A MILP model for single machine family scheduling with sequence-dependent batch setup and controllable processing times

TL;DR

This paper develops and compares MILP models for single machine family scheduling with sequence-dependent batch setups and controllable processing times, aiming to evaluate their effectiveness against dynamic programming strategies.

Contribution

It introduces three MILP models for complex scheduling problems, highlighting the most efficient one using binary variables for job sequencing and position, and incorporates a stage-based state space approach.

Findings

The proposed MILP model with binary variables outperforms others in computational efficiency.

The stage-based state space model effectively captures system dynamics.

Comparison shows MILP models can approximate optimal control strategies.

Abstract

A mathematical programming model for a class of single machine family scheduling problem is described in this technical report, with the aim of comparing the performance in solving the scheduling problem by means of mathematical programming with the performance obtained when using optimal control strategies, that can be derived from the application of a dynamic programming-based methodology proposed by the Author. The scheduling problem is characterized by the presence of sequence-dependent batch setup and controllable processing times; moreover, the generalized due-date model is adopted in the problem. Three mixed-integer linear programming (MILP) models are proposed. The best one, from the performance point of view, is a model which makes use of two sets of binary variables: the former to define the relative position of jobs and the latter to define the exact sequence of jobs. In addition, one of the model exploits a stage-based state space representation which can be adopted to define the dynamics of the system.