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Quality choice and capacity rationing in advance selling

The first author is supported by National Natural Science Foundation of China (NSFC) grants 71771106 and the second author is supported by Postgraduate Research & Practice Innovation Program of Jiangsu Province grants KYCX19_1649
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  • This study considers a seller who sells a single product to strategic consumers sensitive to both price and quality over two periods: advance and spot. Customers' valuations are uncertain in the first period and revealed over time. The seller's decisions include whether to offer the product and, if so, the quality of the product, the prices in both periods, and whether to ration capacity in the advance period. The analysis is separated into two cases: unlimited capacity and limited capacity. The first case acts as a benchmark for the latter. It is found that in each case, the seller's decisions on product offering and quality choice are fully determined by a single parameter, namely the cost coefficient of quality. The optimal rationing policy and its determinants, however, are distinct in these different settings. And the optimal rationing policy is contingent on whether the high- or low-quality product is offered. Further, our numerical studies show that the seller can benefit from capacity rationing and flexibility on quality choice. Specifically, the value of rationing is not evident, whereas the value of flexibility on quality choice is considerably significant.

    Mathematics Subject Classification: Primary: 90B50; Secondary: 49L60.


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  • Figure 1.  Sequence of events

    Figure 2.  Value of rationing

    Figure 3.  Value of flexibility on quality choice

    Figure 4.  Value of flexibility on quality choice when capacity rationing is prohibited

    Figure A1.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ T\leq\frac{N}{3} $

    Figure A2.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{3}<T\leq\frac{N}{2} $ and $ N_{1}\leq\frac{3T-N}{2} $

    Figure A3.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{3}<T\leq\frac{N}{2} $ and $ \frac{3T-N}{2}<N_{1}\leq\overline{N}_{1} $

    Figure A4.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{3}<T\leq\frac{N}{2} $ and $ N_{1}>\overline{N}_{1} $

    Figure A5.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{2}<T\leq\overline{T} $ and $ N_{1}\leq\frac{3T-N}{2} $

    Figure A6.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{2}<T\leq\overline{T} $ and $ \frac{3T-N}{2}<N_{1}\leq\overline{N}_{1} $

    Figure A7.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ \frac{N}{2}<T\leq\overline{T} $ and $ N_{1}>\overline{N}_{1} $

    Figure A8.  Sketch of $ \Pi_{q}^{C}(S_{q}) $ for $ T>\overline{T} $

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