OM&PM/Class 6b1 1Operations Strategy 2Process Analysis 3Lean Operations 4Supply Chain Management 5Capacity 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 6Total Quality Management 7Business Process Reengineering Operations Management & Performance Modeling

OM&PM/Class 6b2  L.L. Bean is planning the order size for winter parkas. Each parka costs the company $70 and sells for $140. Any unsold parkas at the end of the season are disposed off by a sale at $40. Using historical data and a feel for the market, L.L. Bean forecasts the winter season demand: Demand: Probability: 3%4%5%8%10% 15%12%10% Cumulative: 3%7%12%20%30%45%57%67% Demand: Probability: 9%6%5%4%4%3%2% Cumulative:76%82%87%91%95%98%100% è How many parkas should L.L. Bean plan (make/order)? Accurate Response to Demand Uncertainty when you can order only once: L.L. Bean

OM&PM/Class 6b3 Accurate Response: Find optimal order level Q with Excel

OM&PM/Class 6b4 Accurate response: Find optimal Q from formula  Cost of overstocking by one unit = C o –the out-of-pocket cost per unit stocked but not demanded –“Say demand is one unit below my stock level. How much did the one unit overstocking cost me?” E.g.: purchase price - salvage price.  Cost of understocking by one unit = C u –The opportunity cost per unit demanded in excess of the stock level provided –“Say demand is one unit above my stock level. How much could I have saved (or gained) if I had stocked one unit more?” E.g.: retail price - purchase price. Given an order quantity Q, increase it by one unit if and only if the expected benefit of being able to sell it exceeds the expected cost of having that unit left over. At optimal Q, do not order more if è = smallest Q such that stock-out probability < critical fractile C o / (C o + C u ) Prob( Demand > Q ) < C o / (C o + C u ).

OM&PM/Class 6b5 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 6b6 Telemarketing: deterministic analysis  it takes 8 minutes to serve a customer  6 customers call per hour –one customer every 10 minutes  Flow Time = 8 min Flow Time Distribution Flow Time (minutes) Probability

OM&PM/Class 6b7 Telemarketing with variability in arrival times + activity times  In reality service times –exhibit variability  In reality arrival times –exhibit variability

OM&PM/Class 6b8 Telemarketing with variability: The effect of utilization  Average service time = –9 minutes  Average service time = –9.5 minutes

OM&PM/Class 6b9 Why do queues form?  utilization: –throughput/capacity  variability: –arrival times –service times –processor availability

OM&PM/Class 6b10 Cycle Times in White Collar Processes

OM&PM/Class 6b11 Queuing Systems to model Service Processes: A Simple Process Sales Reps processing calls Incoming calls Calls on Hold Answered Calls MBPF Inc. Call Center Blocked Calls (Busy signal) Abandoned Calls (Tired of waiting) Order Queue “buffer” size K

OM&PM/Class 6b12 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 6b13 Performance Measures  Sales –Throughput R –Abandonment  Cost –Server utilization  –Inventory/WIP : # in queue/system  Customer service –Waiting/Flow Time: time spent in queue/system –Probability of blocking

OM&PM/Class 6b14 Queuing Theory: Variability + Utilization = Waiting  Throughput-Delay curve:  Pollaczek-Khinchine Form: –Prob{waiting time in queue < t } = 1 - exp(-t / T i ) where: mean service time utilization effect variability effect xx

OM&PM/Class 6b15 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 6b16 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 6b17 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 6b18 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) Servers Queue ServerQueue ServerQueue 50%

OM&PM/Class 6b19 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 6b20 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 6b21 National Cranberry Cooperative Hourly Berry Arrivals Time Bbls

OM&PM/Class 6b22 Real Processes exhibit variability in order placement time and type Histogram of Truck inter-delivery times Truck interarrival time (min) Frequency (# of trucks) Histogram of Truck Weights Truck Weight (Kpounds) Frequency (# of trucks) National Cranberry on Sept 23, 1970