Supply chain games: modeling in an intertemporal framework

So far we have considered discrete-time, single- and multi-period models of competition and coordination in supply chains. In this chapter, we consider continuous-time, intertemporal supply chain models operating in a dynamic environment arising from rapidly changing market conditions including such factors as so-called “word of mouth” and “customer fatigue”; economies of scale; seasonal, fashion and holiday demand patterns; and uncertainty. Since dynamic changes may occur at any point in time, control actions can be exercised continuously. As a result, intertemporal competition between non-cooperative supply chain agents leads to differential games. In some cases, intertemporal relations can be handled by straightforwardly adjusting decision variables as though there is no long-term effect on the supply chain, i.e., by static (myopic) optimization, at each time point independently. However, in most cases, there is a long-term dynamic effect and thus the results obtained for the corresponding static models are no longer valid.

Our goal in this chapter is to illustrate the effect of dynamic conditions on supply chain performance when decisions can be taken at any time point rather than at the beginning (or end) of a certain review period as was the case with the models studied in Chapters 2 and 3. Both periodic and continuous operational review modes are discussed. When inventories and demands are not observable within a review period, continuous in-time decisions are derived based on expected values and thereby known probability distributions.