Inventory allocation and customer travelling problem in spatial duopoly

The paper is a theoretical study about connecting the inventory allocation and the market area for goods, defined by customers' travelling decisions and influenced by a potential shortage of the goods. In an earlier paper, we discussed the importance of connecting inventory and location analysis. Girlich also studied the problem in 1995. We have also been influenced by Grubbstrom and Molinder's work on optimisation of MRP systems. We have used an approach based on an annuity stream, assuming a spatial duopoly. Here the optimal ordering policy depends on the interaction between the prices and shortages of goods in the duopolies. We define a ‘Customer travelling problem’ which determines the market area for the inventories.