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Improved MILP formulation equipped with valid inequalities for scheduling a batch processing machine with non-identical job sizes

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  • Husseinzadeh Kashan, Ali
  • Ozturk, Onur

Abstract

We consider the problem of minimizing makespan on a single batch processing machine with a limited capacity. The machine can simultaneously process a group (batch) of jobs, each of them having different sizes and processing times. The processing time of a batch is the longest processing time of all jobs in the batch. We analyze the strength of the LP-relaxations of two mixed integer linear programming (MILP) formulations: a straightforward formulation and an advanced formulation. We prove that while the LP-relaxation of the straightforward formulation can perform arbitrarily bad in providing an LP bound on the optimal makespan, the LP-relaxation of the advanced formulation have some merit in providing a relatively good bound of makespan. With a detailed analysis of the problem, we prove a number of properties of the optimal solution and derive their respective valid inequalities (VI). These VIs are exploited in a novel MILP formulation for the problem. Extensive computations reveal that, with the help of the VIs, the proposed MILP formulation can solve large instances of the problem.

Suggested Citation

  • Husseinzadeh Kashan, Ali & Ozturk, Onur, 2022. "Improved MILP formulation equipped with valid inequalities for scheduling a batch processing machine with non-identical job sizes," Omega, Elsevier, vol. 112(C).
    • Handle: RePEc:eee:jomega:v:112:y:2022:i:c:s0305048322000809
    DOI: 10.1016/j.omega.2022.102673
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