Distribution Network Configuration Considering Inventory Cost

Inter-city distribution network structure is considered as one of which determine the quantity of economic activities in each city. In the field of operations research, several types of optimal facility location problem and algorithms for them have been proposed. Such problems typically minimize the logistic cost with given inter-city transportation cost and facility location cost. But, when we take inventory to coop with fluctuating demands into account, facility size becomes different for each location reflecting the level of uncertainty of demand there. As observed in many developed countries, customers require more variety of commercial goods, and we must prepare more number of commercial goods. Moreover, life length of each product becomes shorter. Without highly organized management, large inventory for many products yield large risk of depreciation of commercial value as well as large cost for floor space for stocking. Considering those, inventory cost should be explicitly considered in distribution network configuration problem. There is an essential trade off between inventory cost and transportation cost: when you set smaller number of distribution center having thicker demands there, relative stock size to coop with fluctuations become small and then, we need less inventory cost. But such concentrated location pattern results longer transportation to the customers and larger transportation cost. Nozick and Turnquist(2001) formulated a two-echelon distribution network formation problem considering inventory cost at plant and distribution centers. They used optimal inventory assignment considering the expected penalty of distribution center stock-out and plant stock-out. Stock-out was considered as the situation when Poisson distributed demand exceeded stock size, and the mean demand there was given by optimal facility location model. Inventory size of distribution center alters the location cost of distribution center, therefore optimal facility location problem was refreshed and solved again. The paper proposed iterative algorithm to get optimal inventory locations. Our paper expands their model in two ways; first we admit the difference of unit location cost for distribution centers by geographical locations, and secondly, we consider different uncertainties for customer orders by departing from simple Poisson distribution. The first alternation gives new explanation for the following situations: highly dense metropolitan regions have relatively larger number of centers and smaller coverage of each center. But such propensity usually contradicts with the land price; then center location should be limited considering higher land price in metropolitan areas. Then the optimal locations cannot be prospected in straight forwardly. The second model expansion allows our model to analyze how regularity of demands affects on the network structure. Our paper applies the model to the realistic Japanese transportation network, and show which cities may possess distribution center function in the nationwide distribution network. Without the back-stock in plant level, each distribution center must prepare inventory for their demand, but such inventory sometime requires unrealistic large location cost in metropolitan area such as Tokyo. On the other hand, if distribution center can rely on the back stock in plant, the centers in metropolitan regions stand without their own inventory.