Inventory allocation and customer travelling problem in spatial duopoly

Abstract

The paper is a theoretical study about connecting inventory allocation and market area for the goods, defined by customers’ travelling decisions, influenced by the expected shortages of goods. In the paper “Inventories in Spatial Models” (Bogataj, International Journal of Production Economics 45 (1996) 337–342 [2]) we have emphasized the need for connecting inventory and location analysis. This problem was studied further by H.J. Girlich in his paper “On the Metric Transportation Problems and Their Solution” (Girlich, Lecture Notes of the International Postgraduate Summer School, vol. 2, 1995, pp. 13–24), which gives us proper foundations for our present research. The study is influenced by Grubbström and Molinder’s work on MRP optimization (for details see Grubbström, Management Science 13(7) (1967) 558–567; Grubbström, The Mathematical Scientist 16 (1991) 118–129; Grubbström, International Journal of Production Economics, forthcoming; Grubbström, International Encyclopaedia of Business and Management, 1996; Grubbström and Molinder, Proceedings of the Eight International Working Seminar on Production Economics, 1994; Grubbström and Molinder, International Journal of Production Economics 35 (1994) 299–31 [6–11]). The annuity stream approach has been applied in the environment of spatial duopoly, where the optimal ordering policy depends on the interaction between the prices and shortages of goods in the studied duopolies. Customer travelling problem (CTP) is defined, which determines the market area for allocated inventories.