A novel fill-time window minimisation problem and adaptive parallel tabu search algorithm in mail-order pharmacy automation system

This paper presents a novel fill-time window (FTW) problem in a mail-order pharmacy automation (MOPA) system. The MOPA system uses a batch process to fulfil and distribute tens of thousands of highly customised prescription orders. It has been utilised to accommodate an increasing prescription volume and pharmacy dispensing productivity. Since the majority of prescription orders consist of multiple medications, the long medications’ waiting time in the collation process will increase the makespan or even cause a production deadlock in extreme cases. To minimise the collation time of multiple medication orders, the FTW is defined as the time difference between the first and last dispensed medications within a prescription order and the FTW problem is introduced as a flexible order scheduling problem by considering makespan as a constraint. To minimise the FTW, an integer mathematical model has been developed to find an optimal production schedule. To solve this NP-hard order scheduling problem efficiently, an adaptive parallel tabu search (APTS) algorithm is proposed. The performance of the proposed algorithm has been experimented with different system parameters. Based on the experimental results, the APTS algorithm yields 90-99%$ 90-99\% $ less FTW than LPT, and 13-33%$ 13-33\% $ less FTW than TS.