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A unique optimization model for deterministic bundle pricing of two products with limited stock

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Abstract

In this study a firm in a monopoly environment is considered. The firm sells two types of perishable products using a commodity bundling practice. This study aims to find the optimal strategy of selling these products. We determine whether they should be offered separately or in a bundle, define their optimal prices and determine the initial amount of the bundle which should be made from components with limited stocks. A benefit-lost cost in a case that the customer segment does not find their desirable product is considered along with a shortage cost in a case that the customer segment selects a product or the bundle but there is not enough of it to satisfy all of the customer segment demands. In this study several different customer segments with different behaviors and reservation prices are assumed. The problem is solved using the Mixed-Integer Non-Linear Programming solver in LINGO software and a Genetic Algorithm. Finally, the superiority of obtained model and results are presented. This is the first study to locate optimal strategy of selling two types of perishable products using a commodity bundling practice. This study introduces a new mathematical optimization model based on previous gaps. Moreover, it covers the significant gaps of previous studies with respect to both practical and theoretical aspects.

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Acknowledgements

Funding was provided by University of Tehran (Grant No. 8106013/1/17).

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Authors and Affiliations

  1. School of Industrial and Systems Engineering, Center of Excellence for Intelligent Based Experimental Mechanic and Department of Engineering Optimization Research, College of Engineering, University of Tehran, Tehran, Iran

    Ali Azadeh & Hassan Songhori

  2. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, USA

    Nima Salehi

Authors
  1. Ali Azadeh
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  2. Hassan Songhori
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  3. Nima Salehi
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Correspondence to Ali Azadeh.

Additional information

Motivation and significant This study introduces a new mathematical optimization model based on the following significant considerations. Moreover, it covers the significant gaps of previous studies as discussed next. In this paper, the bundling problem is taken into account in a case that the number of products 1 and 2 are limited. In this case, the firm should make the bundle using limited stocks. They should determine amount of the bundle which is made by these products. Also, in this study, it is assumed that there are different customer segments with different reservation prices for each product. Therefore, when there are not enough products or bundles to satisfy all the customer demands, we have a shortage cost. Another type of cost that is considered in the model is benefit-lost cost. When the customer segment does not find its desirable product, the benefit obtained from purchasing these products is lost (benefit-lost cost).

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Azadeh, A., Songhori, H. & Salehi, N. A unique optimization model for deterministic bundle pricing of two products with limited stock. Int J Syst Assur Eng Manag 8 (Suppl 2), 1154–1160 (2017). https://doi.org/10.1007/s13198-017-0581-0

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  • DOI: https://doi.org/10.1007/s13198-017-0581-0

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