Warehouses play a vital role in mitigating variations in supply and demand, and providing value-added services in a supply chain. However, our observation of supply chain practice reveals that warehousing decisions are not included when developing a distribution plan for the supply chain. This lack of integration has resulted in substantial variation in workload (42%-220%) at our industry partner’s warehouse costing them millions of dollars. We address this real-world challenge by investigating the interdependencies between warehouse, inventory, and transportation decisions, integrate them in a mathematical programming model, and develop managerial insights based on solutions of industry-sized problem instances. Our three contributions to research in supply chain are as follows.
First, we introduce the warehouse-inventory-transportation problem (WITP), which determines the optimal distribution strategy from vendors to customers via one or more warehouses in order to minimize total distribution costs. We model WITP as a nonlinear integer programming model considering multiple vendors, stores, products, and time-periods, and one warehouse. The model also considers worker congestion at the warehouse that could affect worker productivity. Our experiments indicate that the distribution plans obtained via the WITP, as compared to a sequential approach of solving an integrated inventory-transportation problem first and then solving the warehousing problem, result in a substantial reduction in workload variance at the warehouse, while considerably reducing the total distribution cost. These plans, however, are sensitive to the aisle configuration and technology at the warehouse, and the level and productivity of temporary workers. The state-of-the-art commercial solver could only solve small problem instances.
Second, to solve industry-sized problems, we developed a heuristic framework. This framework incorporates key features from the well-established Iterated Local Search (ILS) meta-heuristic. The heuristic implements three sets of neighborhood moves intended to improve warehousing, inventory, and transportation costs. It searches for a better solution in two alternating phases, a local search phase and a perturbation phase. We found that the solutions from the heuristic were close to optimal on small problem instances. Additionally, the heuristic was able to solve efficiently industry-sized problems with up to 500 stores and 1,000 products.
Third, we extend the WITP to model distribution decisions for supply chains that manage the flow of products with varying life cycles. The varying demand patterns of such products (e.g., basic and fashion) require different sets of decisions with different objectives; cost-efficiency for basic products and time-effectiveness for fashion products. These differences are typically handled by supply chains separately when planning for inventory and transportation. But these decisions are not necessarily separable from a warehousing perspective as both these product classes are simultaneously handled by identical resources at the warehouse (i.e., workers and technology). The extension of WITP (from single to multiple products classes) increased the complexity of the nonlinear model further when generating optimal distribution plans. We extend the ILS-based meta-heuristic framework, which we refer to as the Three Phase Heuristic (TPH), to solve industry-sized problems (e.g., 50 vendors, 200 stores, 1,000 products, and 28 time-periods). Experimental results demonstrate that TPH results in higher quality solutions with a reduction of up to 19% in total distribution costs when compared to an ad hoc policy. We also notice that the distribution plans are sensitive to the (i) duration of fashion window, (ii) product mix (basic vs. fashion), (iii) warehouse labor cost, and (iv) warehouse technology adopted for putaway and picking activities. Several managerial insights are presented to help supply chain managers in better aligning their processes to mitigate workload variation and reduce cost.
The algorithms and findings from this research are being embedded as part of an online tool, which is currently being tested in an upper level graduate class on Supply Chain, and will soon be piloted at our partnering facility.