A semi-analytical solution for a newsboy problem with mid-period replenishment
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A semi-analytical solution for a newsboy problem with mid-period replenishment H-S Lau and A H-L Lau Oklahoma State University, USA This paper is an exploratory study of a very common variation of the classical newsboy problem: in addition to the supply at the beginning of the sales period, an additional replenishment opportunity exists sometime during the sales period. A basic model for the problem is presented and a semi-analytical solution procedure is developed. Numerical solutions obtained reveal certain interesting properties of the model. The paper shows that the replenishment extension makes the newsboy problem much more challenging managerially and also that it can be practically solved with signi®cant pro®t implications. Keywords: inventory; stochastic demand; newsboy problem
Introduction Single-period inventory items are prevalent in many commercial/industrial situations and so the extension of the classical newsboy problem to ®t various speci®c situations continues to be a popular research topic. This paper is an exploratory study of a very common variation of the classical newsboy problem: in addition to the supply at the beginning of the sales period, an additional replenishment opportunity exists sometime during the sales period. For example, a buyer of a seasonal good can either order a single lot from a manufacturer, or he can negotiate for the privilege of committing for a smaller initial lot now and exercising an option to replenish sometime later in the season. It is obvious that the latter arrangement is potentially more pro®table to the buyer. Also, very often midperiod replenishments are motivated not by higher pro®ts, but by the need to cope with limited resources. For example, we studied a large multiple-outlet multiple-item urban bakery/pastry ®rm; due to a combination of production, delivery, storage and display capacity limitations, many items offered by this ®rm are baked and delivered to the outlets twice (instead of once) a day from the central bakery. As will be seen, this additional-replenishment extension makes the newsboy problem much more challenging. The remainder of this section provides a brief literature review and summarises the basic results of the `classical' newsboy problem. Our newsboy problem with replenishment is formally stated in the next section, and the Correspondence: Dr H-S Lau, College of Business, Oklahoma State University, Stillwater, OK 74078, USA. E-mail: [email protected]
mathematical modeling is given in the subsequent two sections. Numerical solutions and some basic characteristics of the problem are then provided. Possible extensions are discussed in the concluding section. Brief literature review on the newsboy problem Many extensions to the simple newsboy problem have been considered in the literature. One major direction of extension is the consideration of alternative optimisation objectives, such as the capital-asset-pricing-type objectives,1,2 the objective of
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