Study on column generation for the lot-sizing and scheduling problem with sequencedependent setup time

Dandan Zhang,Canrong Zhang

doi:10.1051/matecconf/201818906002

Dandan Zhang, Canrong Zhang

Open Access

https://doi.org/10.1051/matecconf/201818906002

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Abstract

The capacitated lot-sizing and scheduling problem with sequence-dependent setup time and carryover setup state is a challenge problem in the semiconductor assembly and test manufacturing. For the problem, a new mixed integer programming model is proposed, followed by exploring its relative efficiency in obtaining optimal solutions and linearly relaxed optimal solutions. On account of the sequence-dependent setup time and the carryover of setup states, a per-machine Danzig Wolfe decomposition is proposed. We then build a statistical estimation model to describe correlation between the optimal solutions and two lower bounds including the linear relaxation solutions, and the pricing sub-problem solutions of Danzig Wolfe decomposition, which gives insight on the optimal values about information regarding whether or not the setup variables in the optimal solution take the value of 1, and the information is further used in the branch and select procedure. Numerical experiments are conducted to test the performance of the algorithm.

Highlights

The capacitated lot-sizing and scheduling problem with sequence-dependent setup times (CLSD) is a common problem and frequently encountered in semiconductor assembly and test manufacturing(ATM) factory
We propose a new MIP model and the per-machine Danzig Wolfe decomposition, which are equivalent to the formulation in Xiao et al.[7]
On account of the sequence-dependent setup time and setup state carry-over in this paper, decomposing the primal problem into several single-item lot-sizing sub-problems is not easy due to that the value of setup state variable is decided by two adjacent items instead of only one item and the setup structure is dependent on the previous periods or the setup sequences within periods

Summary

Introduction

The capacitated lot-sizing and scheduling problem with sequence-dependent setup times (CLSD) is a common problem and frequently encountered in semiconductor assembly and test manufacturing(ATM) factory In practice it is often required several hours for schedulers to generate a solution based on their experiences, which leads to the significance of research on the models and solution methods to seek effective and efficient solutions. We propose a new MIP model and the per-machine Danzig Wolfe decomposition, which are equivalent to the formulation in Xiao et al.[7]. Related results show these two models have relative efficiency in obtaining optimal solutions and linearly relaxed optimal solutions.

Mathematical Formulations

An informative Danzig-Wolfe decomposition and column generation

Model validation

Comparison on linearly relaxed optimal solutions

Findings

Conclusions