Warehouse-Retailer Network Design Problem

Abstract

In this paper, we study the distribution network design problem integrating transportation and infinite horizon multiechelon inventory cost function. We consider the trade-off between inventory cost, direct shipment cost, and facility location cost in such a system. The problem is to determine how many warehouses to set up, where to locate them, how to serve the retailers using these warehouses, and to determine the optimal inventory policies for the warehouses and retailers. The objective is to minimize the total multiechelon inventory, transportation, and facility location costs. To the best of our knowledge, none of the papers in the area of distribution network design has explicitly addressed the issues of the 2-echelon inventory cost function arising from coordination of replenishment activities between the warehouses and the retailers. We structure this problem as a set-partitioning integer-programming model and solve it using column generation. The pricing subproblem that arises from the column generation algorithm gives rise to a new class of the submodular function minimization problem. We show that this pricing subproblem can be solved in O(nlog n) time, where n is the number of retailers. Computational results show that the moderate size distribution network design problem can be solved efficiently via this approach.

Cost Allocation for Joint Replenishment Models

“…This fact has been proved by Teo and Shu [23], in the context of supply chain network design, for the case when T 0 and T i are only required to be non-negative real numbers, i.e., when the power-of-two restriction is relaxed. Nonetheless, our proof and presentation follow closely that in [23].…”

Supply chain network optimization: A review of classification, models, solution techniques and future research

“…In designing any supply chain, we should be very precise about the decisions concerned with the definition of the number, size, and location of the supply chain nodes (Canel & Khumawala, 2001;Teo & Shu, 2004;Simchi-Levi et al,. 2005;Zhang et al, 2008), the amount and location of production facilities, the capacity at each facility, the assignment of each market region to one or more locations, and supplier selection for sub-assemblies, components and materials (Meixell & Gargeya, 2005;Paksoy et al, 2010).…”

A Lagrangian relaxation approach to simultaneous strategic and tactical planning in supply chain design

“…Romeijn et al (2007) propose a generic modeling framework for two-echelon supply chains that considers location-specific costs, inventory costs at warehouses and retailers, and safety stock costs; by formulating their model as a set-covering problem, they obtain an efficient solution algorithm based on column generation. Teo and Shu (2004), and Shu (2010) also consider inventory policy at the retailer level in their joint inventory-location models, which are solved using a set-covering formulation.…”

“…Much of the previous work on joint inventory-location models considered the inventory policy at warehouses, but not at retailers. However, there have been a few exceptions: You and Grossman (2010), Romeijn et al (2007), Teo and Shu (2004), and Shu (2010) all consider the inventory policy of the retailers in their joint inventory-location models. There are, however, important differences between our work and these previous works: our inventory policy uses an Economic Order Quantity (EOQ) formulation, whereas You and Grossman formulate their inventory policy in terms of guaranteed service levels; we solve our model using a Lagrangian relaxation approach, whereas Romeijn et al (2007), Teo and Shu (2004), and Shu (2010) solve their models by formulating them as set-covering problems.…”