Modeling and Optimization of Inventory under Stochastic Demand in Uganda: A Case Study of Milk Powder Product


Kizito Paul Mubiru

Keywords: Kizito Paul Mubiru, Inventory, Economic Order Quantity, EOQ, Production Quantity, PQ, Base Stock Levels, BSL, Markov Decision Process, Echelon Inventory System, Diary, Milk Powder, Stochastic Demand
Issue Date: 24 February 2016
Abstract: In today’s fast-paced and competitive market place, organizations need every edge available to them to ensure success in planning and managing inventories of items with demand uncertainty. In an effort to establish optimal production-inventory levels that can sustain random demand of items, cost-effective methods in determining the optimal Economic Production Quantity (EPQ), Economic Order Quantity (EOQ) and Base Stock Levels (BSL) of cycle inventories in a stochastic demand environment are paramount. In this research, mathematical models were developed that optimize economic production quantity, economic order quantity, base stock levels, production lot sizing decisions, ordering policies, production costs, inventory costs and sales revenue given a periodic review inventory system under stochastic demand with particular focus on milk powder product in Uganda.

Adopting a Markov decision process approach, the states of a Markov chain represent possible states of demand for milk powder product. Using weekly equal intervals, the decisions of whether or not to produce additional units or whether or not to order additional units were made using discrete time Markov chains and dynamic programming over a finite period planning horizon. The developed models were tested to establish the optimal economic production quantity, economic order quantity, base stock levels, production lot sizing decisions and ordering policies as well as the corresponding production and inventory costs of milk powder product. Extensions of the study were made to optimize base stock levels of a two-echelon inventory system so that in the long run average system costs are minimized for a given state of demand. The study examined stationary demand cases where theoretical and practical perspectives were put into consideration.

Empirical data was collected from the milk powder plant and three supermarkets within Kampala .The data represented customer transactions and sales of milk powder product on a weekly basis. The data collected was then analyzed and tested using the developed models. Results showed the existence of an optimal state-dependent production lot sizing decision, economic production quantity, base stock level and production-inventory costs at the production plant. Optimality conditions for the economic order quantity, ordering policies, inventory costs and sales revenue were similarly state-dependent at the respective supermarkets. The models can lead to a more profitable dairy sector through optimal production and inventory of milk powder in order to contribute to economic development and nutritional standards in Uganda.

Presented at: Own PhD Defense


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Modeling and Optimization of Inventory under Stochastic Demand in Uganda