Mixed-Integer Programming Model and Tightening Methods for Scheduling in General Chemical Production Environments

We develop a mixed-integer programming (MIP) model to address chemical production scheduling problems in a wide range of facilities, including facilities with many different types of material handling restrictions and a wide range of process characteristics. We first discuss how material handling restrictions result in different types of production environments and then show how these restrictions can be modeled. We also present extensions for some important processing constraints and briefly discuss how other constraints and characteristics can be modeled. Finally, we present constraint propagation methods for the calculation of parameters that are used to formulate tightening constraints that lead to a substantial reduction of computational requirements. The proposed model is the first to address the generalized chemical production scheduling problem

Reformulations and Branching Methods for Mixed-Integer Programming Chemical Production Scheduling Models

Mixed-integer programs for chemical production scheduling are computationally challenging. One characteristic that makes them hard is that they typically have many symmetric solutions, that is, solutions that are different in terms of the values of the decision variables but have the same objective function value, which means that the algorithms used to solve these models must search through all such solutions before improving the bound on the objective. To address this challenge, we propose three reformulations of the widely used state–task network formulation. Specifically, we introduce additional constraints to define the number of batches of each task as an integer variable. Branching on this new integer variable quickly eliminates schedules that have the same number of batches, which, in turn, leads to the elimination of many symmetric solutions. We also study different branching strategies and variable selection rules and compare them. The proposed solution methods lead to orders-of-magnitude reductions in the computational requirements for the solution of scheduling problems