A lexicographic approach to bi-objective scheduling of single-period orders in make-to-order manufacturing

This paper presents a lexicographic approach and integer programming formulations for a dual-objective, long-term production scheduling in make-to-order manufacturing environment. The problem objective is to assign single-period customer orders for various product types to planning periods to complete all the orders with minimum number of tardy orders as a primary criterion and to level the aggregate production or the total capacity utilization over a planning horizon as a secondary criterion. Each order must be completed during one planning period. The basic integer programming formulation has been strengthened by the addition of some cutting constraints derived by relating the demand on required capacity to available capacity for each subset of orders with the same due date. The approach has been applied to optimize production schedules in a flexible flowshop made up of several processing stages in series, with identical, parallel machines, and an output buffer of limited capacity for holding completed products before delivery to the customers. Numerical examples modeled after a real-world make-to-order flexible assembly line in the electronics industry are provided and some computational results are reported.