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 two-part 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 mixed-integer 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.

In the preceding paper, we presented a mixed-integer linear programming model (MILP) for scheduling operation in a multiproduct facility comprising multiple parallel semicontinuous production lines. In this part, we first perform a critical analysis of the model structure and its various constraints and the various solver options. Because, even after that effort, the model remains computationally expensive for large-scale industrial applications, we use it to develop an efficient two-step decomposition algorithm. The main idea behind this algorithm is to first generate several good, feasible item combinations by repeatedly solving the model with a minimum number of slots and then to compose a schedule using these item combinations. A computationally easier new model for sequencing and scheduling item combinations is derived from the original model. When applied to an industrial problem from a detergent plant, the new algorithm gives near-optimal solutions in far less time than the original model.

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