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Joint optimal pricing and inventory management policy and its sensitivity analysis for perishable products: Lost sale case

  • * Corresponding author: Zheng Wang

    * Corresponding author: Zheng Wang 

This work is supported by National Natural Science Foundation of China under grant 61673109

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  • In the real world, the demand cannot be depicted exactly because of customer behavior cannot be forecasted without error. In this paper, we study the effect of the error of the estimated price-demand parameters by analyzing the sensitivity of the optimal joint pricing and ordering policy on the price-demand parameters based on a periodic-review, multi-period and lost sale inventory model for perishable products with constant quantity decay rate and price-sensitive demand. Firstly, we formulate the joint pricing and inventory control problem and find the optimal ordering quantity and the optimal price for deterministic price-demand function. The optimal solutions show that the retailer tends to set a lower price in early periods of each ordering cycle in order to reduce the inventory holding costs. Furthermore, the sensitivity of the optimal joint pricing and inventory control system with respect to the price-demand parameters is examined analytically and evaluated numerically. The sensitivity analysis reveals that compared to the optimal ordering quantity, the optimal prices are less sensitive in the demand-price parameters. Finally, according to the findings of the sensitivity analysis, a heuristic method of regulating the estimated demand-price parameters is employed to improve the average profit. 185 words.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

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  • Figure 1.  Proof of the zero-inventory property

    Figure 2.  Repetitive ordering cycles

    Figure 3.  Change of the optimal ordering cycle

    Figure 4.  Sensitivity coefficient of the optimal ordering quantity

    Figure 5.  Sensitivity coefficient of the optimal price

    Figure 6.  Change of the optimal ordering cycle

    Figure 7.  Sensitivity coefficient of the optimal ordering quantity

    Figure 8.  Sensitivity coefficient of the optimal price

    Figure 9.  Performance of the heuristic regulation method on $ s $

    Figure 10.  Performance of the heuristic regulating method on $ \alpha $

    Table 1.  Sensitivity analysis on perishability problem

    Paper optimization Backlog or lost sale or no shortage Sensitivity analysis objective
    Qin et al.[21] Price, order No shortage Decision variables on price-demand parameter and on deterioration function
    Lu et al.[18] Price, order, quality keeping No shortage Decision variables on all the system parameters
    Chen et al.[3] Price, order backlog Decision variables on decay rate, demand change, holding cost
     | Show Table
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    Table 2.  Sensitivity analysis on perishability problem

    $ \Delta s $ $ \Delta \alpha $ $ TP_{{\rm{new}}}^* $
    $ \Delta s >0 $ $ \Delta \alpha=0 $ $ TP_{{\rm{new}}}^* \le T{P^*} $
    $ \Delta s <0 $ $ \Delta \alpha=0 $ $ TP_{{\rm{new}}}^* \ge T{P^*} $
    $ \Delta s=0 $ $ \Delta \alpha >0 $ $ TP_{{\rm{new}}}^* \ge T{P^*} $
    $ \Delta s=0 $ $ \Delta \alpha <0 $ $ TP_{{\rm{new}}}^* \le T{P^*} $
     | Show Table
    DownLoad: CSV
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