Joint Replenishment Problem in Drug Inventory Management of Pharmacies under Stochastic Demand

Abstract

In today’s fast-paced and competitive market place, organizations need every edge available to them to ensure success in planning and managing inventory of items with demand uncertainty. In such an effort, cost effective methods in determining optimal replenishment policies are paramount. In this paper, a mathematical model is proposed that optimize inventory replenishment policies of a periodic review inventory system under stochastic demand; with particular focus on malaria drugs in Ugandan pharmacies. Adopting a Markov decision process approach, the states of a Markov chain represent possible states of demand for drugs that treat malaria. Using weekly equal intervals, the decisions of whether or not to replenish additional units of drugs were made using discrete time Markov chains and dynamic programming over a finite period planning horizon. Empirical data was collected from two pharmacies in Uganda. The customer transactions of drugs were taken on a weekly basis; where data collected was analyzed and tested to establish the optimal replenishment policy and inventory costs of drugs. Results from the study indicated the existence of an optimal state-dependent replenishment policy and inventory costs of drugs at the respective pharmacies.