Abstract
A distribution-free newsboy problem (DFNP) has been launched for a vendor to decide a product’s stock quantity in a single-period inventory system to sustain its least maximum-expected profits when combating fierce and diverse market circumstances. Nowadays, impacts of transportation cost on determination of optimal inventory quantity have become attentive, where its influence on the DFNP has not been fully investigated. By borrowing an economic theory from transportation disciplines, in this paper the DFNP is tackled in consideration of the transportation cost formulated as a function of shipping quantity and modeled as a nonlinear regression form from UPS’s on-site shipping-rate data. An optimal solution of the order quantity is computed on the basis of Newton’s approach to ameliorating its complexity of computation. As a result of comparative studies, lower bounds of the maximal expected profit of our proposed methodologies surpass those of existing work. Finally, we extend the analysis to several practical inventory cases including fixed ordering cost, random yield, and a multiproduct condition.
Highlights
A newsboy problem has been initiated to determine the stock quantity of a product in a single-period inventory system when the product whose demand is stochastic has a single chance of procurement prior to the beginning of selling period
Economic trade-off for the optimal transportation cost lies between provided service level and shipped quantity [17]
In views of the impact of transportation cost on the distribution-free newsboy problem (DFNP) as well as the gains elicited from our proposed policies, we extend contemplation of the transportation cost into several practical inventory cases such as fixed ordering cost, random yield, and a multiproduct case
Summary
A newsboy (newsvendor) problem has been initiated to determine the stock quantity of a product in a single-period inventory system when the product whose demand is stochastic has a single chance of procurement prior to the beginning of selling period. Traditional models for the newsboy problem assume that a single vendor encounters the demand of a product complying with a particular probability distribution function with known parameters, such as a normal, SchmeiserDeutsch, beta, gamma, or Weibull distribution [1] With this assumption, several recent studies have to a certain extent succeeded in resolution of certain practical problems. We borrowed the idea from the transportation management models [23] that the transportation cost is modeled as a function of delivery quantities; as a result of the computational studies, our proposed optimal-ordering rules increase lower bound of maximized expected profit as much as 4% on average, as opposed to the optimal policies recommended by Gallego and Moon [7]. In order to determine and implement the optimal policies in practice, we perform comprehensive sensitivity analyses for the vital parameters, such as the demand mean and variance, unit cost of product, and transportation cost.
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