Multi-objective optimization of collation delay and makespan in mail-order pharmacy automated distribution system

Abstract

In this research, the collation delay (CD) and makespan minimization problem in a mail-order pharmacy automated distribution (MOPAD) system are studied. The MOPAD systems, which are integrated with pharmaceutical auto-dispenser machines, auto-packer machines, and conveyor, are utilized to fulfill the increasing prescription demand in recent years. The motivation of this research is derived from the practical deadlock problem in a MOPAD system of the central fill pharmacies (CFP). Most of the customer orders consist of multiple medications, which need to be collated together before being packaged and shipped. The CD is defined as the fulfillment completion time difference between the first and last medications within the same order, which is a critical factor of the MOPAD systems throughput. When CD is minimized, the makespan often increases. Therefore, alternative scheduling solutions are often needed to balance the CD and makespan in the MOPAD system. This paper presents the trade-off solutions between minimizing CD and the makespan. Three multi-objective genetic algorithms with a three-tuples chromosome design, including Vector Evaluated Genetic Algorithm (VEGA), Multi-Objective Genetic Algorithm (MOGA), and non-dominated sorted genetic algorithm-II (NSGA-II), are implemented and compared under various system settings. Compared to the current implemented longest processing time (LPT) heuristic, three multi-objective genetic algorithms save the CD by 95.67 %, but only increase the makespan by 5.62 % on average. The results also show that the NSGA-II provided the best frontier.