Mathematical programming formulation for campaign planning of multi-product batch process

This paper deals with a campaign planning problem typical for multi-product batch plants. Here the campaign size (production amount of one continuous production run) is often constrained by the multiples of a batch size, which is limited by a lower and upper bound according to the volume of reactor and safe operations. A new and applicable Mixed Integer Linear Programming (MILP) model formulation is presented that is based on the standard capacitated lot-sizing model with some adaptive innovations, such as adding the value of un-utilized capacity to objective function, non-uniform time division, capacity variations, non-continuous limitation of production quantity, limitation of raw materials etc. In order to solve large-scale problems and lower computational time, some valid inequalities are adopted. The problem size of the proposed formulation is acceptable, and can be solved using commerce optimization software ILOG CPLEX within tolerable CPU time. The performance of the approach is illustrated by one real case study.