A Bi-index Continuous-Time Mixed-Integer Linear Programming Model for Single-Stage Batch Scheduling with Parallel Units

Abstract

This paper presents a mixed-integer linear programming formulation for the short-term scheduling of multiproduct batch plants with parallel nonidentical production units. The formulation efficiently determines the optimal order sequencing and order allocation to various processing units. This scheduling problem is highly combinatorial in nature especially because of the order sequence-dependent changeover constraints. To formulate this type of problem, traditionally tri-index discrete decision variables are applied to represent the order assignments. This approach requires a large number of discrete decision variables and consequently makes the model very time-consuming to solve. To overcome this problem, the proposed formulation applies bi-index discrete variables instead. This reduces the overall number of discrete decision variables to a great extent while still keeping the generality of the model. For handling large-scale problems, pre-ordering heuristics were imposed to further reduce the solution time. Examples with various numbers of units and orders illustrate the effectiveness of the formulation either with or without the pre-ordering constraints.