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doi: 10.3934/jimo.2021052

## Fresh produce price-setting newsvendor with bidirectional option contracts

 1 School of Business, Sichuan Agricultural University, Chengdu, 611830, China 2 School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, 611731, China

* Corresponding author: Xu Chen

Received  August 2020 Revised  December 2020 Early access  March 2021

This paper examines a newsvendor problem for fresh produce with bidirectional option contracts, in which the stochastic demand is price-dependent. The bidirectional option, which may be exercised as either a call or put option, provides the newsvendor the flexibility to increase or decrease the initial order after real demand is realized, respectively. The condition of the fresh produce may deteriorate during circulation. The optimal order and pricing decisions for the newsvendor are analytically derived with the bidirectional option and circulation loss. Comparative statics analysis show that the optimal total order quantity and optimal retail price of the newsvendor decrease with the option price but increase with the exercise price. In addition, numerical examples show that the optimal total order quantity and optimal retail price of the newsvendor increase with the circulation loss. The optimal option order quantity first decreases then increases with the exercise price. The optimal firm order quantity first increases then decreases with the circulation loss. The maximum profit of the newsvendor decreases with the option price and circulation loss but increases with the exercise price. Furthermore, the values of bidirectional option contracts are more significant when the demand uncertainty and the circulation loss become more volatile.

Citation: Chong Wang, Xu Chen. Fresh produce price-setting newsvendor with bidirectional option contracts. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021052
##### References:

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##### References:
Sequence of events and decisions
Effect of CV on the optimal decisions and maximum expected profits of the NV
Effect of CV on the optimal order quantities of the M-NV
Effect of $o$ on the M-NV's optimal decisions and maximum expected profits
Effect of $o$ on the optimal order quantities of the M-NV
Effect of $e$ on the optimal decisions and maximum expected profits of the M-NV
Effect of $e$ on the optimal order quantities of the M-NV
Effect of $\beta$ on the optimal decisions and maximum expected profits of the NVs
Effect of $\beta$ on the optimal order quantities of the M-NV
Notation
 Symbol Description $\varepsilon$ The random demand, $\varepsilon \in[A,B]$, and $E(\varepsilon)=\mu$; $f(x)$ The PDF function of $\varepsilon$; $F(x)$ The CDF function of $\varepsilon$; $D(p,\varepsilon)$ The demand function; $\beta$ The circulation loss of fresh produce, and $0<\beta<1$; $o$ The per unit charge for purchasing bidirectional options (option price); $c$ The per unit charge for firm orders (wholesale price); $e$ The per unit charge/compensation for exercising bidirectional options (exercise price); $s$ The per unit penalty cost for unfilled demand; $p$ The per unit selling price of product; $q_c$ The firm order quantity of the M-NV; $q_o$ The option order quantity of the M-NV; $q$ The total order quantity of the M-NV, note $q=q_c+q_o$; $\pi(\cdot)$ The profit of the M-NV; N Subscript, denoting the case where no bidirectional options are offered for the F-NV.
 Symbol Description $\varepsilon$ The random demand, $\varepsilon \in[A,B]$, and $E(\varepsilon)=\mu$; $f(x)$ The PDF function of $\varepsilon$; $F(x)$ The CDF function of $\varepsilon$; $D(p,\varepsilon)$ The demand function; $\beta$ The circulation loss of fresh produce, and $0<\beta<1$; $o$ The per unit charge for purchasing bidirectional options (option price); $c$ The per unit charge for firm orders (wholesale price); $e$ The per unit charge/compensation for exercising bidirectional options (exercise price); $s$ The per unit penalty cost for unfilled demand; $p$ The per unit selling price of product; $q_c$ The firm order quantity of the M-NV; $q_o$ The option order quantity of the M-NV; $q$ The total order quantity of the M-NV, note $q=q_c+q_o$; $\pi(\cdot)$ The profit of the M-NV; N Subscript, denoting the case where no bidirectional options are offered for the F-NV.
Effect of bidirectional option contracts
 Optimal total order quantity Optimal option order quantity Optimal price Maximum expected profit Fresh produce F-NV 342 — 32.80 3829 Fresh produce M-NV 403 102 33.07 4370
 Optimal total order quantity Optimal option order quantity Optimal price Maximum expected profit Fresh produce F-NV 342 — 32.80 3829 Fresh produce M-NV 403 102 33.07 4370
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