Optimal economic lot schedules with lost demand

Abstract

This paper presents a~new mathematical programming model for the economic lot scheduling problem (ELSP) with a common cycle for all products. The proposed model takes into account lost demand when capacity is insufficient or when set-up and inventory holding costs are too high. Two cases are modeled. In the first case, demand is fully satisfied only during a~fraction of the production cycle. In the second case, a constant fraction of demand is met throughout the entire cycle. The general non-linear model of the considered problem is reformulated as a mixed-integer quadratically constrained programming (MIQCP) model, enabling a general-purpose solver to find an optimal solution in a short time. This paper aims to encourage researchers and engineers to tackle non-convex non-linear optimization problems using modern general-purpose solvers.