Newsvendor problem

The dynamic programming modeling concepts presented in this chapter are iUustrated with an example, which is both a multiperiod extension of the single-period newsvendor problem of Section 2 as weU as an example of a dynamic pricing problem. 

Newspapers, as human-centered product planning/design tool, 1302, 1303 Newsvendor model, 1670 Newsvendor problem, 2626-2627 Newton s method, 2530-2531, 2550-2551 New York Stock Exchange (NYSE), 277 The New York Times, 266 NOT, see Nominal group technique NHANES, see National Health and Nutrition Examination Survey III NIEHS (National Institute for Environmental Health Sciences), 1168... 

Now consider the GT version of the newsvendor problem with two retailers competing on product availability. Parlar (1988) was the first to analyze this problem, which is also one of the first articles modeling inventory management in a GT framework. It is useful to consider only the two-player version of this game because then graphical analysis and interpretations are feasible. Denote the two players by subscripts i and j, their strategies (in this case stocking quantities) by Qi, Qj and their payoffs by tt. ... 

The newsvendor problem assumes that unsatisfied demand is lost. The information available to the decision maker includes the demand D, which follows a known distribution with continuous cdf F(-), the unit production (order) cost c, the selling price p, and the salvage value per unit, v. The objective is to minimize the expected cost. It is well known that the optimal production (order) quantity, 5, can be decided easily, which should satisfy the following condition ... 

See Porteus [124] for an excellent review of research on general newsvendor problems. 

Raz and Porteus [128] study the newsvendor problem with pricing from a discrete service levels perspective. In stead of making specific distributional assumptions about the random component of demand (for example, additive, multiplicative, or some mixture of the two), they assume that demand is a... 

Usually in the newsvendor setting, it is assumed that if any inventory remains at the end of the period, one discount is used to sell it or it is disposed of. Khouja [79] extends the newsvendor problem to the case in which multiple discounts with prices under the control of the newsvendor are used to sell excess inventory. They develop two algorithms, under two different assumptions about the behavior of the decision maker, for determining the optimal number of discounts under fixed discounting cost for a given order quantity and realization of demand. Then, they identify the optimal order quantity before any demand is realized for Normal and Uniform demand distributions. They also show how to get the optimal order quantity and price for the Uniform demand case when the initial price is also a decision variable. 

They also find that the cost of learning is a consequence of censored information and shared with the consumer in the form of a higher selling price when demand uncertainty is additive. They also apply the results to three motivating examples a market research problem in which a product is introduced in a test market prior to a widespread launch a global newsvendor problem in which a seasonal product is sold in two different countries with nonoverlapping selling seasons and a minimum quantity commitment problem in which procurement resources for multiple purchases may be pooled. 

N. C. Petruzzi and M. Dada. Pricing and the newsvendor problem A review with extensions. Operations Research, A1 2) I>- 9A, 1999. 

The problem is modeled as a stationary multi-period newsvendor problem with lost sales. Assuming a coordinated policy (where double marginalization has been eliminated through centralized decision making). The decision to be optimized is the base stock level at the traditional retailers, 5rz,with i g 1,.. ., iV and at the internet store, Sj. Since each traditional retailer is... 

If the entire demand being supported by the inventory decision in question can be considered to occur in a single period, we have the "spike" case discussed earlier. This is the situation of the classic newsvendor problem. Clearly, demand for today s newspaper is concentrated solely in the current day. There will be, effectively, no demand for today s newspaper tomorrow (it is "yesterday s news," after all) or at any point in future. Therefore, if we run a newsstand, we will stock papers only to satisfy this 1-day spike in demand. If we do not buy enough papers, we will run out and lose sales— and potentially also lose the "goodwill" of those customers who wanted to buy but could not. If we buy too many papers, then we will have to return them or sell them to a recycler at the end of the day, in either case at pennies on the dollar, if we are lucky. 

A less rigorous approach to finding a (Q, R) solution would be to solve for Q and R separately. Note that z = R - MoltV dlt gives a fractile of the distribution of demand over the lead time. Thus, we could set R to achieve a desired in-stock probability, along the lines of the newsvendor problem solution discussed earlier (i.e., to accumulate a given amount of probability under the DLT distribution). In this setting, the in-stock probability is typically referred to as the cycle service level (CSL), or the expected in-stock probability in each replenishment cycle. Specifically, for normally distributed lead-time demand, DLT, we set... 

Retail inventory management is concerned with determining the amount and timing of receipts to inventory of a particular product at a retail location. Retail inventory management problems can be usefully segmented based on the ratio of the product s life cycle T to the replenishment lead-time L. If T/L < 1, then only a single receipt to inventory is possible at the start of the sales season. This is the case considered in the well-known newsvendor problem. At the other extreme, if T/L 1, then it s possible to assemble sufficient demand history to estimate the probability density function of demand and to apply one of several well-known approaches such as the Q,R model. 

The middle case, where T/L > 1 but is sufficiently small to allow only a single replenishment or a small number of replenishments, has received much less attention both in the research literature and in retail practice. As we will describe in Sect. 2, there is a small, but growing literature on limited replenishment inventory problems. Perhaps because of the lack of published analysis tools, we have found that retailers often ignore the opportunity to replenish when T/L is close to 1 and treat this case as though it were a newsvendor problem. This is unfortunate, since, as we ll show in the numeric computations in this section, planning for even a single replenishment in this case can dramatically increase profitabihty. 

Consider n retailers who order a single product from the manufacturer and sell it over a short sales season (typical of the high-tech or fashion industry). At the beginning of the season, retailer / orders from the manufacturer at a unit price, which is delivered immediately. Retailer sales z- are realized over the sales season where z, is a random variable independently drawn from F(), a twice differentiable distribution function over [0,Go) with a finite mean p and finite variance. Each unit is sold at to end consumers, and the salvage value of the units left unsold is zero. Unfilled orders are lost. Under this standard setting for the newsvendor problem, the optimal stock level Q° for retailer i is ... 

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