Stochastic optimization for joint decision making of inventory and procurement in humanitarian relief

Highlights

• The joint decision-making of inventory and procurement is considered.

• A scenario-based two-stage stochastic programming model is proposed.

• The lead time specific discounts and variation in return price are utilized.

• CVaR is employed to reveal extreme impacts of disaster with low probability.

Abstract

This paper presents a two-stage stochastic programming model for integrating decisions on pre-disaster inventory level and post-disaster procurement quantity with supplier selection in humanitarian relief. Three features are considered in the model, including lead time discount, return price, and equity. Given the uncertainty about the disaster type and occurrence location, a scenario-based approach is applied to represent the uncertain demand. Conditional Value-at-Risk is employed to measure risk at different confidence levels. Based on a real-world example where a surge in demand was incurred by a snowstorm, earthquake, flood and typhoon in China in 2008, a case study is presented to investigate the applicability of the proposed model, and its implications are discussed based on numerical studies. The model can assist relief agencies in managing supplies for disaster response.

Introduction

A large, varied demand for basic supplies such as water, food, lighting equipment and tents may occur after a natural disaster. Relief supplies are largely collected from government-owned or other rented warehouses, and then transported to disaster-affected locations. Authorities often perform procurement decisions after a disaster if supplies turn out to be insufficient.

Disaster-induced demand is uncertain, as occurrence time, location, and the intensity of disasters are all highly unpredictable. The inventory costs of maintaining a sufficient amount of physical inventory at strategic locations in order to deal with demand uncertainty and to be able to react swiftly can thus be very high (Balcik & Beamon, 2008). When relief supplies are not available in sufficient amounts at local markets, reliance solely on post-disaster procurement cannot satisfy the needs of a rapid response, and may lead to gaps in supply.

Pre-disaster storage can provide a buffer that gives the supplier the time to produce supplies to satisfy a surge in demand. Incorporating post-disaster procurement into pre-disaster inventory decisions is beneficial for reducing the stock of relief supplies. Hence, joint decisions for determining the pre-disaster inventory level (PDIL) and the post-disaster procurement quantity (PDPQ) might be helpful in the pursuit of accelerating disaster response and savings on inventory costs. In this study, decisions regarding PDIL determine how much relief supplies should be stored before a disaster hits. Depending on PDIL and unsatisfied demand, decisions regarding PDPQ determine how much relief supplies should be procured after a disaster hits, which is limited by the production capacity of suppliers.

Commercial suppliers may have lower inventory costs than relief agencies because of their experience in matters of inventory control. Moreover, perishable supplies generally have a fixed lifetime, which may go to waste if the consumption of the supplies ends up being less than the quantity on stock. Their inventory strategy (e.g. first-in-first-out) may be beneficial for increasing the utility of relief supplies. Although relief agencies play a vital role in successful disaster response in highly uncertain disaster situations, allowing commercial suppliers to reserve and produce the most needed types of supplies may be a better choice since it saves inventory costs. In accordance with relief practice, relief agencies and suppliers all focus on long-term agreements. The main benefit to the suppliers is business that can be guaranteed over a given period of time in the future. Based on the above explanation, supplier selection is incorporated into the proposed model.

This study is conducted as follows. First, a two-stage stochastic programming model for determining the number of selected suppliers, PDIL, locations, and PDPQ with given scenarios is presented. Second, PDIL and PDPQ decisions are characterized as uncertain and equitable. The uncertain parameters (disaster types, locations, and demand) are then used to set scenarios. Finally, the value of perfect information and the stochastic solution are identified. The Conditional Value-at-Risk is employed as a risk measurement method for revealing the extreme impact of a disaster with low probability.

The paper is organized as follows. Section 2 reviews the literature. In Section 3, a two-stage stochastic programming model is formulated. Section 4 describes the case study and summarizes the results. The findings of the numerical analysis and managerial implications are outlined in Section 5. Conclusions are given in Section 6.