Article

# 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

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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.Knowledge-Based Systems 11/2013; 53(C):147-156. · 4.10 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, a multi-item multi-period inventory control model is developed for known-deterministic variable demands under limited available budget. Assuming the order quantity is more than the shortage quantity in each period, the shortage in combination of backorder and lost sale is considered. The orders are placed in batch sizes and the decision variables are assumed integer. Moreover, all unit discount for a number of products and incremental quantity discount for some other items are considered. While the objectives are to minimize both the total inventory cost and the required storage space, the model is formulated into a fuzzy multi-criteria decision making (FMCDM) framework and is shown to be a mixed integer nonlinear programming type. In order to solve the model, a multi-objective particle swarm optimization (MOPSO) approach is applied. A set of compromise solution including optimum and near optimum ones via MOPSO has been derived for some numerical illustration, where the results are compared with those obtained using a weighting approach. To assess the efficiency of the proposed MOPSO, the model is solved using multi-objective genetic algorithm (MOGA) as well. A large number of numerical examples are generated at the end, where graphical and statistical approaches show more efficiency of MOPSO compared with MOGA.The Scientific World Journal 05/2014; · 1.73 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, a multiproduct 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.Knowledge-Based Systems. 11/2013; 53:147-156.

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