Optimizing multi-product multi-constraint inventory control systems with stochastic replenishments

Journal of Applied Sciences 07/2008; 8(7):1228-1234. DOI: 10.3923/jas.2008.1228.1234
Source: DOAJ


Multi-periodic inventory control problems are mainly studied employing two assumptions. The first is the continuous review, where depending on the inventory level orders can happen at any time and the other is the periodic review, where orders can only happen at the beginning of each period. In this study, we relax these assumptions and assume that the periodic replenishments are stochastic in nature. Furthermore, we assume that the periods between two replenishments are independent and identically random variables. For the problem at hand, the decision variables are of integer-type and there are two kinds of space and service level constraints for each product. We develop a model of the problem in which a combination of back-order and lost-sales are considered for the shortages. Then, we show that the model is of an integer-nonlinear-programming type and in order to solve it, a search algorithm can be utilized. We employ a simulated annealing approach and provide a numerical example to demonstrate the applicability of the proposed methodology.

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Available from: Seyed Taghi Akhavan Niaki, Oct 04, 2015
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    • " Simulating annealing (Aarts & Korst 1989; Taleizadeh et al. 2008 "
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    ABSTRACT: In this study, a multi-item economic order quantity model with shortage under vendor managed inventory policy in a single vendor single buyer supply chain is developed. This model explicitly includes warehouse capacity and delivery constraints, bounds order quantity, and limits the number of pallets. Not only the demands are considered imprecise, but also resources such as available storage and total order quantity of all items can be vaguely defined in different ways. An ant colony optimization is employed to find a near-optimum solution of the fuzzy nonlinear integer-programming problem with the objective of minimizing the total cost of the supply chain. Since no benchmark is available in the literature, a genetic algorithm is developed as well to validate the result obtained. Furthermore, the applicability of the proposed methodology along with a sensitivity analysis on its parameter is shown by four numerical examples containing different numbers of items.
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    • "Meta-heuristic algorithms have been suggested to solve some of the existing developed inventory problems in the literature. Some of these algorithms are: Tabu search [18] [19] [20], genetic algorithms (GA) [21] [22] [23] [24], simulating annealing (SA) [25] [26] [27], evolutionary algorithm [28] [29], threshold accepting [30], neural networks [31], ant colony optimization [32], fuzzy simulation [33], and harmony search [34 35, 36, 37, 38]. "
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    • "Sale representatives visiting grocery stores randomly to advertize his/her goods and receiving orders is an example of this situation. In this regard, Taleizadeh et al. (2008a) considered a multi-product system in which the space and the service level for each product were constraints and a combination of backorders and lost sales was allowed. They modeled the problem and employed a simulated annealing approach to solve it. "
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    ABSTRACT: In this paper, a multi-product multi-chance constraint stochastic inventory control problem is considered, in which the time-periods between two replenishments are assumed independent and identically distributed random variables. For the problem at hand, the decision variables are of integer-type, the service-level is a chance constraint for each product, and the space limitation is another constraint of the problem. Furthermore, shortages are allowed in the forms of fuzzy random quantities of lost sale that are backordered. The developed mathematical formulation of the problem is shown to be a fuzzy random integer-nonlinear programming model. The aim is to determine the maximum level of inventory for each product such that the total profit under budget and service level constraints is maximized. In order to solve the model, a hybrid method of fuzzy simulation, stochastic simulation, and particle swarm optimization approach (Hybrid FS-SS-PSO) is used. At the end, several numerical illustrations are given to demonstrate the applicability of the proposed methodology and to compare its performances with the ones of another hybrid algorithm as a combination of fuzzy simulation, stochastic simulation, and genetic algorithm (FS-SS-GA). The results of the numerical illustrations show that FS-SS-PSO performs better than FS-SS-GA in terms of both objective functions and CPU time.
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