Article ID: | iaor20061637 |
Country: | Netherlands |
Volume: | 165 |
Issue: | 1 |
Start Page Number: | 231 |
End Page Number: | 250 |
Publication Date: | Aug 2005 |
Journal: | European Journal of Operational Research |
Authors: | Grosfeld-Nir Abraham |
Keywords: | inventory |
This study considers multistage production systems where production is in lots and only two stages have non-zero setup costs. Yields are binomial and demand, needing to be satisfied in its entirety, is “rigid”. We refer to a stage with non-zero setup cost as a “bottleneck” (BN) and thus to the system as “a two-bottleneck system” (2-BNS). A close examination of the simplest 2-BNS reveals that costs corresponding to a particular level of work in process (WIP) depend upon costs for higher levels of WIP, making it impossible to formulate a recursive solution. For each possible configuration of intermediate inventories a production policy must specify at which stage to produce next and the number of units to be processed. We prove that any arbitrarily “fixed” production policy gives rise to a finite set of linear equations, and develop algorithms to solve the two-stage problem. We also show how the general 2-BNS can be reduced to a three-stage problem, where the middle stage is a non-BN, and that the algorithms developed can be modified to solve this problem.