# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020107

## Quality choice and capacity rationing in advance selling

 School of Economics and Management, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212003, China

Received  September 2019 Revised  February 2020 Published  June 2020

Fund Project: 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

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.

Citation: Taofeng Ye, Yan Zhao. Quality choice and capacity rationing in advance selling. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020107
##### References:

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##### References:
Sequence of events
Value of rationing
Value of flexibility on quality choice
Value of flexibility on quality choice when capacity rationing is prohibited
Sketch of $\Pi_{q}^{C}(S_{q})$ for $T\leq\frac{N}{3}$
Sketch of $\Pi_{q}^{C}(S_{q})$ for $\frac{N}{3}<T\leq\frac{N}{2}$ and $N_{1}\leq\frac{3T-N}{2}$
Sketch of $\Pi_{q}^{C}(S_{q})$ for $\frac{N}{3}<T\leq\frac{N}{2}$ and $\frac{3T-N}{2}<N_{1}\leq\overline{N}_{1}$
Sketch of $\Pi_{q}^{C}(S_{q})$ for $\frac{N}{3}<T\leq\frac{N}{2}$ and $N_{1}>\overline{N}_{1}$
Sketch of $\Pi_{q}^{C}(S_{q})$ for $\frac{N}{2}<T\leq\overline{T}$ and $N_{1}\leq\frac{3T-N}{2}$
Sketch of $\Pi_{q}^{C}(S_{q})$ for $\frac{N}{2}<T\leq\overline{T}$ and $\frac{3T-N}{2}<N_{1}\leq\overline{N}_{1}$
Sketch of $\Pi_{q}^{C}(S_{q})$ for $\frac{N}{2}<T\leq\overline{T}$ and $N_{1}>\overline{N}_{1}$
Sketch of $\Pi_{q}^{C}(S_{q})$ for $T>\overline{T}$
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