Newsvendor inventory decisions under risk: Analytical and evolutionary agent models

A common challenge facing all businesses today is the increasingly uncertain environments in which they operate. These uncertainties have been magnified in the context of global supply chains. Most of the Operations Research literature ignores an important component of the system, the Decision Makers (DMs) who run it. This thesis deals with inventory management under risk in the newsvendor model while incorporating the DM's risk preferences. The newsvendor is modeled as being risk averse, risk neutral or risk seeking, collectively referred to as the risk aware newsvendor.;We then look at the effect of changes in demand risk on the optimal ordering quantities of the risk aware newsvendor. Changes in demand risk are characterized by first and second order stochastic dominance shifts in the underlying random variables. With minimal assumptions on the utility functions for the newsvendor, we develop relationships between the optimal ordering quantities in two demand scenarios, one scenario being riskier than the other. The stochastic dominance approach is more generic than comparisons made using the variances of the two demand distributions. We then test the effect of first order stochastic dominance and second order stochastic dominance shifts in risk in the evolutionary agent model. In the latter, we restrict our attention to mean preserving spreads.;The performance of the evolutionary agent models is then analyzed and we provide computational support for the insufficient adjustment bias proposed in the literature. The critical role of mutation probabilities (in the evolutionary algorithms) in guaranteeing convergence to the optimal (risk neutral) order quantity is demonstrated. The insights from this analysis are then linked to the insufficient adjustment bias seen in practice. A simple penalty based mechanism is then proposed to mitigate the effect of risk preferences on inventory orders. The mechanism allows the DM to order any quantity he/she chooses but deviations from a reference/suggested quantity are penalized using a penalty function. A simple expression is provided for the risk neutral newsvendor to obtain the optimal order quantity when the cost of deviation is included in the newsvendor's objective function. We then consider the special case of setting the reference quantity to the classic risk neutral order quantity. In this setting, only the risk averse and risk seeking newsvendors will be penalized for deviations. This policy is tested and shown to be very effective in inducing optimal ordering in the evolutionary agent model.;We also investigate a common assumption on the existence of an interior point solution to the expected utility maximization problem. We provide intuitive arguments on why (and when) the assumption is reasonable. Using Monte-Carlo simulation, we obtain the distribution of expected utility for a newsvendor with a power utility function considering both risk averse and risk seeking preferences. An analysis of these distributions using stochastic dominance results is also performed.;The first model looks at a risk aware newsvendor who sells a single product over a single selling season. We consider the associated expected utility maximization problem to find the optimal order quantity. Without any assumptions on the actual form of the utility function of the newsvendor, we extend the current literature on the risk averse newsvendor (who orders less than the risk neutral newsvendor) to the risk seeking case and show that the risk seeking newsvendor orders more than the risk neutral newsvendor. We also show that these relationships are not just necessary but also sufficient. The ordering strategies of the risk aware newsvendor are then modeled as agents in an evolutionary algorithm. We develop a directional ordering rule based on the above theory which is used by all the agents. The rule uses the risk neutral solution as the anchor and allows the agent to adjust and order less or more than the risk neutral newsvendor based on its risk preference. The adjustment quantity is not pre-specified and is learnt by the agents. The emergent ordering patterns from the evolutionary agent model are compared with the analytical utility models as well as experimental results in the literature.;Finally, we study the effect of incorporating supply disruption risk in addition to the demand risk faced by the newsvendor. The newsvendor assures capacity at the supplier by reserving it at some cost. Orders are placed with the supplier and arrive, in full, if no disruption in supply occurs (or not at all otherwise). Assuming a Power utility function for the newsvendor, we provide closed form solutions for all risk preferences for the optimal order quantity. The effect of supply disruptions in the evolutionary agent model is investigated.