Inventory Replenishment Costs Research Articles

Location and two-echelon inventory network design with economies and diseconomies of scale in facility operating costs

Most existing facility location and network design models assume the facility cost as either a fixed cost term or a linear/concave function of the volume of demand assigned to a facility. In particular, a concave cost function implies decreasing marginal cost and exhibits economies of scale. However, when the assigned demand volume exceeds a certain level, diseconomies of scale may occur due to facility congestions, overuse of resources, increasing operational complexity, and so on, leading to a convex cost function with increasing marginal cost. This paper studies a warehouse–retailer network design problem, which simultaneously optimizes the warehouse locations, the warehouse–retailer assignment, and the multi-echelon inventory replenishment policy to minimize the total cost, including the warehouse location and operating costs, the inventory replenishment cost, and the transportation cost. In this paper, the warehouse operating cost is defined as a general function of the volume of demand assigned to a warehouse, which could be concave first due to economies of scale and then convex due to diseconomies of scale. We formulate this problem as a set-covering model and propose a column generation algorithm to solve its linear relaxation. The pricing problem of the column generation process, although formulated as a nonlinear mixed integer program, has nice structural properties and can be solved efficiently by a branch-and-bound method. To validate the effectiveness and efficiency of the proposed column generation algorithm, we conduct numerical studies based on randomly generated instances. Numerical results also demonstrate the impact of economies and diseconomies of scale on network design decisions and warehouse operating cost.

Heuristic algorithms for inventory replenishment with perishable products and multiple transportation modes

ABSTRACTThis study extends classic economic lot-sizing problems to permit the replenishment of age-dependent perishable inventories via multiple transportation modes. Inventory replenishment costs include a multiple-setup cost function that considers order setup, purchase, and cargo container costs. The objective is to identify the timing of orders, order quantities, and a choice from among I transportation modes that minimizes the cost of replenishing perishable inventories during a planning horizon of length T. We present a mixed-integer programming formulation of this problem and characterize properties of optimal solutions. We propose a primal-dual heuristic algorithm that runs in O(IT2). In addition, we provide heuristic algorithms for two special cases of the problem involving one or two replenishment modes. For the single replenishment mode problem, we propose (i) a dynamic programming algorithm that explores solutions that satisfy the Zero Inventory Ordering Policy and runs in O(T2) and (ii) a dynamic programming algorithm that explores solutions that satisfy the Less-than-Truckload first positioning property and runs in O(T3). For the two replenishment mode problem, we present a knapsack-based algorithm that identifies the minimum number of cargo containers required to meet demand. The running time of this algorithm is O(T2). We evaluate the quality of the solutions generated by these different approaches via extensive numerical analyses.

A Joint Replenishment Inventory-Location Model

We introduce a distribution center location model that incorporates joint replenishment inventory costs at the distribution centers. The model is formulated as a Fixed Charge Location Problem (FCLP) which objectively considers not only location specific costs but also inventory replenishment costs. In the joint replenishment problem we consider a single item and several distribution centers in different locations and apply a similar algorithm to the one used to solve the multi-item problem. We propose a Greedy Randomized Adaptive Search Procedure (GRASP) to solve the problem.

Inventory Cost Effect of Consolidating Several One-Warehouse Multiretailer Systems

Consolidation of warehouses is a new trend in global logistics management, and the reduction in order processing and inventory costs is often cited as one of the main motivations. In this note we show that when retailers face constant demand rates and their ordering costs are independent of the warehouse that services them, consolidated systems are rarely suboptimal and always lead to close-to-optimal inventory replenishment costs. In particular, we prove that using two (one) properly selected warehouses, the systemwide inventory replenishment cost is in the worst case at most 2% (14.75%) more than the optimal.

Warehouse sizing to minimize inventory and storage costs

AbstractThis paper considers a warehouse sizing problem whose objective is to minimize the total cost of ordering, holding, and warehousing of inventory. Unlike typical economic lot sizing models, the warehousing cost structure examined here is not the simple unit rate type, but rather a more realistic step function of the warehouse space to be acquired. In the cases when only one type of stock‐keeping unit (SKU) is warehoused, or when multiple SKUs are warehoused, but, with separable inventory costs, closed form solutions are obtained for the optimal warehouse size. For the case of multi‐SKUs with joint inventory replenishment cost, a heuristic with a provable performance bound of 94% is provided. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 299–312, 2001