Completion times and optimal scheduling for serial multi-product processes with transfer and set-up times in zero-wait policy

Calculation of completion times and optimal scheduling for serial multi-product, multi-unit problems have been studied for the different types of intermediate storage options. In this study, a set of simple recurrence relations for serial multi-product multi-batch processes in ZW policy is suggested, which calculates completion times with or without non-zero transfer times and non-zero sequence dependent set-up times of the last unit (j = M) for each product (i = 1, 2, ... N). An algorithm is also proposed which calculates completion times of each unit (j = 1, 2, ..., M - 1) for a given product i, not recursively but independently in ZW policy. For the case of zero transfer times and zero sequence dependent set-up times, a mixed-integer linear programming (MILP) formulation is developed, and for the case of non-zero transfer times and non-zero sequence dependent set-up times, a mixed-integer nonlinear programming (MINLP) formulation is developed for optimal scheduling in ZW policy using newly proposed algorithm which calculates completion times of each product at each stage.