Admission control in queue-time loop production-mixed integer programming with Lagrangian relaxation (MIPLAR)

Abstract

Flow shop scheduling problems with queue time constraints abound in many types of industries. The waiting times between consecutive steps in flow shop production with queue time constraints cannot exceed a given interval. Typically, managers use mixed integer linear programming (MILP) to schedule the process starting times of jobs in a queue. However, as the number of jobs in the system increases, the MILP-based model cannot return an optimal solution within a reasonable time because of its combinatorial nature. This paper proposes a mixed integer programming with Lagrangian relaxation (MIPLAR) method to solve the time-indexed MILP model with a separable structure for the production scheduling problem with queue time constraints. Lagrangian relaxation techniques are used to decompose the problem into job-level subproblems, which are solved by dynamic programming. The subgradient method is used to solve the Lagrangian dual problem. A 4.6-month simulation study demonstrates that the proposed MIPLAR method improves the scrap count by a percentage range from 32.1% to 83.7% across the studied 16 scenarios compared to the first-in-first-out (FIFO) rule while maintaining the same range of the throughput.