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A multiobjective model of wholesaler-retailers' problem via genetic algorithm
Nirmal Kumar Mahapatra,Asoke Kumar Bhunia,Manoranjan Maiti 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1-2
In the existing literature, most of the purchasing models were developed only for retailers problem ignoring the constraint of storage capacity of retailers shop/showroom. In this paper, we have developed a deterministic model of wholesaler-retailers’ problem of single product. The storage capacity of wholesaler’s warehouse/showroom and retailers’ showroom/shop are assumed to be finite. The items are transported from wholesaler’s warehouse to retailers’ Own Warehouse (OW) in a lot. The customer’s demand is assumed to be displayed inventory level dependent. Demands are met from OW and that spaces of OW will immediately be filled by shifting the same amount from the Rented Warehouse (RW) till the RW is empty.The time duration between selling from OW and filling up its space by new ones from RW is negligible. According to relative size of the retailers’ existing (own) warehouse capacity and the demand factors, different scenarios are identified. Our objectives are to optimize the cost functions of wholesaler and two retailers separately. To solve this problem, a real coded Genetic Algorithm (GA) with roulette wheel selection/ reproduction, whole arithmetic crossover and non-uniform mutation is developed. Finally a numerical example is presented to illustrate the results for different scenarios. To compare the results of GA, Generalised Reduced Gradient Method has been used for the problem. Also, a sensitivity analysis has been performed to study the variations of the optimal average cost with respect to the different parameters.
A MULTIOBJECTIVE MODEL OF WHOLESALER-RETAILERS' PROBLEM VIA GENETIC ALGORITHM
MAHAPATRA, NIRMAL KUMAR,BHUNIA, ASOKE KUMAR,MAITI, MANORANJAN 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1
In the existing literature, most of the purchasing models were developed only for retailers problem ignoring the constraint of storage capacity of retailers shop/showroom. In this paper, we have developed a deterministic model of wholesaler-retailers' problem of single product. The storage capacity of wholesaler's warehouse/showroom and retailers' showroom/shop are assumed to be finite. The items are transported from wholesaler's warehouse to retailers' Own Warehouse (OW) in a lot. The customer's demand is assumed to be displayed inventory level dependent. Demands are met from OW and that spaces of OW will immediately be filled by shifting the same amount from the Rented Warehouse (RW) till the RW is empty. The time duration between selling from OW and filling up its space by new ones from RW is negligible. According to relative size of the retailers' existing (own) warehouse capacity and the demand factors, different scenarios are identified. Our objectives are to optimize the cost functions of wholesaler and two retailers separately. To solve this problem, a real coded Genetic Algorithm (GA) with roulette wheel selection/reproduction, whole arithmetic crossover and non-uniform mutation is developed. Finally a numerical example is presented to illustrate the results for different scenarios. To compare the results of GA, Generalised Reduced Gradient Method has been used for the problem. Also, a sensitivity analysis has been performed to study the variations of the optimal average cost with respect to the different parameters.
Some properties of fuzzy soft groups
Soumi Manna,Nirmal Kumar Mahapatra,Shyamal Kumar Mondal 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.13 No.1
The aim of this paper is two folded. Firstly, we have defined the order of an element of a fuzzy soft group and the order of an e-approximate element of a fuzzy soft group with respect to some parameters and secondly, we have introduced the notion of a fuzzy soft cyclic group with respect to some parameters. Some theorems related to these concepts have been developed. To justify the existence of these definitions and theorems some examples have been also provided.