David Simchi-Levi is here at CMU today speaking on inventory systems where the decision maker is not risk neutral. David is a professor at MIT and Editor-in-Chief of Operations Research. He also runs his own company, LogicTools. I think he has given up sleep.
It is surprising that there is so little research on risk-averse decision makers in the operations management context. This clearly is a useful integration of economic theory and operations research and also involves the interface between finance and operations in a firm. In David’s work, even marketing comes into play since prices can be set in the model in order to influence demand.
Work like this often spends time in pages of greek letters with subscripts, and this paper is no different (though David is an excellent lecturer, so it was not as mind-numbing as some lectures like this).
With fixed costs for ordering, even models with risk neutral decision makers are hard to solve. Normally, the optimal decisions are set with an (s,S,p) policy: if inventory is under s, order up to S, and set price p. But suppose the inventory level is a bit above s. Should price be set high in order to decrease demand or should the order go up to S, and price be set low. This example shows that the price has a discontinuity, making it hard to get characteristics of the solution.
With risk aversion, things get more complicated. For the case where there is no fixed ordering cost, the optimal policy is a base stock policy, but the base stock level depends on the wealth level of the decision maker. With fixed costs, for exponential utility, the optimal inventory policy is independent of wealth, making things a bit easier (though it is still hard to figure out the exact policy).
One interesting aspect of this that came up in Q&A is the need to combine pricing and inventory decisions. Most companies are not aligned this way: marketing sets price, while operations sets inventory. Even in these complicated models, though, the results generally look like “Operations, do (s,S); Marketing, set price p”. This suggests very tight integration is not needed: coordination is enough.
When you add financial hedging aspects, there is still this decoupling aspect: the financial decisions do not affect the operational decisions.
It would take someone more skilled than I to explain these results to a general audience, but I find it interesting that models that contain all of marketing (price setting), operations (inventory setting) and finance (hedging) are amenable to analytical solution. This seems a very rich research area.