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Dynamic versus static rebates: an investigation on price, displayed stock level, and rebate-induced demand using a hybrid bat algorithm

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Abstract

Joint determination of price, rebate, investment in preservation technology, and order quantity is a complex task for retailers today. To help retailers, this paper presents an investigation on a replenishment policy for deteriorating products that focused on the choice between dynamic and static rebates under the price, displayed stock level, and rebate-induced demand. With the objective of maximizing the retailer’s profit, six different models were formulated under static and dynamic environments to identify optimal price-and-rebate pair and preservation technology investment policy. Optimal control theory was employed to determine the rate of dynamic rebate. A hybrid bat algorithm (HBA) is developed to find solutions for the proposed non-linear optimization problems. The efficiency of the proposed algorithm was verified with standard test functions. Price sensitivity, the nature of the product, and display stock elasticity were found to be decisive parameters for a retailer’s rebate strategy. Dynamic rebate on initial price of the product can significantly improve the profit of the retailer. The retailer’s investment decision was also significantly influenced by the nature of the product. Sensitivity analyses were carried out to offer managerial insights.

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Acknowledgements

The authors are grateful for the valuable comments from the associate editor and anonymous reviewers. This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning [Grant no. 2017R1A2B2007812].

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Authors and Affiliations

  1. Department of Mathematics, University of Engineering and Management, Kolkata, India

    Kartick Dey

  2. Indian Institute of Information Technology and Management (IIITM-Kerala), Thiruvananthapuram, India

    Debajyoti Chatterjee

  3. Department of Materials and Production, Aalborg University, 9220, Aalborg East, Denmark

    Subrata Saha

  4. Department of Industrial Engineering, Seoul National University, Seoul, 08826, Republic of Korea

    Ilkyeong Moon

  5. Institute for Industrial Systems Innovation, Seoul, 08826, Republic of Korea

    Ilkyeong Moon

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  1. Kartick Dey
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  2. Debajyoti Chatterjee
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  4. Ilkyeong Moon
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Corresponding author

Correspondence to Ilkyeong Moon.

Appendix A

Appendix A

Ten popular benchmark functions are used to verify the performance of the new HBA and compared with that of standard BA. The solution obtained after each trial was recorded for computing mean values. The best solution, the worst solution, and the mean values are shown in Table 7. Each algorithm was run 30 times with the maximum number of iterations set as 1000.

Table 7 Performance of HBA and BA on some standard test functions
Full size table
Fig. 3
figure 3

Convergence evolutions of objective functions

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Additionally, Fig. 3 represents the evolution at each iteration for two classical benchmark functions.

From the above Table 7 and Fig. 3, one can find that the hybridization of BA with Mantegna Algorithm and Chaotic inertia function induced accelerated convergence rate and enabled HBA to traverse a large area of objective landscape, which in turn reduced the probability of premature convergence. The Chaotic inertia function made the trajectory of virtual bats more diverse and stabilized. The proportion of global search can also be set by changing the value of switch probability depending on the optimization problem of interest. Therefore, the hybridization and modifications makes the algorithm robust.

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Dey, K., Chatterjee, D., Saha, S. et al. Dynamic versus static rebates: an investigation on price, displayed stock level, and rebate-induced demand using a hybrid bat algorithm. Ann Oper Res 279, 187–219 (2019). https://doi.org/10.1007/s10479-018-3110-x

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