A New Mathematical Model for Simultaneous Lot-sizing and Production Scheduling Problems Considering Earliness/Tardiness Penalties and Setup Costs

This paper investigated the problem of simultaneous determination of lot-sizing and production scheduling with earliness/tardiness penalties. In this problem, decisions about lot-sizing and scheduling are made so that the sum of holding, tardiness, and setup costs is minimized. There are n orders waiting to be processed on a machine. Each order has its own due date as well as tardiness and earliness cost being the same as holding cost .Each order is delivered only once. If the production is completed before or on the due date, delivery will be on the due date. Otherwise, the order will be delivered immediately after its production is completed. In spite of its wide applications, this problem has not yet been reported in the literature. A mathematical model was presented as solution methods for the problem. Two meta-heuristics, namely, Simulated Annealing and Ant Colony System meta-heuristic algorithms are presented for solving the problem. Also, lower bounds are obtained from solving the problem relaxation, and they are compared with the optimal solutions to estimate the goodness of two meta-heuristic algorithms. They are difficult benchmarks, widely used to measure the efficiency of metaheuristics with respect to both the quality of the solutions and the central. The results show that the Simulated Annealing recorded a lower solution time and average percentage deviation than did the Ant Colony System algorithm. The presented SA is capable to solve large instances that are mostly compatible with the real-world problems.