Economic lot sizing problem with inventory dependent demand
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Economic lot sizing problem with inventory dependent demand Mehmet Önal1
· Erinç Albey1
Received: 16 January 2019 / Accepted: 2 January 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We consider an economic lot sizing problem where the demand in a period is a piecewise linear and concave function of the amount of the available inventory after production in that period. We show that the problem is N P-hard even when the production capacities are time invariant, and propose a polynomial time algorithm to the case where there are no capacity restrictions on production. Keywords Economic lot-sizing · Inventory dependent demand · Complexity analysis
1 Introduction The classical economic lot sizing (ELS) problem is described in [24] as follows. There is a finite planning horizon consisting of discrete periods. The demand in each period is satisfied either by producing in that period or by the inventories carried from the previous periods. There are no capacity restrictions on the production amount. The leftover items, after the demand of the period is satisfied, are carried to the following period. The aim is to find a cost minimizing production plan where the demand of every period is satisfied on time. Several extensions of the ELS has been studied since then. To name a few, Zangwill [26] incorporated backlogging, Florian [5] worked on the ELS problem under production capacity restrictions, Love [14] and Önal et al. [19] assumed finite storage capacities, Hoesel et al. [10] worked on multi level ELS problems, and Friedman and Hoch [7] and Önal et al. [18] incorporated perishability into the ELS. All the ELS models cited above, and a great majority of the ELS models in the literature, assume that demand is known in advance. However, in many settings, decisions
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Mehmet Önal [email protected] Erinç Albey [email protected]
1
Department of Industrial Engineering, Özye˘gin University, Çekmeköy, ˙Istanbul, Turkey
123
M. Önal, E. Albey
that might affect the demand should also be integrated into the production planning decisions. That is, demand should be treated as a function of some other decision variables. There is very litte work on such ELS models. These include [13,16,17,23], which assume that the demand is a function of the price chosen for the item. With the incorporation of pricing decisions, the aim is not just to minimize costs but to maximize profits. In this paper, we contribute to this slightly explored line of research. We consider an ELS problem where the demand is not known in advance, but is a function of the amount of items in the stock. It is a well known phenomenon that, for many product categories, increased stock levels are associated with increased customer demand. Some retail managers refer to this as the “Stack them high, let them fly” phenomenon. Koschat [12] present empirical evidence from magazine retailing that demand varies with inventory. Similarly Chuang and Zhao [4] provide evidence from the automotive dealerships that high inventory l
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