Decision Models for a Two-Stage Supply Chain Planning under Uncertainty with Time-sensitive Shortages and Real Option Approach

Abstract

The primary objective of this research is to develop analytical models for typical supply chain situations to help inventory decision-makers. We also derive closed form solutions for each model and reveal several managerial insights from our models through numerical examples. Additionally, this research gives decision-makers insights on how to implement demand uncertainty and shortage into a mathematical model in a two-stage supply chain and shows them what differences these proposed analytical models make as opposed to the traditional models. First, we model customer impatience in an inventory problem with stochastic demand and time-sensitive shortages. This research explores various backorder rate functions in a single period stochastic inventory problem in an effort to characterize a diversity of customer responses to shortages. We use concepts from utility theory to formally classify customers in terms of their willingness to wait for the supplier to replenish shortages. Additionally, we introduce the notion of expected value of risk profile information (EVRPI), and then conduct additional sensitivity analyses to determine the most and least opportune conditions for distinguishing between customer risk-behaviors. Second, we optimize backorder lead-time (response time) in a two-stage system with time-dependent partial backlogging and stochastic demand. In this research, backorder cost is characterized as a function of backorder response time. We also regard backorder rate as a decreasing function of response time. We develop a representative expected cost function and closed form optimal solutions for several demand distributions. Third, we adopt an option approach to improve inventory decisions in a supply chain. First of all, we apply a real option-pricing framework (e.g., straddle) for determining order quantity under partial backlogging and uncertain demand situation. We establish an optimal condition for the required order quantity when a firm has an desirable fill rate. We develop a closed form solution for optimal order quantity to minimize the expected total cost. Finally, we implement an option contract to hedge the risk of the demand uncertainty. We show that the option contract leads to an improvement in the overall supply chain prof- its and product availability in the two-stage supply chain system. This research considers a standard news-vendor problem with price dependent stochastic demand in a single manufacturer and retailer channel. We derive closed form solutions for the appropriate option prices set by the manufacturer as an incentive for the retailer to establish optimal pricing and order quantity decisions for coordinating the channel.