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SPEAKER: |
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TITLE: |
"Workload Allocation in Multi-Product, Multi-Facility Production Systems with Setup Times," or "Applications of Optimization of Queues in the Design of Manufacturing Systems" |
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DAY: |
Wednesday, November 26, 1997 |
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TIME: |
3:30 p.m. [Coffee in BSB-202 at 3:00 p.m.] |
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PLACE: |
BSB-108 |
Consider a firm with M heterogeneous servers, or production facilities, that faces a demand for N items. Each server can produce any item, but if it is required to produce more than one type, a non-zero setup time is incurred every time the server switches production. How should work be assigned to each server in this situation in order to minimize total expected work-in-progress (WIP) inventory? Does the contribution of a server to the total WIP (all servers combined) increase upon increasing its load, or the number of products assigned to it, or both? Is it always beneficial to add more servers? In order to answer questions such as these, we formulate the workload allocation problem as a nonlinear optimization problem and provide several insights gleaned from first order necessary conditions and from numerical examples. These insights are then used to devise a heuristic workload allocation as well as a lower bound.
Our model assumes that product demands arrive according to independent Poisson processes and that production facilities use a group scheduling policy to determine production batch sizes (relevant only when a facility produces more than one product). Under the group scheduling regime (also known as the cyclic-exhaustive policy in queuing literature), the manufacturing facility manufactures products in a rotation cycle. Also, once set up for a particular item, it continuously processes requests for the same type of items until there is no pending demand for that item. We choose this policy because it minimizes the amount of unfinished work at the production facility. No restrictions are placed upon the distributions of processing and setup times. Our modelling approach applies to produce-to-order as well as produce-to-stock manufacturing environments, where in the latter case, replenishment is triggered by a base-stock control policy. The talk is based on joint work with Professor S. Benjaafar from University of Minnesota.
Dr. Diwakar Gupta received a Bachelor's degree in Mechanical Engineering from the Indian Institute of Technology, Delhi, a Master's degree in Industrial Engineering from the University of Windsor, and a Ph.D. degree in Management Science from the University of Waterloo. Currently, he is an associate professor of production and management science at McMaster University. His research interests include manufacturing strategy, measurement and evaluation of manufacturing flexibility, design and operational control of manufacturing systems, health operations management, stochastic models, and analysis of polling systems. He is a member of the Editorial Board of IIE Transactions - Scheduling and Logistics, and an Associate Editor for the International Journal of Flexible Manufacturing Systems.
The following articles have been provided by Dr. Gupta to be used as background for his talk. They are on reserve at Thode Library (STATS 770: Statistics Seminar).
[1] Ni, L. M., and K. Hwang (1985), "Optimal Load Balancing in a Multiple Processor System with Many Job Classes," IEEE TRANSACTIONS ON SOFTWARE ENGINEERING SE-11, 491-496.
[2] Green, L. V., and D. Guha (1995), "On the Efficiency of Imbalance in Multi-Facility Multi-Server Service Systems," MANAGEMENT SCIENCE 41, 179-187.
[3] Benjaafar, S., and D. Gupta (1997), "Workload Allocation in Multi-Product, Multi-Facility Production Systems with Setup Times," submitted for publications (35 pages).