اولویت های ریسک و تصمیم گیری موجودی مستحکم

Recently in inventory management instead of maximizing expected profit or minimizing expected cost risk-averse objective functions have been used for determining the optimal order quantity. We use the well-known newsvendor model to determine the optimal order quantity for an objective function with two risk parameters, which can describe risk-neutral, risk-averse as well as risk-taking behaviour of the inventory manager. This approach can also be applied to situations in which the demand distribution cannot be specified uniquely. We consider robust optimization procedures—maximin and minimax regret—to determine optimal order quantities if the set of potential demand variables can be partially ordered by stochastic dominance rules.

We consider a company, typically a retailer, sourcing a product with short life cycle to stock using the framework of the newsvendor model. Traditionally, risk-neutral inventory managers are considered optimizing the expected profit or cost. But experimental findings state that the actual quantity ordered deviates from the optimal quantity derived from the classical newsvendor model. Only recently, inventory models have been analyzed with objective functions, which do not represent risk neutrality. Here, we propose a newsvendor model where the objective function is given by a mixture of expected profit and expected shortfall (conditional value at risk). It is a special case of mean deviation rules. Moreover, we consider the newsvendor model under conditions of uncertainty, i.e. the demand distribution is not known exactly; it is assumed that it belongs to a set of distribution functions. Robust inventory decisions take into account the possibility that the distribution of demand may change from the time of ordering to the start of the selling season (Gallego and Moon, 1993; Brown and Tang, 2006; Perakis and Roels, 2006). We suggest the maximin and the minimax regret approach to handle this kind of uncertainty. Optimal robust decisions minimize the maximal opportunity cost that occurs if the optimal quantity with respect to some demand distribution is not ordered. In general the optimal robust inventory decisions can only be obtained by simulation. If the demand distributions are stochastically ordered we are able to derive some analytical results. Using our objective function we show that for the risk-neutral and for the risk-averse decision maker the maximin decision is the optimal order quantity corresponding to the dominated demand distribution. Contrary, the optimal robust decision using the minimax regret approach is not uniquely determined. Thus, the main contributions of the paper are: • We propose a newsvendor model for risk-averse and risk-taking inventory managers—including also the risk-neutral case—under conditions of uncertainty with respect to the demand distribution. • Contrary to existing distribution-free newsvendor models we do not assume to know some moments of the demand distribution (e.g. expected value, variance) but state that there is a set of potential demand distributions that are stochastically ordered. • For the maximin approach and the minimax regret approach we derive analytical results concerning the robust order quantity in case of first- and second-order stochastic dominance, respectively. The paper is organized as follows. In Section 2, we shortly review the classical newsvendor model. In Section 3, we introduce our approach of the newsvendor model. The following sections deal with robust inventory decisions. After a general introduction in Section 4 optimal order quantities are determined when first- and second-order stochastic dominance prevail in 5 and 6, respectively. Section 7 presents conclusions and further developments.

Empirical and experimental findings state that observed order quantities often deviate from the optimal order quantities derived from inventory models. Therefore, in this paper we extend the classical newsvendor model to include the risk preferences of the inventory manager expressed by two parameters considering loss aversion as well as stockout aversion. Using this newsvendor model with risk preferences for a given set of demand distributions robust ordering decisions can be derived from assumptions on stochastic dominance. Robust inventory decisions also can be derived using other objective functions. For the cycle service level the maximin order quantity is View the MathML sourceyX* if X⩾1ZX⩾1Z. On the other hand, if the probability of loss is specified as objective function the salvage value is determined endogenously. Then, the maximin order quantity depends on the risk behaviour of the newsvendor. Instead of using the maximin or the minimax regret criterion a Bayesian approach can be applied where the order quantity depends on the prior distribution over the set of possible demand distributions.