Stochastic Transportation-Inventory Network Design Problem

Abstract

In this paper, we study the stochastic transportation-inventory network design problem involving one supplier and multiple retailers. Each retailer faces some uncertain demand. Due to this uncertainty, some amount of safety stock must be maintained to achieve suitable service levels. However, risk-pooling benefits may be achieved by allowing some retailers to serve as distribution centers (and therefore inventory storage locations) for other retailers. The problem is to determine which retailers should serve as distribution centers and how to allocate the other retailers to the distribution centers. Shen et al. (2000) and Daskin et al. (2001) formulated this problem as a setcovering integer-programming model. The pricing subproblem that arises from the column generation algorithm gives rise to a new class of submodular function minimization problem. They only provided efficient algorithms for two special cases, and assort to ellipsoid method to solve the general pricing problem, which run in O(n 7 log(n)) time, where n is the number of retailers. In this paper, we show that by exploiting the special structures of the pricing problem, we can solve it in O(n 2 log n) time. Our approach implicitly utilizes the fact that the set of all lines in 2-D plane has low VC-dimension. Computational results show that moderate size transportation-inventory network design problem can be solved efficiently via this approach.

A Conic Integer Programming Approach to Stochastic Joint Location-Inventory Problems

“…The solution algorithms developed in Shen et al (2003), Daskin et al (2002), andOzsen et al (2008) assume that the mean and variance of demand are uniform across retailers. Shu et al (2005) and Shen and Qi (2007) offer more flexible methods and allow the proportion of retailer mean and variance to be nonuniform. However, these latter references solve the uncapacitated facility problem with uncorrelated demands.…”

“…In these cases the objective function simplifies to one with a single nonlinear (concave) term for each retailer, which underlies the efficient solution approach. Shu et al (2005) and Shen and Qi (2007) study more general models in which these assumptions on demand are relaxed. As a result, multiple nonlinear terms appear in the objective functions.…”

“…As a result, multiple nonlinear terms appear in the objective functions. Specifically, Shu et al (2005) study a subproblem with two concave terms and Shen and Qi (2007) added a third term to accommodate routing costs. More general problems are studied by Qi and Shen (2007), Shen (2005), Shen and Daskin (2005), and Snyder et al (2007).…”

Uncertain Centralized/Decentralized Production-Distribution Planning Problem in Multi-Product Supply Chains: Fuzzy Mathematical Optimization Approaches

“…The relevant research works in this area have been reviewed through the last decade and summarized in Table1. As can be seen in Table 1, the previous researches considered demand-side uncertainty (Hegeman et al, 2014;Arikan, 2013;Vahdani et al, 2012;Lu et al, 2012;Pishvae et al, 2011;Peidro et al, 2009;Xu et al, 2008;Selma et al, 2007;Shu et al, 2005). Moreover, it can be deduced that a large number of centralized mathematical programming models have been developed to simultaneously optimize the integration of the entire SC.…”

Stochastic Programming for the Optimization of Transportation-Inventory Strategy

“…Pyke (1993) have developed a stochastic programming model that can be used to determine the optimal replenishment policies as well as the optimal dispatch strategy simultaneously. Shu (2005) dealt with the problem of minimizing the sum of transportation and inventory costs for shipping several products on a common link where the demand is a random variable. Zhang (2005) presented a model to design simple inventory policies and transportation strategies to satisfy uncertainty demands over a finite horizon, while minimizing system wide cost by taking advantage of quantity discount in the transportation cost structures.…”