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1 Operations Strategy 2 Process Analysis 3 Lean Operations 4 Supply Chain Management

Operations Management & Performance Modeling. 1 Operations Strategy 2 Process Analysis 3 Lean Operations 4 Supply Chain Management 5 Capacity Management in Services Class 6b: Capacity Analysis and Queuing Why do queues build up? Performance measures for queuing systems

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1 Operations Strategy 2 Process Analysis 3 Lean Operations 4 Supply Chain Management

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  1. Operations Management & Performance Modeling 1 OperationsStrategy 2 Process Analysis 3 Lean Operations 4 Supply Chain Management 5 Capacity Management in Services • Class 6b: Capacity Analysis and Queuing • Why do queues build up? • Performance measures for queuing systems • The need for safety capacity • Throughput of queuing system with finite buffer • Pooling of capacity 6 Total Quality Management 7 Business Process Reengineering OM&PM/Class 6b

  2. Telemarketing at L.L.Bean • During some half hours, 80% of calls dialed received a busy signal. • Customers getting through had to wait on average 10 minutes for an available agent. Extra telephone expense per day for waiting was $25,000. • For calls abandoned because of long delays, L.L.Bean still paid for the queue time connect charges. • In 1988, L.L.Bean conservatively estimated that it lost $10 million of profit because of sub-optimal allocation of telemarketing resources. OM&PM/Class 6b

  3. it takes 8 minutes to serve a customer 6 customers call per hour one customer every 10 minutes Flow Time = 8 min 100% 100% 90% 90% 80% 80% 70% 70% 60% 60% 50% 50% 40% 40% 30% 30% 20% 20% 10% 10% 0% 0% 0 15 30 45 60 75 90 105 120 135 150 165 180 195 Telemarketing: deterministic analysis Flow Time Distribution Probability Flow Time (minutes) OM&PM/Class 6b

  4. In reality service times exhibit variability In reality arrival times exhibit variability 25% 100% 90% 20% 80% 15% 60% Probability 10% 40% 5% 20% 0% 0% 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 More Flow Time 30% 100% 90% 25% 80% 70% 20% 60% Probability 15% 50% 40% 10% 30% 20% 5% 10% 0% 0% 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 More Flow Time Telemarketing with variability in arrival times + activity times OM&PM/Class 6b

  5. Average service time = 9 minutes Average service time = 9.5 minutes 8% 100% 90% 7% 80% 6% 70% 5% 60% Probability 4% 50% 40% 3% 30% 2% 20% 1% 10% 0% 0% 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 More Flow Time 25% 100% 90% 20% 80% 70% 15% 60% Probability 50% 10% 40% 30% 5% 20% 10% 0% 0% 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 More Flow Time Telemarketing with variability: The effect of utilization OM&PM/Class 6b

  6. Call # 10 9 8 7 6 5 4 3 2 1 0 0 20 40 60 80 1 0 0 TIME Inventory (# of calls in system) 5 4 3 2 1 0 0 20 40 60 80 1 0 0 TIME Why do queues form? • utilization: • throughput/capacity • variability: • arrival times • service times • processor availability OM&PM/Class 6b

  7. Cycle Times in White Collar Processes OM&PM/Class 6b

  8. Queuing Systems to model Service Processes: A Simple Process Order Queue “buffer” size K Sales Reps processing calls Incoming calls Answered Calls Calls on Hold MBPF Inc. Call Center Blocked Calls (Busy signal) Abandoned Calls (Tired of waiting) OM&PM/Class 6b

  9. What to manage in such a process? • Inputs • InterArrival times/distribution • Service times/distribution • System structure • Number of servers • Number of queues • Maximum queue length/buffer size • Operating control policies • Queue discipline, priorities OM&PM/Class 6b

  10. Performance Measures • Sales • Throughput R • Abandonment • Cost • Server utilization r • Inventory/WIP : # in queue/system • Customer service • Waiting/Flow Time: time spent in queue/system • Probability of blocking OM&PM/Class 6b

  11. Queuing Theory: Variability + Utilization = Waiting • Throughput-Delay curve: • Pollaczek-Khinchine Form: • Prob{waiting time in queue < t } = 1 - exp(-t / Ti ) where: mean service time utilization effect variability effect x x OM&PM/Class 6b

  12. Levers to reduce waiting and increase QoS: variability reduction + safety capacity • How reduce system variability? • Safety Capacity = capacity carried in excess of expected demand to cover for system variability • it provides a safety net against higher than expected arrivals or services and reduces waiting time OM&PM/Class 6b

  13. Example 1: MBPF Calling Center one server, unlimited buffer • Consider MBPF Inc. that has a customer service representative (CSR) taking calls. When the CSR is busy, the caller is put on hold. The calls are taken in the order received. • Assume that calls arrive exponentially at the rate of one every 3 minutes. The CSR takes on average 2.5 minutes to complete the reservation. The time for service is also assumed to be exponentially distributed. • The CSR is paid $20 per hour. It has been estimated that each minute that a customer spends in queue costs MBPF $2 due to customer dissatisfaction and loss of future business. • MBPF’s waiting cost = OM&PM/Class 6b

  14. Example 2: MBPF Calling Center limited buffer size • In reality only a limited number of people can be put on hold (this depends on the phone system in place) after which a caller receives busy signal. Assume that at most 5 people can be put on hold. Any caller receiving a busy signal simply calls a competitor resulting in a loss of $100 in revenue. • # of servers c = 1 • buffer size K = 6 • What is the hourly loss because of callers not being able to get through? OM&PM/Class 6b

  15. 50% Queue Server 50% Queue Server Queue Servers Example 3: MBPF Calling Center Resource Pooling • 2 phone numbers • MBPF hires a second CSR who is assigned a new telephone number. Customers are now free to call either of the two numbers. Once they are put on hold customers tend to stay on line since the other may be worse ($111.52) • 1 phone number: pooling • both CSRs share the same telephone number and the customers on hold are in a single queue ($61.2) OM&PM/Class 6b

  16. Example 4: MBPF Calling Center Staffing • Assume that the MBPF call center has a total of 6 lines. With all other data as in Example 2, what is the optimal number of CSRs that MBPF should staff the call center with? • c = 3 OM&PM/Class 6b

  17. Class 6b Learning objectives • Queues build up due to variability. • Reducing variability improves performance. • If service cannot be provided from stock, safety capacity must be provided to cover for variability. • Tradeoff is between cost of waiting, lost sales, and cost of capacity. • Pooling servers improves performance. OM&PM/Class 6b

  18. Hourly Berry Arrivals 2500 2298 2000 1792 1713 1680 1477 1341 1335 1395 1500 1269 1317 Bbls 1032 1016 1000 539 500 0 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Time National Cranberry Cooperative OM&PM/Class 6b

  19. Histogram of Truck inter-delivery times Histogram of Truck Weights 40 40 35 35 30 30 25 25 Frequency (# of trucks) 20 Frequency (# of trucks) 20 15 15 10 10 5 5 0 0 4 6 10 14 16 20 0 2 8 12 18 0 16 20 24 28 32 36 40 4 12 8 Truck interarrival time (min) Truck Weight (Kpounds) Real Processes exhibit variability in order placement time and type National Cranberry on Sept 23, 1970 OM&PM/Class 6b

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