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Dynamic pricing and advertising of perishable products with inventory holding costs

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  • Schlosser, Rainer

Abstract

We examine a special class of dynamic pricing and advertising models for the sale of perishable goods, including marginal unit costs and inventory holding costs. The time horizon is assumed to be finite and we allow several model parameters to be dependent on time. For the stochastic version of the model, we derive closed-form expressions of the value function as well as of the optimal pricing and advertising policy in feedback form. Moreover, we show that for small unit shares, the model converges to a deterministic version of the problem, whose explicit solution is characterized by an overage and an underage case. We quantify the close relationship between the open-loop solution of the deterministic model and the expected evolution of optimally controlled stochastic sales processes. For both models, we derive sensitivity results. We find that in the case of positive holding costs, on average, optimal prices increase in time and advertising rates decrease. Furthermore, we analytically verify the excellent quality of optimal feedback policies of deterministic models applied in stochastic models.

Suggested Citation

  • Schlosser, Rainer, 2015. "Dynamic pricing and advertising of perishable products with inventory holding costs," Journal of Economic Dynamics and Control, Elsevier, vol. 57(C), pages 163-181.
  • Handle: RePEc:eee:dyncon:v:57:y:2015:i:c:p:163-181
    DOI: 10.1016/j.jedc.2015.05.017
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    References listed on IDEAS

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    1. Helmes, Kurt L. & Schlosser, Rainer, 2013. "Dynamic advertising and pricing with constant demand elasticities," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2814-2832.
    2. Helmes, Kurt & Schlosser, Rainer & Weber, Martin, 2013. "Optimal advertising and pricing in a class of general new-product adoption models," European Journal of Operational Research, Elsevier, vol. 229(2), pages 433-443.
    3. Kurt Helmes & Rainer Schlosser, 2015. "Oligopoly Pricing and Advertising in Isoelastic Adoption Models," Dynamic Games and Applications, Springer, vol. 5(3), pages 334-360, September.
    4. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    5. Krishnamoorthy, Anand & Prasad, Ashutosh & Sethi, Suresh P., 2010. "Optimal pricing and advertising in a durable-good duopoly," European Journal of Operational Research, Elsevier, vol. 200(2), pages 486-497, January.
    6. S. P. Sethi & A. Prasad & X. He, 2008. "Optimal Advertising and Pricing in a New-Product Adoption Model," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 351-360, November.
    7. Zhan Pang & Oded Berman & Ming Hu, 2015. "Up Then Down: Bid-Price Trends in Revenue Management," Production and Operations Management, Production and Operations Management Society, vol. 24(7), pages 1135-1147, July.
    8. Gabriel Bitran & René Caldentey, 2003. "An Overview of Pricing Models for Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 5(3), pages 203-229, August.
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    Cited by:

    1. Schlosser, Rainer, 2017. "Stochastic dynamic pricing and advertising in isoelastic oligopoly models," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1144-1155.
    2. R. Schlosser, 2021. "Scalable relaxation techniques to solve stochastic dynamic multi-product pricing problems with substitution effects," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 20(1), pages 54-65, February.
    3. Schlosser, Rainer, 2016. "Joint stochastic dynamic pricing and advertising with time-dependent demand," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 439-452.
    4. Rainer Schlosser, 2016. "Stochastic dynamic multi-product pricing with dynamic advertising and adoption effects," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 15(2), pages 153-169, April.

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    More about this item

    Keywords

    Dynamic pricing and advertising; Optimal stochastic and deterministic control; Inventory holding costs; Finite horizon; Feedback heuristics;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • M37 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Advertising

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