Early/tardy scheduling with sequence dependent setups on uniform parallel machines

Abstract

We consider the problem of scheduling N jobs on M parallel machines that operate at different speeds (known as uniform parallel machines), to minimize the sum of earliness and tardiness costs. Jobs are assumed to arrive in a dynamic albeit deterministic manner, and have nonidentical due dates. Violations of due dates result in earliness or tardiness penalties that may be different for different jobs. Setup times are job-sequence dependent and may be different on different machines based on the characteristics of the machines. For this problem, we present a mixed integer formulation that has substantially fewer zero–one variables than typical formulations for scheduling problems of this type. We present our computational experience in using this model to solve small sized problems, and discuss solution approaches for solving larger problems. Scope and purpose In JIT environments, firms face the need to complete jobs as close to their due dates as possible. Failure to do so would result in earliness and/or tardiness costs and the optimum schedule would seek to minimize functions of these costs. In many real-world situations, the problem is greatly complicated by the presence of disparate issues such as: (i) uniform parallel machines that are capable of processing these jobs at different speeds; (ii) sequence-dependent setup times; (iii) distinct job due dates; (iv) distinct job ready dates; and (v) distinct earliness and/or tardiness costs for each job. For this complex problem, we present a compact mathematical model and describe our computational experience in using this model to solve small sized problems.