A Multi-Objective Approach to Modelling the Integrated Resource Selection and Operation Sequences Problem in a Production System

This paper addresses the integrated resource selection and operation sequences problem. This production scheduling problem is an extension of the flow shop, job shop and flexible job shop problems, its main characteristics being the precedence relationship between operations that are part of customer orders, the lot size of orders and the flexibility of the machines. A mixed-integer programming model is proposed to solve the problem, simultaneously optimising two objectives. This class of problems with more than one objective is known as multi-objective optimization, which consists of obtaining the non-dominated solutions that are part of the Pareto frontier. The problem's first objective is to minimize the makespan or the shortest time to complete all the orders. The second objective of the problem is to balance the workload of the machines, which aims to prevent specific machines from having a low workload and other machines from having an excessive workload. The computational results show that the mathematical model could satisfactorily solve the cases or instances.