Dynamic programming algorithms for scheduling parallel machines with family setup times

We address the problem of scheduling jobs with family setup times on identical parallel machines to minimize total weighted flowtime. We present two dynamic programming algorithms — a backward algorithm and a forward algorithm — and we identify characteristics of problems where each algorithm is best suited. We also derive two properties that improve the computational efficiency of the algorithms.Scope and purposeWhile most production schedulers must balance conflicting goals of high system efficiency and timely completion of individual jobs, consideration of this conflict is underdeveloped in the scheduling literature. This paper examines a model that incorporates a fundamental cause of the efficiency/timeliness conflict in practice. We propose solution methodologies and properties of an optimal solution for the purpose of exposing insights that may ultimately be useful in research on more complex models.