Scheduling parallel production lines with resource constraints. 1. Model formulation

Abstract

Parallel semicontinuous production lines producing multiple items are quite common in many multiproduct chemical plants. The operation of such lines may be constrained by the structure and capacity of upstream and/or downstream material handling facilities and the availability of common resources. In addition, sequence-dependent transitions may be required. In this twopart paper, we address the short-term scheduling of such plants with a composite objective of minimizing transitions and maximizing productivity. In this part, we present a novel mixedinteger linear programming (MILP) formulation employing a single set of nonuniform time slots for all lines. The formulation improves upon a previous treatment of minimum campaign lengths and proposes new continuous resource constraints that are derived from binary ones. Application of the model to an illustrative example suggests that the solution time increases exponentially with the number of time slots and that adding transition time to the makespan improves both model performance and schedule quality. Although suitable only for small problems in its present form, the model forms the backbone of a more efficient decomposition algorithm presented in the second part.