Production planning with multiple production lines: Forward algorithm and insights on process design for volume flexibility

This paper considers the production planning problem of a firm that produces a single product using a process that has multiple production lines (or machines) in parallel, each with a finite production capacity. Specifically, the firm has m parallel production lines, each with capacity of P units per period. If needed, the firm can adjust the production rate in a period by adjusting the number of lines it operates in the period. The firm faces time-varying demands. The objective is to find a production plan that meets the demands over the problem horizon and minimizes the sum of setup, holding and variable production costs. The paper develops an efficient forward dynamic programming algorithm and uses it to develop managerial insights on the effect of process design on volume flexibility, which is defined as the ability to be operated profitably at different output levels. Some forecast horizon results are also developed. The firm can use the results in the paper to optimize the process design for the demand it faces.