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Abstract

Consider the problem of establishing a service quota that sets the maximum number of items, entities, or people that should be scheduled for service during a particular period. Service is performed by a multiserver system using a first-come, first-serve discipline. If the number of customers seeking service is less than or equal to the quota, then they are all scheduled for service; otherwise, the quota is serviced, and remaining customers are delayed. Some delayed customers may leave the system before receiving service. Determination of an economic service quota requires the trade-off of possible overtime cost of scheduling too many customers for service in the period and the postponement cost of scheduling too few. A Markov chain analysis is used to develop a distribution for the number of customers postponed. Simulation is needed to estimate the expected total overtime given a fixed number of parallel servers. This method permits the estimation of the expected total cost of using the service quota policy and finding the optimal quota. A numerical example is provided.

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References

Chaudhry, M. L. and J. G. C. Templeton (1983), A First Course in Bulk Queues. New York: John Wiley.

Cox, D. R. and D. V. Hinkley (1970), “Some Properties of Multiserver Queues with Appointments,” Journal of the Royal Statistical Society Series A, 133, 1-13.

Duenyas, Izak , Wallace J. Hopp , and Yehuda Bassok (1997), “Production Quotas as Bounds on Interplant JIT Contracts,” Management Science, 43 (October), 1372-1386.

Gerchak, Yigal , Diwaker Gupta , and Mordechai Henig , “Reservation Planning for Elective Surgery under Uncertain Demand for Emergency Surgery,” Management Science, 42 (March), 321-334.

Hogg, Robert V. and Allen T. Craig (1970), Introduction to Mathematical Statistics, 3rd ed. New York: Macmillan.

Hopp, Wallace J. , Mark L. Spearman , and Izak Duenyas (1993), “Economic Production Quotas for Pull Manufacturing Systems,” IIE Transactions, 25 (March), 71-79.

Johnson, Lynwood A. and Douglas C. Montgomery (1974), Operations Research in Production Planning, Scheduling, and Inventory Control. New York: John Wiley.

Ross, Sheldon M. (1983), Stochastic Processes. New York: John Wiley.

Schaak, Christian and Richard C. Larson (1986), “An N-Server Cut-off Priority Queue,” Operations Research, 34 (March-April), 257-266.

10.

Shonick, William and James R. Jackson (1973), “An Improved Stochastic Model for Occupancy Related Random Variables in General Acute Hospital,” Operations Research, 21 (July-August), 952-965.

11.

Taylor, I. D. S. and J. G. C. Templeton (1980), “Waiting Time in Multi-Server Cut-off-Priority Queue, and Its Application to an Urban Ambulance Service,” Operations Research, 28 (September-October), 1168-1188.

12.

Winston, Wayne L. (1994), Operations Research: Applications and Algorithms, 3rd ed. Belmont, CA: Duxbury.

Economic Service Quotas

Abstract

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References