The interplay between learning effect and order acceptance in production planning

Abstract

Learning takes time and hence its effects should be considered in short-term production planning (i.e., scheduling). This is especially true when human involvement is high and the shop floor experiences changes in workflow, workforce, or technology. The Single-Machine Scheduling Problem (SMSP) with the learning effect is considered to explore this interplay. The study first proves that the shortest processing time scheduling rule can solve the mathematical problems. Pseudo-polynomial solution algorithms based on Dynamic Programming (DP) are developed to solve the SMSPs with learning effects and job rejection to minimize the maximum completion time (makespan), total completion time, and total tardiness, separately. We found that the algorithms tend to reject a small number of orders with longer production times and retain more of those with shorter production times when the objective is to minimize the average response time for the new orders. This is contrary to situations when the system’s resource utilization or the delays in fulfilling demand are sought to be minimized. The study also found that orders requiring longer processing times should be scheduled later to improve all three performance metrics with higher learning rates. Finally, we establish that all three extended problems are solvable in pseudo-polynomial time, with complexities of $O\left(n^{2}E\right)$ for makespan and total completion time minimization, and $O\left(n^{2}PE\right)$ for total tardiness minimization. The DP algorithms efficiently solve practical-sized instances, as validated by numerical experiments.