Production Lot Sizes on a Single Imperfect Machine: FPTAS vs ILP models

摘要

A single machine multi-product lot-sizing and sequencing problem for a single period is studied. In this problem, n different product types are manufactured in lots. A demand for good quality items as well as a per item processing time are known for all product types. There is a sequence dependent set-up time between lots of different types. Machine yields and product lead times are uncertain because of the non-perfect production and breakdowns. The objective is to minimize the cost of the demand dissatisfaction, subject to the total processing time does not exceed a given time limit. We propose two integer linear programming (ILP) models for the NP-hard "fraction defective" case of this problem and compare effectiveness of their ILOG CPLEX realizations with the earlier developed FPTAS via a computer experiment.