Analysis of single and two-echelon inventory systems under disruptions in supply

Abstract

In this thesis, we analyze two different models. In the first model, we consider a two-echelon supply chain with a supplier, a manufacturer and two retailers. The manufacturer is subject to non-stationary supply disruptions. The length of a supply unavailability duration is a non-stationary geometric type random variable. In every period the manufacturer places an order with the supplier by taking into account any possible supply disruptions in the planning horizon, and subsequently makes an allocation of available stock to retailers. At the retailer level, customer demand is observed and it is assumed to be deterministic but time-dependent. The aim is to find the optimal ordering policy for the manufacturer and the optimal allocation amounts to the retailers that will minimize expected system-wide costs over a finite planning horizon. We present a dynamic programming model and structural properties of the optimal ordering policy under a simplified allocation rule. The structural results that we obtain lead to an easy computational procedure for the optimal system-wide orderup- to level. We also discuss the effectiveness of the allocation rule through a numerical study. In the second model, the environment is very similar to the first model, except we have a single echelon system. In the second model, we have a supplier and a manufacturer. The manufacturer is subject to stochastic demand and stochastic supplier availability. The supplier’s availability structure is same as the supplier availability structure in the first model. Demand uncertainty is also modeled similar to supplier availability. Demand is either a fixed amount represented by d, or zero, with respective probabilities. On the contrary to the first model, there is no retailer in this model and demand is observed at manufacturer. The objective is to minimize expected holding and backlogging costs over a finite planning horizon considering stochastic demand amounts under the supply uncertainty. We present a dynamic programming model and a formula which explicitly determines the order-up-to levels. An algorithm is developed to compute the optimal inventory levels over the planning horizon using the formula. We also present a numerical study for the model..