1. S. D. Deshmukh OM V. Capacity Planning in Services u Matching Supply and Demand u The Service Process u Performance Measures u Causes of Waiting u Economics of Waiting u Management of Waiting Time u The Sof-Optics Case 1

2. S. D. Deshmukh OM Matching Supply and Demand u Goods vs. Services –Make to Stock vs. Make to Order –Produce in advance vs. on demand –Safety Inventory vs. Safety Capacity u Examples –Banks (tellers, ATMs, drive-ins) –Fast food restaurants (counters, drive-ins) –Retail (checkout counters) –Airline (reservation, check-in, takeoff, landing, baggage claim) –Hospitals (ER, OR, HMO) –Call centers (telemarketing, help desks, 911 emergency) –Service facilities (repair, job shop, ships/trucks load/unload) 2

3. S. D. Deshmukh OM Sales Reps Processing Calls (Service Process) Incoming Calls (Customer Arrivals) Calls on Hold (Service Inventory) Answered Calls (Customer Departures) Blocked Calls (Due to busy signal) Abandoned Calls (Due to long waits) The DesiTalk Call Center Calls In Process (Due to long waits) The Call Center Process 3

4. S. D. Deshmukh OM The Service Process u Customer Inflow (Arrival) Rate (R i ) –Inter-arrival Time = 1 / R i u Processing Time T p –Processing Rate per Server = 1/ T p u Number of Servers (c) –Number of customers that can be processed simultaneously u Total Processing Rate (Capacity) = R p = c / T p u Buffer Capacity (K) –Maximum Queue Length

5. S. D. Deshmukh OM Operational Performance Measures u Flow time T=T i +T p u Inventory I= I i + I p  Flow Rate R =Min (R i, R p  u Stable Process= R i < R p,, so that R = R i  Little’s Law: I = R i  T, I i = R i  T i, I p = R i  T p  Capacity Utilization  = I p / c = R i  T p / c = R i / R p < 1 u Safety Capacity R s = R p - R i  Number of Busy Servers = I p = c  = R i  T p u Fraction Lost P b = P(Blocking) = P(Queue = K)

6. S. D. Deshmukh OM Financial Performance Measures u Sales –Throughput Rate –Abandonment Rate –Blocking Rate u Cost –Capacity utilization –Number in queue / in system u Customer service –Waiting Time in queue /in system 6

7. S. D. Deshmukh OM Flow Times with Arrival Every 4 Secs Customer Number Arrival Time Departure Time Time in Process 1055 24106 38157 412208 516259 6203010 7243511 8284012 9324513 10365014 What is the queue size? What is the capacity utilization? 7

8. S. D. Deshmukh OM Customer Number Arrival Time Departure Time Time in Process 1055 26115 312175 418235 524295 630355 736415 842475 948535 1054595 Flow Times with Arrival Every 6 Secs What is the queue size? What is the capacity utilization? 8

9. S. D. Deshmukh OM Customer Number Arrival Time Processing Time Time in Process 1077 21011 32077 42227 53288 633714 736415 843816 952512 1054111 Effect of Variability What is the queue size? What is the capacity utilization? 9

10. S. D. Deshmukh OM Customer Number Arrival Time Processing Time Time in Process 1088 21088 32022 42277 53211 63311 73677 84377 95244 105457 Effect of Synchronization What is the queue size? What is the capacity utilization? 10

11. S. D. Deshmukh OM Conclusion u If inter-arrival and processing times are constant, queues will build up if and only if the arrival rate is greater than the processing rate u If there is (unsynchronized) variability in inter- arrival and/or processing times, queues will build up even if the average arrival rate is less than the average processing rate u If variability in interarrival and processing times can be synchronized (correlated), queues and waiting times will be reduced 11

12. S. D. Deshmukh OM Summary: Causes of Delays and Queues u High Unsynchronized Variability in –Interarrival Times –Processing Times  High Capacity Utilization  = R i / R p, or Low Safety Capacity R s = R p – R i, due to –High Inflow Rate R i –Low Processing Rate R p = c/ T p 12

13. S. D. Deshmukh OM The Queue Length Formula Utilization effect Variability effect x where  R i / R p, where R p = c / T p, and C i and C p are the Coefficients of Variation (Standard Deviation/Mean) of the inter-arrival and processing times (assumed independent)

14. S. D. Deshmukh OM Variability Increases Average Flow Time T Utilization (ρ)  100% TpTp Throughput- Delay Curve 14

15. S. D. Deshmukh OM Computing Performance Measures u Given –Interarrival times: 10, 10, 2, 10, 1, 3, 7, 9, and 2 –Processing times: 7, 1, 7, 2, 8, 7, 4, 8, 5, 1 –c = 1 u Compute –Capacity Utilization  = R i / R p = 0.833 –C i = 3.937/6 = 0.6562 –C p = 2.8284/5 = 0.5657 u Queue Length Formula –I i = 1.5633 u Hence –T i = I i / R = 9.38 seconds, and T p = 5 seconds, so –T = 14.38 seconds, so –I = RT = 14.38/6 = 2.3966 15

16. S. D. Deshmukh OM Effect of Increasing Capacity u Given –Interarrival times: 10, 10, 2, 10, 1, 3, 7, 9, and 2 –Processing times: 7, 1, 7, 2, 8, 7, 4, 8, 5, 1 –c = 2 u Compute –Capacity Utilization  = R i / R p = 0.4167 –C i = 3.937/6 = 0.6562 –C p = 2.8284/5 = 0.5657 u Queue Length Formula –I i = 0.07536 u Hence –T i = I i / R = 0.45216 seconds, and T p = 5 seconds, so –T = 5.45216 seconds, so –I = RT = 5.45216/6 = 0.9087 16

17. S. D. Deshmukh OM The Exponential Model u Poisson Arrivals –Infinite pool of potential arrivals, who arrive completely randomly, and independently of one another, at an average rate R i  constant over time u Exponential Processing Time –Completely random, unpredictable, i.e., during processing, the time remaining does not depend on the time elapsed, and has mean T p u Computations –C i = C p = 1 –If c = 1, T = 1/(R p  R i ), then I = R i  T,... –If c ≥ 2, and K < ∞, use Performance.xls 17

18. S. D. Deshmukh OM Example u Interarrival time = 6 secs, so R i = 10/min u T p = 5 secs = 0.833 mins cρRsRs IiIi TiTi TI 10.8330.03334.1620.4160.4994.995 20.4170.23330.1750.0180.1011.0087

19. S. D. Deshmukh OM Synchronization u Matching Capacity with Demand u Capacity –Short term Control –Long term Planning u Demand –Pricing –Scheduling 19

20. S. D. Deshmukh OM Performance Improvement Levers u Capacity Utilization / Safety Capacity –Demand Management (arrival rate) »Peak load pricing –Increase Capacity (processing rate) »Number of Servers (scale) »Processing Rate (speed) u Variability Reduction –Arrival times »Scheduling, Reservations, Appointments –Processing times »Standardization, Specialization, Training u Synchroniztion –Matching capacity with demand 20

21. S. D. Deshmukh OM Server 1 Queue 1 Server 2 Queue 2 Server 1 Queue Server 2 Effect of Pooling RiRi RiRi R i /2 21

22. S. D. Deshmukh OM Effect of Buffer Capacity u Process Data –R i = 20/hour, T p = 2.5 mins, c = 1, K = # Lines – c u Performance Measures K456 IiIi 1.231.521.79 TiTi 4.104.945.72 PbPb 0.10040.07710.0603 R17.9918.4618.79  0.7490.7680.782 22

23. S. D. Deshmukh OM Economics of Capacity Decisions u Cost of Lost Business C b –$ / customer –Increases with competition u Cost of Buffer Capacity C k –$/unit/unit time u Cost of Waiting C w –$ /customer/unit time –Increases with competition u Cost of Processing C s –$ /server/unit time –Increases with 1/ T p u Tradeoff: Choose c, T p, K –Minimize Total Cost/unit time = C b R i P b + C k K + C w I (or I i ) + c C s

24. S. D. Deshmukh OM Optimal Buffer Capacity u Cost Data –Cost of telephone line = $5/hour, Cost of server = $20/hour, Margin lost = $100/call, Waiting cost = $2/customer/minute u Effect of Buffer Capacity on Total Cost K$5(K + c)$20 c$100 R i P b $120 I i TC ($/hr) 42520200.8147.6393.4 53020154.2182.6386.4 63520120.6214.8390.4 24

25. S. D. Deshmukh OM Optimal Processing Capacity cK = 6 – cPbPb IiIi TC ($/hr) = $20c + $5(K+c) + $100R i P b + $120 I i 150.07711.542$386.6 240.00430.158$97.8 330.00090.021$94.2 420.00040.003$110.8 25

26. S. D. Deshmukh OM Performance Variability u Effect of Variability –Average versus Actual Flow time u Time Guarantee –Promise u Service Level –P(Actual Time  Time Guarantee) u Safety Time –Time Guarantee – Average Time u Probability Distribution of Actual Flow Time –P(Actual Time  t) = 1 – EXP(- t / T) 26

27. S. D. Deshmukh OM Flow Time Management: Review u Waiting occurs due to –low processing capacity in relation to the inflow rate –variability in inter-arrival and processing times u Waiting can be reduced by –managing demand –pooling arrival streams –increasing capacity (number of servers  service rate) –reducing the variability in arrivals and processing u Optimal level of service involves a tradeoff –cost of waiting, lost business and cost of service 27

28. S. D. Deshmukh OM Flow Time Management Levers u Manage Arrivals –Demand Management: Price incentives –Pool arrivals u Increase Capacity –Scale: Servers, Part-timers, customer participation –Speed: Simplify, Automation, Information, Training u Decrease Variability –Arrivals: Forecast, Reservations, Pooling –Processing: Standardize u Reduce Impact of Waiting –Comfortable, Distract, Entertain, Perception 28