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

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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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Correspondence to Gaby Pinto.

Appendix: MRCCSP notations

Appendix: MRCCSP notations

Indices:

figure a

Parameters:

Notice that the following sets used here, R, R i,m , R un , R ba , S f , F, are defined later.

figure b

Sets:

figure c
figure d

Decision variables:

figure e
figure f

MRCCSP size reduction constraints—reduced constraints are listed below

(2R)
(3R)
(4R)
(7R)
(8R)
(9R)
(12R)
(13R)
(14R)
(17R)

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Pinto, G., Ben-Dov, Y.T. & Rabinowitz, G. Formulating and solving a multi-mode resource-collaboration and constrained scheduling problem (MRCCSP). Ann Oper Res 206, 311–339 (2013). https://doi.org/10.1007/s10479-012-1256-5

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