It explains what needs to be installed how to run the program the description of each input parameter file It is recommended to consult the detailed guides describing the simulation programs and the XML parameters written by Eric Buist The details of the optimization algorithm are described in Cezik and L Ecuyer 4 and Avramidis et al 2 It explains the choice and reason of the values given to some parameters of the algorithm principally for the cut generation 2 Installation The current version of the optimization programs are developed on Sun Microsystems Java 5 A version of Java 5 is required for the execution of the programs If one doesn t need to compile the programs the Java Runtime Environment JRE is sufficient other wise installs the Jave Development Kit JDK For linear optimization library the user must assure the proper installation of their library such as Cplex 6 Note that for OR Objects 1 2 4 no installation is req
4. warmupBatches 2 gt lt batchSimParams gt Listing 1 Example of the simulator parameter file 5 3 Cutting Plane Optimizer Parameter File The cutting plane optimizer parameter file is only used by the optimization program and the documentation can be found in the class CuttingPlaneParams Some parameters are very technical and depend on the call center s characteristics they should be used by users who understand the optimization algorithm See the paper Cezik and L Ecuyer 4 for details The cost vector c can be set by defining the parameter busyCost for each agent group in the simulator s parameter file or by setting the skillCost parameter in uk this file Important parameters are followed by a Here s the description of each parameter e currentPeriod integer select the period to optimize The period count starts with 0 5 3 Cutting Plane Optimizer Parameter File 9 e skillCost real If the parameter busyCost of an agent group in the simulator s parameter file is greater than zero gt 0 the cost per agent of that group is equal to busyCost Otherwise the cost per agent of that group is defined as 1 skillCost x skill count 1 where skillCost is this parameter e minEachQosH real for the heuristic cut generation if the QoS of a call type is below this value then that call type is subject to generate a heuristic cut not based on the subgradient We suggest to set a low value
5. JAVA CALL CENTERS OPTIMIZATION LIBRARY INSTALLATION AND USER S GUIDE Package umontreal iro lecuyer ccoptim Laboratoire de Simulation Chaire de Recherche du Canada en Simulation et Optimisation Stochastiques DIRO Universit de Montr al November 20 2006 Contents Contents io bk SESS Rs Wa a ati Este te te eo Ny D AR hh a d ek Res eG 3 Progtaiii BOUIB buno eus Ale eae ore etek el Bowe a ic Leake ee eee E Be ee Bee 3 2 Windows 2000 XP 4 su en eA a a RS ae da de oe eS BOS ep Soe Ge a we oe ae ges ata are oe Bee oe Sad ee ee ee ee ee eee 4 1 Cutting Plane Optimizer o 6 24 Re wR Ris RE ERE RSH 4 2 Randomised Search e coxis Pb EN bh ewe sp ee rm es 5 Parameter Files 5 1 Call Center Parameter File 2 a a a a a a a a a a a 5 2 Simulator Parameter Filej a a a a 5 3 Cutting Plane Optimizer Parameter File 5 4 Randomized Search Parameters a a a a a a 0000 a eee 5 5 Loss Delay Approximation Parameters 9 1 Introduction 1 Introduction This document is a short user s guide for a staffing optimization program for multiskill call centers It includes two differents optimization programs a cutting plane algorithm based on simulation and linear programming 4 and a randomized search using approximations 1 both developed in the simulation laboratory of DIRO under the Canada Research Chair in Stochastic Simulation and Optimization I
6. ams xml rsParams xml where e ccParams xml is the call center s parameter file It contains the descriptions of the call center which includes the arrival rates service rates routing scheme global target service level and more e IdParams xml is the loss delay approximation parameter file e simParams cml is the simulator s parameter file This file is used only by the sim ulator e rsParams xml is the randomized search parameter file The user can set different multistarts position a time limit to the execution and others options related to the optimization See Section 5 4 5 Parameter Files For XML files the parameter tags are all described in their respective Java class parser Please look in the HTML API or PDF to find the complete list of parameters A fully detailed description on how to use the XML configuration files is available the guides for the simulation and XML parameters Some parameters are optional if they are not specified the default values will be used while others are essential parameters like the arrival rates If an essential parameter is missing the program will terminate and print an error requiring the missing parameter before starting the algorithm The type of value accepted by each parameter is the variable type described in the HTML API and PDF It can be a boolean true or false an integer no decimal or a real number with decimals A parameter can also be an array of those 3 types
7. arameter affects the heuristic used when the service levels are too poor to generate subgradients If false a constant number of network flow equa tions are incorporated at the beginning of the problem Solving with a maxflow subproblem keeps the number of variables equal to the number of agents but gen erating these heuristic cuts can be costly in large problems When solving the the network flow equations a limited number of non negative real variables are added and the constraints are already known By default set to false e verbose boolean if false then the program will print only the simulation results the staffing vector the objective value and the QoS for the optimal solution If true then the program will also print a trace of every step of the algorithm every contraint added intermediate staffing solutions quality of service and the objective value By default set to false lt cuttingPlaneParams currentPeriod 0 skillCost 0 05 minEachQosH 0 1 testConvexity false errorOnConvexity false cutPriority 0 defaultSubStep 2 lowOverallSubStep 3 pivotOverallQos 0 65 pivotPerCallQos 0 70 changeHeuristicCut true solvelP false solverClass umontreal iro lecuyer ccoptim cp OR124Solver solveWithMaxFlowCut false verbose false gt lt loadCoefficient gt lt row repeat 65 gt 1 lt row gt lt loadCoefficient gt lt cuttingPlaneParams gt
8. ccoptim lib Then the next step is to set the CLASSPATH variable 1 Right click on My Computer and select properties 2 Select the tab Advanced and click on the button named Environment Variables 3 If a variable named CLASSPATH already exists select it and click on Edit otherwise click on New and type CLASSPATH as the Variable name 99 99 4 In Variable value add the location of each jar separete with a colon Such as C ccoptim lib ccoptim jar C ccoptim lib ssj jar C ccoptim lib colt jar C ccoptim lib contactcenters jar C ccoptim lib 3 3 Linux Unix Suppose for example that the folder lib has been copied to the directory home username ccoptim lib The user need to define the CLASSPATH environment variable if not already defined and e Using C shell add to file cshrc in one line setenv CLASSPATH home username ccoptim lib ccoptim jar home username ccoptim lib contactcenters jar home username ccoptim lib colt jar home username ccoptim lib ssj jar home username ccoptim lib CLASSPATH Using Bourne shell add to file bashrc in one line export CLASSPATH CLASSPATH home username ccoptim lib contactcenters jar home username ccoptim lib colt jar home username ccoptim lib ssj jar home username ccoptim lib ccoptim jar home username ccoptim lib 4 Running the Optimization Programs Since the CLASSPATH environment variable has been set the programs ca
9. e at http www iro umontreal ca lecuyer 8 DRA Systems Or objects 1 2 4 2000 Java mathematic library Available at opsresearch com
10. e g 0 1 e testConvexity boolean if true then the program will test the convexity of the QoS function around the current staffing vector solution by testing one dimension at a time with a length of defaultSubStep 1 This adds more simulations and this test is not needed for the optimization It is only to check the convexity of the problem By default set to false e errorOnConvexity boolean if testConvexity is false this option has no ef fect If testConvexity is true and this is true then whenever the program finds a convexity region it will throw an error and terminate If false then it will only print a convexity warning message and continue the algorithm By default set to false e cutPriority integer if equals to 1 then between a heuristic and a subgradient cut the priority goes to the subgradient cut Otherwise the priority goes to the heuristic cut Default value is 0 heuristic cut e defaultSubStep integer the default step length used to compute the subgradi ent around the current staffing vector Default value is 1 but should be set according to the call center It is recommended to set to gt 2 if using short simulations and large call centers e lowOverallSubStep integer when the global QoS is lower than the pivotOverallQos point the algorithm uses this value to compute the subgradient instead of the defaultSubStep Default value is 2 it should be higher than defaultSubStep e p
11. ference for a performance measure between two iterations The program iterates until every performance measure choosen with the parameter accuracyType satisfies this tolerance A big value ie 0 01 would diminish the quality of the approximation We suggest a value of 1e 4 or 107 e accuracyType integer represents the type of convergence to test If set to 1 then the convergence is tested on the blocking probability of each skill groups Else if set to 2 the convergence is tested on the inflows of each skill groups We suggest to set it to 1 e queueAbandon boolean should be set according to the possibility of abandon ment Set to false if there are no abandonment This parameter decides on the CTMC to be used to estimate the blocking and queueing probabilities e queueCapacity integer set the queuing length at each agent group This pa rameter is only needed when queueAbandon is true Setting to lt 0 for automatic selection rule which is 6 m where m is the number of agents in the group and is the defined by the parameter delta We suggest to set to 1 16 REFERENCES e delta double is used compute the queue length when queueCapacity is true otherwise it is ignored See the parameter queueCapacity We suggest a value of 2 e debug boolean if set to true prints out the unstable skill group when the queues are unstable We suggest to set it to false e verbose boolean if set to true p
12. ivotOverallQos real if the global QoS is lower than this point then the pro gram will use lowOverallSubstep instead of defaultSubStep This parameter is used to reduce the noise of the simulation in convex region The value should be around halfway between 0 and the global target service level 10 5 Parameter Files e pivotPerCallQos real if the global QoS is equal or higher than this value then the algorithm can choose to generate the subgradient per call type instead of a subgradient for the global QoS when the QoS of call type doesn t satisfy its target QoS This parameter is justified by the reason that improving a call type also improves the global service level However we don t want to start at the beginning since the noise is higher per call type The value should be close to the global service level target loadCoefficient array of real this is the coefficient that is multiplied to the arrival rate when solving the minimum load problem Default value is 1 0 These values should varie with the blocking and abandon rates Set it sligthly lower when there is abandonment This parameter is important to determine an initial starting point where the service levels shouldn t be too far in the convex region very low service levels If the array has more elements than the number of call types let s say m only the first m elements are used changeHeuristicCut boolean if true then the program will follow
13. me false useLDOTargetServiceLevel false gt lt opTargetServiceLevel gt 0 8 0 8 0 8 0 75 0 6 0 6 0 6 lt opTargetServiceLevel gt lt rootL gt 0 8 lt rootL gt lt lowestCostRatio gt 0 5 lt lowestCostRatio gt lt randomSeeds gt 19992 6210 1414 595 56558 2146 lt randomSeeds gt lt randomizedSearchParams gt 5 5 Loss Delay Approximation Parameters 15 Listing 3 Randomized Search parameters 5 5 Loss Delay Approximation Parameters This file contains all the configuration variables for the Loss Delay approximation program It approximates the performance levels of a multi skill call center of a staffing vector for a single period If the user only wants to approximate the performance of a staffing vector this vector must be defined in the Call Center parameter file see Section 5 1 e currentPeriod integer specifies the period to approximate It is important to select the right period Period O corresponds to the first period of the Call Center parameter file e maxIteration integer sets the maximum number of iterations to execute while waiting for convergence of the approximation If the values don t converge the program returns non convergent which means the convergence failed This pa rameter affects directly the speed of the program We suggest a value of 400 e absErrorTolerance double represents the convergence test value It is the minimum accepted dif
14. n a staffing problem a multiskill call center is composed by multiple agent groups and different call types A call requires the appropriate skill in order to be served Agents of the same groups share an identical skills set and the cost an agent depends on his group skills set The objective is to minimize the staffing cost while satisfying the service level SL targets The service levels taken into account in our problem are defined as the proportion of calls having waited less than awt time where awt is called the acceptable waiting time Many variants of the service level formula exist the user must assure than the desired formula is available in the call center evaluator library to be given to the optimization programs To formulate as a mathematical problem we have a set M 1 2 m of agent groups and a set NV 1 2 n of call types the cost vector c c Cm and staffing vector x 11 Tm The service levels are complex functions denoted as g x or g x for call type k that are approximated by simulations or analytically The solution is constrained to satisfy the service level targets l for the global target and per call type target l for each k M We obtain the integer problem min CxX gt aa i 1 subject to g x 21 g x gt lk Vk EN x gt 0 and integer In the current version the programs are developed on Sun Microsystems Java 5 The programs use the ContactCenters Java
15. n be executed in any directory 4 1 Cutting Plane Optimizer The cutting plane optimization program needs 3 parameter files which will be detailed along with examples in Section 5 It is important to setup the parameters accordingly to obtain the best performance To open a text console in Windows click on Start Run and type cmd Command line to run the program java umontreal iro lecuyer ccoptim cp CuttingPlaneOptimizer ccParams xml simParams xml cpParams xml where e ccParams cml is the call center s parameter file It contains the descriptions of the call center which includes the arrival rates service rates routing scheme global target service level and more e simParams rml is the simulator s parameter file This file is used only by the sim ulator e cpParams rml is the cutting plane optimization parameter file The user can change the cut generation rules the type of cuts used and others options related to the optimization See Section 5 3 6 5 Parameter Files 4 2 Randomized Search The randomized search requires 4 parameter files which will be detailed along with exam ples in Section 5 It is important to setup the parameters accordingly to obtain the best performance To open a text console in Windows goto Start Run and type cmd Command line to run the program java umontreal iro lecuyer ccoptim rs RandomizedSearch ccParams xml ldParams xml simPar
16. rints out at each iteration Set if to false the program doesn t print while in the randomized search Here s the parameter file for the Loss Delay approximation lt lossDelayParams currentPeriod 0 maxlteration 400 absErrorTolerance le 4 accuracyType 1 queueAbandon true queueCapacity 1l delta 2 debug false verbose false gt Listing 4 Loss Delay approximation parameter file References 1 A N Avramidis W Chan and P L Ecuyer Staffing multi skill call centers using a performance approximation and search methods Manuscript 2006 A N Avramidis W Chan and P L Ecuyer Staffing multi skill call centers via search methods and a performance approximation Manuscript 2006 E Buist and P L Ecuyer ContactCenters A Java Library for Simulating Contact Centers 2005 Software user s guide forthcoming M T Cezik and P L Ecuyer Staffing multiskill call centers via linear programming and simulation Management Science 2006 To appear Wolfgang Hoschek The Colt Distribution Open Source Libraries for High Perfor mance Scientific and Technical Computing in Java CERN Geneva 2004 Available at http dsd 1bl gov hoschek colt REFERENCES 17 6 ILOG inc Ilog cplex 2006 Optimization library See http www ilog com products cplex 7 P L Ecuyer SSJ A Java Library for Stochastic Simulation 2004 Software user s guide Availabl
17. t e lowestCostRatio array of doubles represents the proportion of the inflow calls that goes to the cheapest agent group that can serve call type The rest are divided equally to the other agent groups that can answer to that call type If there is only one agent group that can serve then a ratio of 1 0 is automatically used 14 5 Parameter Files This parameter seems to have a bigger impact on the quality of the initial solution Setting multiple values triggers a multi start We suggest a value of 0 8 e randomSeeds array of integer contains the initial seed of the random number generator used by the randomized search program but not the simulation This program use the MRG32k3a generator which needs 6 integer numbers If this pa rameter is omitted then it will use the default values e verbose boolean if set to true prints the status of each iteration cost global QoS the staffing move number of agents If set to false then only the final after simulation staffing solution the staffing cost and the QoS are printed Here s an example of the parameter file for the optimizer lt randomizedSearchParams n1 1 n2 10 delta 1 0 verbose true findInitialStaffing true opGlobalTargetServiceLevel 0 8 simPriority 1 useBusyCost false skillPremiumCost 0 05 searchMode 0 useSimRemove true useSimSwitch false maxRSCPUsec 300000000 useRealTi
18. the improve ment resulted from a heuristic cut If the last heuristic cut added brought a big improvement to the QoS of the call type it will change that heuristic cut to find the right cut constraint so that the QoS of that call type is at minEachQosH By default set to true solverClass string input the name and package name of the linear solver interface class without the suffix class to be used in the optimization This class is used by the optimizer to interact with existing linear solver libraries The currently implemented interfaces included as extra files are umontreal iro lecuyer ccoptim cp 0R124Solver class OR Objects 1 2 4 umontreal iro lecuyer ccoptim cp Cplex8Solver class Cplex 8 umontreal iro lecuyer ccoptim cp Cplex9Solver class Cplex 9 Note While OR Object 1 2 4 is free but the implemented solver does not solve IP The user must install his copy of Cplex in order to use the Cplex solvers solveIP boolean depends on solverClass If the solver can solve IP instance setting to true will enable to solve the IP instead of the LP The setting also depends on the difficulties of the problem Solving the IP could take a high amount of time in large size problems 5 3 Cutting Plane Optimizer Parameter File 11 e solveWithMaxFlowCut boolean If the service time distribution are independent of the agent groups the user can choose to add heuristic cuts based on a maxflow subproblem This p
19. to true The global QoS of the optimal solution computed by approximation must be equal or greater than this parameter Note This value is not used with the correction by simulations step The target service level used to test the feasibility of the simulations are in the Call Center parameter file e opTargetServiceLevel array of real array of elements that are the target service level per call type used for the approximated values feasibility test The array contains a target service level for each call type This is the corresponding parameter of opGlobalTargetServiceLevel to the call types The program will use these values only if useLDOTargetServiceLevel is set to true ATTENTION This value is not used with the correction by simulations step The target service level used to test the feasibility of the simulations are in the Call Center parameter file 5 4 Randomized Search Parameters 13 e useBusyCost boolean element represents the cost type for the agent groups If set to false then the agent group cost is computed with the number of skills which is 1 0 of skills 1 skillPremiumCost If set to true then the program will use the busy cost defined for each agent group in the Call Center parameter file e skillPremiumCost real element is the premium cost of an agent group for each additional skill over 1 e searchMode integer enables the user to select the type of search 0 for mix mix of remove and s
20. uired A copy of the ContactCenters SSJ and colt are included in the distribution and no executable installation is required 3 Program Setup The following Java archives jar included in the distribution are required for the op timization programs to run ccoptim jar ssj jar contactcenters jar colt jar The jar need to be declared in the system environment variable CLASSPATH Additionnal steps would be required to setup the linear optimization library If using OR Objects 1 2 4 or124 jar must also be included in the CLASSPATH If using Cplex cplex jar must also be included in the CLASSPATH We suggest the user to consult their user s manual for an appropriate setup of their libraries Note To use the pre implemented solver interfaces with Cplex 8 Cplex 9 or OR Objects 1 2 4 the folder lib must be added to the CLASSPATH 4 3 Program Setup 3 1 Windows 95 98 Me Suppose for example that the folder 1ib has been copied to the directory C ccoptim lib Then the next step is to set the CLASSPATH variable Open a text console and type in a single line set CLASSPATH Y CLASSPATH C XccoptimiXlibXccoptim jar C ccoptim lib ssj jar C ccoptim lib colt jar C ccoptim lib contactcenters jar C ccoptim lib It would be preferable to insert the line in the file C autoexec bat if C is the system drive 3 2 Windows 2000 XP Suppose for example that the folder 1ib has been copied to the directory C
21. wever long simulation requires more time The length of the optimization program can be greatly affected by the time used for simulations Again here s a short description for a few parameters other parameters could be used For more details please refer to the ContactCenters simulation user s guide PDF e targetError real the target relative error to adjust the simulation length dy namically Set to 1 to disable this We suggest 1 to control the simulation length manually e level real the level of confidence intervals when computing relative errors or displaying statistical reports 8 5 Parameter Files e initNonEmpty boolean if true then indicates that the system will be initialized with n x targetInitOccupancy agents busy and all queues empty where n is the total number of agents We suggest true e batchSize real batch size in simulation time units e minBatches integer minimal number of batches When simulation length adjust ment is not used targetError lt 0 this corresponds to the number of simulated batches The total length of the simulation is batchsizex minbatches warmupBatches e warmupBatches integer number of warmup batches to simulate before collecting statistical observations Example of the simulator parameter file lt batchSimParams targetError 1 level 0 95 targetInitOccupancy 0 9 initNonEmpty true batchSize 10 minBatches 10
22. witch or 1 for sequential remove then switch We suggest to set it to 0 e useSimRemove boolean if set to true will execute the SimRemove procedure in the correction by simulation phase We suggest to set it to true e useSimSwitch boolean if set to true will execute the SimSwitch procedure in the correction by simulation phase Because this procedure requires a huge amount of time and the cost saved might not always be worth the extra time we suggest to set it to false Set to true if time is not a constraint e maxRSCPUsec int is the maximum number of seconds spent in search mode this does not include finding an initial staffing Since the program doesn t take hours to finish this parameter should be omitted We suggest to set a high value e useRealTime boolean if set to true will compute the execution time as the real world time If set to false the program will compute the execution time as the amount of time spent in the CPU the CPU time This value is used to truncate the randomized search if the execution time goes above maxRSCPUsec e rootL array of doubles is used to generate the initial staffing It uses a root solver to find the number of agents for each skill group to satisfy the inflows with a quality of service of rootL The AWT is the same as declared in the Call Center parameter file Setting multiple values triggers a multi start We suggest a value around the global service level targe
Download Pdf Manuals
Related Search