Risk averse sourcing in a stochastic supply chain: A simulation-optimization approach

Highlights

• Presenting a novel multi-period scenario based newsvendor problem.

• Considering risk attitudes in the newsvendor model with multiple retailers.

• Presenting an agent based simulation model for the newsvendor problem.

• Developing a Monte Carlo approach to calculate the risk averse objective functions.

Abstract

A growing need for global sourcing has forced firms to manage more complex supply chains with increasing risks of supply disruptions. Multi sourcing is a common method to hedge against these risks. In the presence of demand uncertainties and supply disruptions, minimizing the downside risk is necessary. Hence, in this paper a new multi-period and scenario based supply chain model consists of a number of unreliable suppliers and a number of retailers is developed in the form of a multi-period newsvendor problem with a risk averse objective function. In the model, there are two types of retailers both faced uncertain demands: risk sensitive and risk neutral. Retailers have three choices to respond to the customer demand: a forward contract, and two option contracts include reserving a certain capacity in the secondary supplier and buying from the spot market. The problem has also developed as an agent-based system. As a solution approach in the large scale problem instances, a simulation-optimization algorithm is developed. Two kinds of heuristics are compared in order to optimize the simulation procedure: genetic algorithm and q-learning. Results showed the efficiency of the q-learning algorithm.

Introduction

In today's competitive marketplaces, firms are increasingly relying on numerous suppliers in different regions to respond to their customer needs efficiently. As these dependencies increase, uncertainties are also increase and result in a more complex supply chain design. There are many uncertainties in a supply chain but two major categories are of growing importance in supply chain management: demand uncertainty and supply uncertainty. The newsvendor problem (NVP) is a classic problem which deals with the demand uncertainty in the supply chain. The newsvendor model plays an important role in the real-life inventory problems (Abdel-Malek and Areeratchakul, 2007, Adhikary et al., 2018). Some of the researchers extended the problem to include the supply uncertainty (Dada et al., 2007, Merzifonluoglu and Feng, 2014, Ray and Jenamani, 2013). Supply disruption is one of the supply uncertainties which have a great effect on the supply chain operations. The results of a research done in UK showed an estimated 20.4 million pounds due to the supplier failing to deliver the products of the expected quality and 17.2 million pounds due to suppliers failing to deliver products on time.² Another report shows 1 million dollar loss for one in every three organizations (34% of the organizations) during 2016 due to supply chain disruption.³ Loss of productivity, increased cost of working, and damage to brand reputation are some of the most important negative impacts caused by the supply disruptions. Development of a resilient supply chain system is an approach to deal with disruptions.

Generally, there is a dilemma in balancing the financial efficiency of the supply chain on the one hand and the supply chain resiliency whose goal is risk reduction on the other hand. Demand uncertainties force the managers to focus on the financial efficiency but disruptions force them to pay attention to the resiliency of their supply chain. Neglecting the effect of the disruptions on the supply chain operations is far more expensive in the long term (Sodhi & Tang, 2012).

Adopting a proper risk management approach protects the firm against the costs of the disruptions. Increasing the inventory level, reserving capacity at different locations and having multiple suppliers are some of the common practices used to avoid disruptions (Ray & Jenamani, 2016b). But these practices increase the overall costs of the supply chain. Thus, decision making in the presence of the demand fluctuations and supply disruptions in the long term is very important.

Hence, in this paper we developed a multi-period supply chain model with multiple suppliers and multiple retailers. The basic framework of our model is based on the assumptions of Merzifonluoglu (2015b) which studied a single period NVP with unreliable suppliers. We extend the model to multi period NVP with multiple retailers. The main purpose of this study is to investigate the effects of different risk attitudes on the decisions of the retailers under demand and supply uncertainties. Integration of demand and supply uncertainties is an important extension of the stochastic inventory management problem in the recent years (Qin, Wang, Vakharia, Chen, & Seref, 2011).

In this paper we assumed that there are two types of retailers: risk sensitive and risk neutral. All retailers have to satisfy the uncertain customer demands during the multiple time units. They have to sign a forward and a capacity reservation contract at the beginning of certain points of time for a fixed period of time called contract period. Each contract period consists of a number of time units. At each time unit, uncertainties (demand and disruption) are revealed. Decisions of the retailers are divided into two stages: 1- signing a forward and capacity reservation contract (at the beginning of each contract period and before the realization of uncertainties) and 2- ordering from the reserved capacities and from the spot market (at each time unit and after the realization of uncertainties). The main difference between the risk sensitive and risk neutral retailers is their risk attitude toward the first stage decisions. A risk averse retailer prefers to sign a large forward contract to avoid any potential shortages. On the other hand, a risk taking retailer accepts more risks and signs a smaller forward contract rather than the risk averse retailer and therefore relies more on the option contracts. Decisions of the risk neutral retailers are based on the average values of the uncertainties. Details of the decision making process of retailers are explained in the Section 3.

In the Fig. 1, the chronological decision sequence of each retailer is shown.

Fig. 1 shows a schematic view of the two-stage decision of each retailer in a contract period. At the beginning of each contract period (first stage decision point) uncertainties are unknown. Retailers determine a fixed amount of order which they want to receive at each time unit (forward contract) and also reserve a fixed amount of capacity to cope with the potential shortages. The first stage decision depends on the risk attitude of the retailers. During the contract period, at each time unit, demand and disruption are revealed. Consequently, if the predetermined amount of the forward contract does not satisfy the demand, retailers use the option contracts (second stage decision points). In the case that retailer’s demand is less than the primary capacity of the supplier, remained capacity of the supplier could be used to satisfy the option contract with another retailer. Furthermore, disruptions decrease the ability of suppliers to meet the retailer’s order. This process continues in each contract period until the end of the time horizon. Details of the formulations will be discussed in the Section 3.

Remaining parts of the paper are organized as follows: in the Section 2 related works are reviewed. In the Section 3, the problem formulation is presented. In the Section 4, solution approaches are described. In the Section 5, some numerical examples are solved using the solution approaches introduced in the Section 4. Finally some concluding remarks are explained in the Section 6.