1. Beyond Spam: OR/MS Modeling Opportunities for Email Response Management Ramesh Sharda Robert A. Greve, Ashish Gupta, Manjunath Kamath, Mohan R. Chinnaswamy Robert A. Greve, Ashish Gupta, Manjunath Kamath, Mohan R. Chinnaswamy Oklahoma State University Ramesh.Sharda@okstate.edu

2. APMOD2004 Sharda/OSU2 Managing Email Pull the plug!Pull the plug! Spam controlSpam control Email filtering and organizationEmail filtering and organization Effective management policies and strategiesEffective management policies and strategies –Organizational and Individual level –Modeling opportunities

3. APMOD2004 Sharda/OSU3 Our Projects Routing and priority decisions in an email contact centerRouting and priority decisions in an email contact center –Simulation and queuing theory How often should we process our emailsHow often should we process our emails –Simulation Which email messages to processWhich email messages to process –Stochastic Programming with Recourse

4. APMOD2004 Sharda/OSU4 Queuing and Simulation Models For Analyzing Customer Contact Center Operations

5. APMOD2004 Sharda/OSU5 Inbound E-mail Contact Center Issues Operational planningOperational planning –Number of agents –Agents’ schedule Routing policies and prioritiesRouting policies and priorities –Routing to agents –Processing order Performance measuresPerformance measures –Response/Resolution time –Agent utilization Organizational behaviorOrganizational behavior –Human factors

6. APMOD2004 Sharda/OSU6 Call/Contact Center Literature Koole and Talim [2000]Koole and Talim [2000] –Exponential approximation in the design of call centers Koole and Mandelbaum [2002]Koole and Mandelbaum [2002] –Queueing models of call centers Koole, Pot and Talim [2003]Koole, Pot and Talim [2003] – Performance of call center with skill-based routing Armony and Maglaras [2002, 2003]Armony and Maglaras [2002, 2003] –Optimal staffing policy –Estimation scheme for the response time Whitt [2002]Whitt [2002] –Challenges and research directions in the design of customer contact centers

7. APMOD2004 Sharda/OSU7 Contact Center Description START END RECEIVE E-MAIL IDENTIFY E-MAIL TYPE USING SOFTWARE DIRECT E- MAIL TO AN AGENT PRE-PROCESS E-MAIL FORWARD E-MAIL ? PROCESS E-MAIL DELAY RESOLVED ? NO YES E-MAIL HANDLING LOGIC

8. APMOD2004 Sharda/OSU8 Model Details Poisson arrivalsPoisson arrivals Agents process e-mails according to a FCFS disciplineAgents process e-mails according to a FCFS discipline For an unresolved problem, the e-mail enters the system with a delay independent of the prior processingFor an unresolved problem, the e-mail enters the system with a delay independent of the prior processing The pre-processing time follows a uniform distributionThe pre-processing time follows a uniform distribution The processing time follows a general distributionThe processing time follows a general distribution –Erlang, Exponential, and Hyperexponential 2 types of e-mail and 3 agents2 types of e-mail and 3 agents

9. APMOD2004 Sharda/OSU9 Open Queuing Network Model Nodes represent agentsNodes represent agents Customers represent e-mailsCustomers represent e-mails Model parametersModel parameters –Number of nodes and the number of servers at each node –Markovian routing probability matrix –Mean and SCV (=Variance/Mean 2 ) service time at each node –Arrival rate and SCV for new e-mails

10. APMOD2004 Sharda/OSU10 Numerical Experiments Queueing model was solved using the Rapid Analysis of Queueing Systems (RAQS) packageQueueing model was solved using the Rapid Analysis of Queueing Systems (RAQS) package –RAQS is a software package for analyzing general queueing network models based on a two-moment framework [http://www.okstate.edu/cocim/raqs/] Simulation results obtained using a model in Arena 7.0Simulation results obtained using a model in Arena 7.0 –Replications – 10 –Run length – 9,240 hours –Warm up – 840 hours

11. APMOD2004 Sharda/OSU11 EXPERIMENTAL DESIGN * Numbers refer to priorities assigned to new email, previously processed (by the same agent) email, and previously processed (by the a different agent) email, respectively. First Come First Served (FCFS) gives priority only based on arrival time. FACTORLEVELS Routing Directly routed to the same agent Randomly routed Routed to agent with the lightest current load Priority Scheme* 1, 2, 3 1, 3, 1 2, 1, 3 2, 3, 1 3, 1, 2 3, 2, 1 FCFS

12. APMOD2004 Sharda/OSU12 EXPERIMENTAL DESIGN PERFORMANCE MEASURESPERFORMANCE MEASURES –Purchase Inquiry Response Time –Purchase Inquiry Resolution Time –Problem Resolution Request Response Time –Problem Resolution Request Resolution Time

13. APMOD2004 Sharda/OSU13 RESULTS (high utilization) Prioritization schemes that gave last priority to new email messages result in longer response and resolution times. By routing incoming messages to the agent with the fewest messages waiting for processing, the load is balanced across the agents. Routing messages to the agent who previously processed the message may result in disparity in individual agent utilizations, causing a gap between the best and worst performance.

14. APMOD2004 Sharda/OSU14 CONCLUSIONS Simulation, which has been used for modeling customer call centers, can also be used to model the unique characteristics of customer contact centersSimulation, which has been used for modeling customer call centers, can also be used to model the unique characteristics of customer contact centers Management decisions regarding routing and priority schemes can impact performanceManagement decisions regarding routing and priority schemes can impact performance The queuing model consistently underestimates the system performance measures.The queuing model consistently underestimates the system performance measures.

15. APMOD2004 Sharda/OSU15 Scheduling Email Processing to Reduce Information Overload and Interruptions

16. APMOD2004 Sharda/OSU16 Prior relevant research on Email Overload & interruptions research First reported by Peter Denning (1982),Later by Hiltz, et al. (1985), Whittaker, et al.(1996) and many…First reported by Peter Denning (1982),Later by Hiltz, et al. (1985), Whittaker, et al.(1996) and many… According to distraction theory, interruption is “an externally generated, randomly occurring, discrete event that breaks continuity of cognitive focus on a primary task“ (Corragio 1990; Tétard F. 2000).According to distraction theory, interruption is “an externally generated, randomly occurring, discrete event that breaks continuity of cognitive focus on a primary task“ (Corragio 1990; Tétard F. 2000). –Research done in HCI is rich but in MS/OR??? Research that looks at the problem of information overload and interruptions simultaneously is scarce. (Speier et al.1999, Jackson, et al., 2003, 2002, 2001), Venolia et al. (2003)Research that looks at the problem of information overload and interruptions simultaneously is scarce. (Speier et al.1999, Jackson, et al., 2003, 2002, 2001), Venolia et al. (2003)

17. APMOD2004 Sharda/OSU17 Research Model *Utilization: Probability of a knowledge worker being busy (λ/µ) Resource utilization change Task Complexity mix Task Completion time Resource utilization Number of Interruptions per task Interrupt arrival pattern Email Policy

18. APMOD2004 Sharda/OSU18 Our approach- SIMULATION Interrupt arrives IL + Interrupt processing Interrupt departs Recall time- RL Pre-processingPost-processing Policies that we are comparing :- Triage: (C1-morning, C1-Afternoon) Scheduled: (C2, C4, C8(Jackson et al. 2003)) Flow (continuous): C Phases of task processing (Miyata & Norman, 1986):- Planning Execution Evaluation

19. APMOD2004 Sharda/OSU19 Notations used iTask types- simple (S), complex (C), email(E) thus, i = {S, C, E} PrimPrimary task, which is either a simple or a complex task. Prim ={S, C} ρ Minimum utilization of knowledge worker i arrival rate for task of type i i arrival rate for task of type i μ i Service rates for task of type i PPlanning phase of a task ExeExecution phase of task EvalEvaluation phase of task StageCurrent stage of task processing. Thus Stage= {P, Exe, Eval} I Prim-Stage Interruption lag for a primary task at a particular processing stage. R Prim-Stage Resumption lag for a primary task at a particular processing stage. R Prim, Ĭ Prim Mean Resumption lag & Mean Interruption lag for a primary task

20. APMOD2004 Sharda/OSU20 Mathematical conditions and equations Following conditions were implemented in the simulation model:

21. APMOD2004 Sharda/OSU21 Mathematical conditions & equations 0 ≤ ≤ 1

22. APMOD2004 Sharda/OSU22 Mathematical conditions & equations Parameters chosen for Beta distribution are k=2 & l =1 For positive linear relationship between ε and.

23. APMOD2004 Sharda/OSU23 Model Implementation Sn, Cn- new simple & complex task Si, Ci – interrupted simple & complex task E – Email (Interrupt)

24. 9 Profile plots RU % increase in utilization # of interruptions per simple or complex task Results Policy C4 resulted in (1)minimum percentage increase in utilization (2)minimum # of interruptions per simple task (3)minimum # of interruptions per complex tasks Result holds under: The work environment requires high, medium or low utilization of knowledge worker, or The work environment requires processing of either more simple or more complex tasks, or For both arrival patterns (Pattern I: when all email arrived during office hrs, Pattern II: when 80% emails arrived during office hrs).

25. APMOD2004 Sharda/OSU25 Practical implications If other tasks are more important and email communication is secondary !If other tasks are more important and email communication is secondary ! Process emails 4 times a day with each processing block not exceeding 45 min.Process emails 4 times a day with each processing block not exceeding 45 min. Is timely email processing a survival issue for your kind of organization?Is timely email processing a survival issue for your kind of organization? –Use flow (continuous) policy

26. APMOD2004 Sharda/OSU26 A Stochastic Programming Approach to Managing Email Overload

27. APMOD2004 Sharda/OSU27 Email Overload Inability to respond to all email in a timely mannerInability to respond to all email in a timely manner The knowledge worker must not only take into consideration the current email that is in need of processing and the timeliness of this email, but he or she must also consider what future email demands may be on the horizon.The knowledge worker must not only take into consideration the current email that is in need of processing and the timeliness of this email, but he or she must also consider what future email demands may be on the horizon. Stochastic Programming takes possible FUTURE scenarios into considerationStochastic Programming takes possible FUTURE scenarios into consideration All other efforts consider only the present stateAll other efforts consider only the present state

28. APMOD2004 Sharda/OSU28 An Illustrative Example: Optimizing Email Processing With respect to email processing, the optimization involves maximizing the utility or value of the emails that are processed.With respect to email processing, the optimization involves maximizing the utility or value of the emails that are processed. The optimal solution must take into consideration that the utility of a processed email may decrease with time.The optimal solution must take into consideration that the utility of a processed email may decrease with time. The optimal solution must also consider the potential arrival of different types of email in the future.The optimal solution must also consider the potential arrival of different types of email in the future. The decision variables correspond to whether or not to process an email in a given stage (time frame).The decision variables correspond to whether or not to process an email in a given stage (time frame). The stochastic parameters include the potential arrival of various types of emails.The stochastic parameters include the potential arrival of various types of emails.

29. APMOD2004 Sharda/OSU29 An Illustrative Example: Optimizing Email Processing Beginning Inbox (i = type, j = age)Beginning Inbox (i = type, j = age) j i 43220 58401

30. APMOD2004 Sharda/OSU30 An Illustrative Example: Optimizing Email Processing Utility of email processed (i = type, j = age)Utility of email processed (i = type, j = age) j i 1010630 870-4-4

31. APMOD2004 Sharda/OSU31 An Illustrative Example: Optimizing Email Processing Arrival scenarios (number of type i email arriving)Arrival scenarios (number of type i email arriving) Arrival Scenarios Probabilities.2.2.1.5 i 3258 2354

32. APMOD2004 Sharda/OSU32 An Illustrative Example: Optimizing Email Processing Time needed to process email (days)Time needed to process email (days) i.1.1

33. APMOD2004 Sharda/OSU33 Formulations LP – Single-periodLP – Single-period LP – Multi-periodLP – Multi-period SP – Perfect InformationSP – Perfect Information SP – Here and NowSP – Here and Now

34. APMOD2004 Sharda/OSU34 Formulation Sets and Indices Tis the set of the different days under considerationTis the set of the different days under consideration Iis the set of possible types of email messagesIis the set of possible types of email messages Jis the set of possible ages of an email message in daysJis the set of possible ages of an email message in days Qis the set of possible arrival scenariosQis the set of possible arrival scenarios t = 1..4denotes the day under considerationt = 1..4denotes the day under consideration i = 1..2denotes the type of email messagei = 1..2denotes the type of email message j = 1..5denotes the age of an email messagej = 1..5denotes the age of an email message q = 1..64denotes the arrival scenarioq = 1..64denotes the arrival scenario

35. APMOD2004 Sharda/OSU35 SP Formulation (Here and Now) Parameters N t = 1,i,j,q This represents the number of email of type i that are jN t = 1,i,j,q This represents the number of email of type i that are j days old on day one. This represents the beginning inbox. A t,i,q This represents the number of arriving email of type i, given scenario q.A t,i,q This represents the number of arriving email of type i, given scenario q. U i,j This represents the utility or value of an email of type i,U i,j This represents the utility or value of an email of type i, having an age of j. P q This represents the probability of scenario q.P q This represents the probability of scenario q. D i This represents the time needed, in days, to process an email of type i.D i This represents the time needed, in days, to process an email of type i.

36. APMOD2004 Sharda/OSU36 SP Formulation (cont.) (Here and Now) Variables X t,i,j,q This represents the number of email that are processed on day t, that are of type i and have an age of j, given scenario q.X t,i,j,q This represents the number of email that are processed on day t, that are of type i and have an age of j, given scenario q. N t,i,j,q This represents the number of email of type i that are j daysN t,i,j,q This represents the number of email of type i that are j days old on day t, given scenario q. Objective Function Max Σ q Σ i Σ j P q X t,i,j,q U i,jMax Σ q Σ i Σ j P q X t,i,j,q U i,j

37. APMOD2004 Sharda/OSU37 SP Formulation (cont.) (Here and Now) Constraints N t,i,j,q = N t-1,i,j-1,q – X t-1,i,j-1,q t > 1, i = 1..2, j > 1, q = 1..64N t,i,j,q = N t-1,i,j-1,q – X t-1,i,j-1,q t > 1, i = 1..2, j > 1, q = 1..64 N t,i,j,q = A t,i,q t > 1, I – 1..2, j = 1, q = 1..64N t,i,j,q = A t,i,q t > 1, I – 1..2, j = 1, q = 1..64 X t,i,j,q <= N t,i,j,q t = 1..4, i = 1..2, j < 5, q = 1..64X t,i,j,q <= N t,i,j,q t = 1..4, i = 1..2, j < 5, q = 1..64 X t,i,j,q = N t,i,j,q t = 1..4, i = 1..2, j = 5, q = 1..64X t,i,j,q = N t,i,j,q t = 1..4, i = 1..2, j = 5, q = 1..64 Σ i Σ j X t,i,j,q D i <= 1 t = 1..4, i = 1..2, j = 1..5, q = 1..64Σ i Σ j X t,i,j,q D i <= 1 t = 1..4, i = 1..2, j = 1..5, q = 1..64 X t,i,j,q = X t,i,j,q+1 t = 1, i = 1..2, j = 1..5, q < 63X t,i,j,q = X t,i,j,q+1 t = 1, i = 1..2, j = 1..5, q < 63 X t,i,j,q = X t,i,j,q+1 t = 2, i = 1..2, j = 1..5, q < 63X t,i,j,q = X t,i,j,q+1 t = 2, i = 1..2, j = 1..5, q < 63 X t,i,j,q = X t,i,j,q+1 t = 3, i = 1..2, j = 1..5, q < 63X t,i,j,q = X t,i,j,q+1 t = 3, i = 1..2, j = 1..5, q < 63 X t,i,j,q = X t,i,j,q+1 t = 4, i = 1..2, j = 1..5, q < 63X t,i,j,q = X t,i,j,q+1 t = 4, i = 1..2, j = 1..5, q < 63

38. APMOD2004 Sharda/OSU38 Sample Results FCFS LP – Single- period LP – Multi- period SP – Perfect Infor- mation SP – Here & Now Total 4-day Utility 120.68166.60264.00258.78218.00

39. APMOD2004 Sharda/OSU39 Extensions More realistic modeling of the problem needed:More realistic modeling of the problem needed: –Differences in service times for different email classes Identification of utilitiesIdentification of utilities Automatic identification of email categoriesAutomatic identification of email categories Real time solution of the SPR problem before the Inbox is shown to the userReal time solution of the SPR problem before the Inbox is shown to the user –Another optimization challenge

40. APMOD2004 Sharda/OSU40 Future research Perform these studies in experimental or field settings.Perform these studies in experimental or field settings. –Use measures of Perceived Information Overload (NASA-TLX, SWAT) More realistic modeling by incorporating email characteristics as well as knowledge worker differencesMore realistic modeling by incorporating email characteristics as well as knowledge worker differences Single vs. multi-user settings/Network modelingSingle vs. multi-user settings/Network modeling Nonlinear formulationsNonlinear formulations Stochastic knapsackStochastic knapsack A really rich domain for OR/MS modeling!!!