Abstract
In this paper, a new mathematical model is developed to optimize replenishment policies and inventory costs of a two-echelon supply chain system of kerosene product under demand uncertainty. The system consists of a fuel depot at the upper echelon and four petrol stations at the lower echelon. The petrol stations face stochastic stationary demand where inventory replenishment periods are uniformly fixed over the echelons. Adopting a Markov decision process approach, the states of a Markov chain represent possible states of demand for the inventory item. The replenishment cost, holding cost and shortage costs are combined with demand and inventory positions in order to generate the inventory cost matrix over the echelons. The matrix represents the long run measure of performance for the decision problem. The objective is to determine in each echelon of the planning horizon an optimal replenishment policy so that the long run inventory costs are minimized for a given state of demand. Using weekly equal intervals, the decisions of when to replenish additional units are made using dynamic programming over a finite period planning horizon. A numerical example demonstrates the existence of an optimal state-dependent replenishment policy and inventory costs over the echelons. DOI:10.12660/joscmv8n2p67-76URL: http://dx.doi.org/10.12660/joscmv8n2p67-76
Highlights
The goal of a supply chain network is to procure raw materials, transform them into intermediate goods and final products
The stochastic Two-Echelon supply chain Model incorporates demand uncertainty in determining optimal replenishment decisions where “shortage” or “no shortage” conditions are catered for when calculating total inventory costs over the echelons
A two-echelon supply chain model with stochastic demand was presented in this paper
Summary
The goal of a supply chain network is to procure raw materials, transform them into intermediate goods and final products. To cope with current turbulent market demands, there is still need to adopt coordinated inventory control across supply chain facilities by establishing optimal replenishment policies in a stochastic demand environment. Large industries continually strive to optimize replenishment policies of products in multi-echelon inventory systems. This is a considerable challenge when the demand for manufactured items follows a stochastic trend. One major challenge is usually encountered: determining the most desirable period during which to replenish additional units of the item in question given a periodic review production-inventory system when demand is uncertain. At the beginning of each period, a major decision has to be made, namely whether to replenish additional units of fuel or not to replenish and keep fuel at prevailing inventory position in order to sustain demand at a given echelon.
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