Formulating and solving a multi‐mode resource‐collaboration and constrained scheduling problem (MRCCSP)

Formulating and solving a multi‐mode resource‐collaboration and constrained scheduling problem (MRCCSP)

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Article ID: iaor20133926
Volume: 206
Issue: 1
Start Page Number: 311
End Page Number: 339
Publication Date: Jul 2013
Journal: Annals of Operations Research
Authors: , ,
Keywords: scheduling, programming: branch and bound
Abstract:

The main motivation of this study is to provide, for the first time, a formulation and solution for a class of production scheduling problems (as in cluster tools) characterized mainly by resource collaboration to perform an operation and while allowing batches and considering alternative production methods. We develop a formulation for the new problem and term it a multiple mode per operation, resource collaboration, and constrained scheduling problem (MRCCSP). Some of the important new characteristics we consider are: multiple products (families); multiple orders (jobs) per family; precedence restrictions among the operations that constitute a job; alternative modes for the performance of an operation (each of which needs a set of collaborating resources) may be defined; complementary and exclusive restrictions between operation‐modes; batch production is allowed; and setup times may depend on sequence and batch‐size. The objective of the MRCCSP is to minimize makespan. We formulate the MRCCSP as a mixed integer linear programming model, and acknowledging the considerable size of the monolithic formulation required, we prescribe a specific method to achieve size reduction. Finally, a customized branch and bound algorithm for optimally solving this problem is proposed and examined experimentally.

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