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A multiobjective model of wholesaler-retailers' problem via genetic algorithm

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Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Panskura Banamali College, Panskura R.S., 721152, Purba Medinipur, WB, India

    Nirmal Kumar Mahapatra

  2. Department of Mathematics, University of Burdwan, Burdwan, WB, India

    Asoka Kumar Bhunia

  3. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, 721102, Midnapore, WB, India

    Manoranjah Maiti

Authors
  1. Nirmal Kumar Mahapatra
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  2. Asoka Kumar Bhunia
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  3. Manoranjah Maiti
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Corresponding author

Correspondence to Nirmal Kumar Mahapatra.

Additional information

N. K. Mahapatra is a lecturer in Mathematics at Panskura Banamali College. He received his B. Sc (Honours) in 1996 and M. Sc. in 1998 from Vidyasagar University, Midnapore-721102, WB, India and doing Ph. D. at this university. His research interests focus on inventory and production management, fuzzy mathematics, interval mathematics, multi-objective optimization and mathematical programming methods.

A. K. Bhunia is a senior lecturer in Mathematics. His fields of research are inventory management and Genetic Algorithm. He has published papers in various international journals includingEuropean Journal of Operations Research, Computers & Operations Research, OBSEARCH.

M. Maiti is a Professor in the Department of Applied Mathematics with Oceanology and Computer Programming, Ex-Dean, Faculty of Science and Ex-Vice Chancellor in Vidyasagar University. Several students have obtained Ph. D. degree under his guidance. His fields of research are inventory management, elasticity and catastrophic theory. He has published papers in various international journals includingEuropean Journal of Operations Research, Journal of Operational Research Society (UK), Computers & Operations Research, Applied Mathematical Modelling, Fuzzy Mathematics, OPSEARCH etc.

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Mahapatra, N.K., Bhunia, A.K. & Maiti, M. A multiobjective model of wholesaler-retailers' problem via genetic algorithm. JAMC 19, 397–414 (2005). https://doi.org/10.1007/BF02935814

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  • DOI: https://doi.org/10.1007/BF02935814

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