Optimal Inventory Policies in Perturbed Demand Models

Abstract

Investigation is continued of inventory models in which customer good will is lost when stockout occurs. Several models are formulated and optimal policies for the firm are derived conceptually (i.e., algebraic equations satisfied by the optimal parameter values are determined). Both constant and distributed demand are considered, and it is shown that the same formulation applies to both.

Note: The Newsvendor Model with Endogenous Demand

“…For example, Baker and Urban (1988), Datta and Pal (1990), Gerchak and Wang (1994), Balakrishnan et al (2000), and Wang and Gerchak (2001) develop static inventory-control models in which it is assumed that demand is an increasing function of the firm's inventory level; Eilon (1965), Caine and Plaut (1976), Ernst and Cohen (1992), and Ernst and Powell (1995) specify similar models in which the firm's service level affects the distribution of demand. Dynamic models in which future demand depends on consumers' past experience with stockouts include Schwartz (1966, 1970), Fergani (1976, and Robinson (1988). More recently, Hall and Porteus (2000) examine a dynamic duopoly model of firm inventory competition in which consumers switch suppliers at an exogenously specified rate after experiencing a stockout.…”

Competition in Price and Availability When Availability is Unobservable

“…These papers include Schwartz (1966 and1970), Balcer (1980), Fergani (1976, and Robinson (1990). Conslik and Smallwood (1979) consider competition in the probability of a breakdown when firm quality choice is unobservable, a problem which is extremely similar to competition in service rates, however they also treat price and consumer behavior as exogenous.…”

Ποσοτική Ανάλυση Της Επίδρασης Της Έλλειψης Προϊόντων Στη Διαχείριση Αποθεμάτων

“…Caine and Plaut (1976) come to the same conclusion as Hill (1976). Moreover, they obtain steady-state results for a stochastic periodic review model, similar to that studied by Schwartz (1970), where the demand is assumed to be follow an exponential distribution whose mean depends on the long run expected disappointment caused by stockouts rather than by the actual service received. They only look at a single-period problem with no cost on either ending inventory or backlogged demand.…”

“…The concept of service level-dependent demand is further developed by Schwartz (1965Schwartz ( , 1966Schwartz ( , 1970, who develops an innovative "perturbed demand" model in which there is no fixed stockout cost but stockouts directly affect future demand. Our work in Chapter 2 relies heavily on Schwartz's perturbed demand model.…”

“…When B = 9, the demand rate drops to only 1/10 of its maximum value as F' drops from 1 to 0. In a follow-up paper, Schwartz (1970) continued his investigation of the PD model by formulating three variations of this model that correspond to the three variations of the PB model discussed in the previous section. In fact, he also considered the same variations with lost sales instead of order backlogging, but we will not discuss these variations in this chapter for space considerations.…”