A genetic algorithm for the vendor-managed inventory routing problem with lost sales

Highlights

• A genetic algorithm is proposed for vendor-managed inventory routing problems with lost sales.

• The proposed genetic algorithm demonstrates the excellent performance.

• The solution quality of the proposed genetic algorithm is affected by some problem parameters.

• The resource capacity should be considered as decision variables to optimize the system operation.

Abstract

This paper proposes a genetic algorithm (GA) for the inventory routing problem with lost sales under a vendor-managed inventory strategy in a two-echelon supply chain comprised of a single manufacturer and multiple retailers. The proposed GA is inspired by the solving mechanism of CPLEX for the optimization model of the problem. The proposed GA determines replenishment times and quantities and vehicle routes in a decoupled manner, while maximizing supply chain profits. The proposed GA is compared with the optimization model with respect to the effectiveness and efficiency in various test problems. The proposed GA finds solutions in a short computational time that are very close to those obtained with the optimization model for small problems and solutions that are within 3.2% of those for large problems. Furthermore, sensitivity analysis is conducted to investigate the effects of several problem parameters on the performance of the proposed GA and total profits.

Introduction

Vendors and their customers often adopt vendor-managed inventory (VMI) strategies to improve the profitability of the vendors’ brand for both customers and vendors through collaboration. With VMI, vendors are responsible for all decisions regarding customer inventory management. As a result, control of replenishment decisions resides with the vendors instead of their customers. In many cases of VMI, the inventory is owned by the vendor until it is sold by the customer. Accordingly, vendors require their customers to supply them with information about product sales, current inventory levels, dates for receipt of goods, and dead stock and returns through an EDI or other electronic network, so that the information is up-to-date at all times. With VMI, the vendors are able to send the products to the customers at an earlier stage and will be charged for inventory carrying costs. On the other hand, the increased costs are mitigated by a reduced bullwhip effect, increased sales, freight consolidation, and aggregate production planning. This leads to higher levels of production efficiency and much lower transportation costs, which constitute a significant portion of overall supply chain costs. Many researchers have studied the potential benefits of the VMI strategy according to various aspects of supply chain management (Chen and Wei, 2012, Choudhary et al., 2014, Savaşaneril and Erkip, 2010, Zachariassen et al., 2014).

In the existing literature, the class of problems in which inventory management and vehicle routing problems are integrated into a unified framework is often referred to as the inventory routing problem (IRP). Effective implementation of the IRP is critical, especially in a VMI environment. Some surveys on the IRP are shown in the works of Bertazzi, Savelsbergh, and Speranza (2008), and Coelho, Cordeau, and Laporte (2012). Several real-world applications of the IRP are surveyed in the work of Coelho et al. (2012). Although the IRP has been extensively researched over the last two decades, some important characteristics inherent to VMI are rarely treated in a complex way in the literature. First, under VMI, intentional lost sales are often allowed (as opposed to full backorders for customer stock-outs) when the supply chain cost per product exceeds the unit profit in the supply chains of grocery or consumer products. Therefore, it is more sensible to set a goal of maximizing supply chain profits through the collaboration of customers and vendors when lost sales are allowed, rather than a goal of minimizing total costs. It is notable that the problem of establishing a network of agents (or retailers) under VMI, which is an extended version of the IRP, sets a goal that maximizes total profits while allowing lost sales (Rabbani, Baghersad, & Jafari, 2013). Second, the customer's storage space for an item is pre-assigned under VMI. Thus, the delivery quantity from the vendor cannot exceed the available storage space. Third, under VMI, customers are likely to set due times (e.g., store opening times) or time windows for delivery based on their operational preferences.

Considering the characteristics synthetically, we define the vendor-managed inventory routing problem with lost sales (VMIRPL) as follows. The VMIRPL determines optimal replenishment times and quantities for customers and vehicle routes that maximize supply chain profits during a planning horizon in a VMI environment, while allowing lost sales at customers and while restricting transportation capacity, storage space at customers, and due times for delivery. Several costs are incurred in the VMIRPL. Vendors incur production costs, inventory carrying costs (their own and the inventory carrying costs of customers), and fixed and variable transportation costs. Customers incur purchasing and space costs. Central to the VMIRPL is trade-off analysis, which, in turn, leads to a concept of weighing total costs against the satisfaction of demand at customers. For instance, transportation costs due to consolidated replenishments and the direct effects on inventory carrying costs at customers are in conflict with each other. Profit loss and supply chain costs due to lost sales are also in conflict. In a VMI environment, the problem becomes one of balancing the combined conflicting costs so that they are collectively optimized.

This paper proposes a genetic algorithm (GA) for the VMIRPL in a two-echelon supply chain comprised of a single manufacturer and multiple retailers. The proposed GA is compared with the optimization model with respect to effectiveness and efficiency in various test problems. Furthermore, sensitivity analysis is conducted to investigate the effects of several problem parameters on the performance of the proposed GA and total profits. Evolutionary algorithms are a versatile and effective approach to finding solutions to problems with high levels of complexity or interdependency (Simon, 2013). In recent years, GAs, the most popular type of evolutionary algorithms, have been advocated for solving IRPs.

The remainder of this paper is organized as follows. Section 2 reviews previous studies on IRPs. Section 3 describes and presents a mathematical formulation for the VMIRPL. Section 4 proposes a new GA, which includes an improvement process for the VMIRPL. Section 5 conducts computational experiments and sensitivity analysis to evaluate the performance of the proposed GA. Finally, Section 6 draws conclusions and presents topics for future research.