(313e) Joint Optimization of Fair Facility Allocation and Robust Inventory Management for Perishable Consumer Products

Perishable goods, such as food, cosmetics, and household chemicals (e.g., detergents and pesticides), constitute a large portion of consumer products. The perishable nature of these products puts stringent requirements on their supply chain network design and inventory management, both of which are subject to various uncertainties in product transportation and demand. This requires both supply chain network design and inventory management to be simultaneously considered in an optimization framework. In this study, we explore the joint optimization of facility allocation and inventory management under uncertainty for perishable products. Given locations of manufacturing facilities, our goal is to identify the optimal locations of distribution centers, their serving customers, as well as each distribution center’s inventory management strategy to meet the customers’ demands that are subject to uncertainties.

Our two-stage mixed-integer linear joint optimization model formulation consists of the following key factors. First, we incorporate fairness measures based on the Jain’s index in facility allocation, and study how a disadvantaged community could benefit from having a distribution center allocated to it. Second, we explicitly account for shelf-life considerations for perishable products to minimize spoilage waste and ensure product freshness upon delivery. Specifically, we enforce the inventory to follow the FIFO (First-In, First-Out) policy, which leads to a set of bilinear constraints. We present a strategy to linearize these FIFO-related constraints and show that the reformulated model retains the optimal solution. Third, to navigate the complexities of demand uncertainty in real-world applications, we present a robust optimization formulation to ensure operational resilience. Specifically, for each time period and each location, our model uses an affine demand function to accommodate every possible scenario. Overall, our joint optimization model identifies optimal locations for opening distribution centers and to optimize inventory management even in the worst-case scenarios.

Next, we explore various solution strategies, including decomposition techniques, to solve the joint optimization problem. Specifically, we attempt to apply Bender’s decomposition by solving the facility allocation problem as the master problem and then address robust inventory management as the sub-problem, integrating the solutions through Bender’s cuts. A second strategy involves reformulating the facility allocation into a set-covering problem and subsequently solving its linear relaxation using an efficient column generation algorithm. We compare the computational efficiency of these decomposition algorithms in a range of test cases. We also illustrate the need for decomposition by comparing the computational performance of these algorithms against direct solving the entire joint optimization model.