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A loss-averse two-product ordering model with information updating in two-echelon inventory system

The Paper is supported by NNSF grants (No. 71221061, 71210003, 71431006, 71471178, 71171201, 71671189) and NCET grant( No. NCET-11-0524)

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  • This paper integrates the prospect theory with two-product ordering problem and adopts Bayesian forecasting model under Brownian motion to propose a loss-averse two-product ordering model with demand information updating in a two-echelon inventory system. We also derive all psychological perceived revenue functions for sixteen supply-demand cases as well as the expected value functions and prospect value function for the loss-averse retailer. To solve this model, a Monte Carlo algorithm is presented to estimate the high dimensional integrals with curved polyhedral integral region of unknown volume. Numerical results show that the optimal order quantities of both high-risk product and low-risk product vary across different psychological reference points, which are also affected by information updating, and the loss-averse retailer benefits considerably from information updating. All results suggest that our model provides a better description of the retailer$'$s actual ordering behavior than existing models.

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

    Citation:

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  • Figure 1.  The Time Line of the Event

    Table 1.  Updated Demand Information Values of Two products

    $\ u^{IU}_{A1}\ $ $\ \sigma^{IU2}_{A1}\ $ $\ u^{IU}_{A2}\ $ $\ \sigma^{IU2}_{A2}\ $ $\ u^{IU}_{B1}\ $ $\ \sigma^{IU2}_{B1}\ $ $\ u^{IU}_{B2}\ $ $\ \sigma^{IU2}_{B2}\ $
    200123.6940063.7220057.4440059.79
     | Show Table
    DownLoad: CSV

    Table 2.  Optimal Order Quantity with Different Psychological Reference Points and Information Updating

    $\ \pi_0\ $ $\ x^{*}_{A1}\ $ $\ x^{*}_{B1}\ $ $\ x^{*}_{A2}\ $ $\ x^{*}_{B2}\ $ $\ U^*(\mathbf{x^*})\ $
    02712814274293283.9
    10002702784264282475.8
    20002652734214271347.2
    3000270268413427643.9
    4000298280410403-235.7
    5000315285460305-785.4
    8000335290459303-1436.7
    10000333285457302-2578.8
    30000331283455301-3521.6
    50000333288454300-4076.4
     | Show Table
    DownLoad: CSV

    Table 3.  Optimal Order Quantity with Different Psychological Reference Points and No Information Updating

    $\ \pi_0\ $ $\ x^{*}_{A1}\ $ $\ x^{*}_{B1}\ $ $\ x^{*}_{A2}\ $ $\ x^{*}_{B2}\ $ $\ U^*(\mathbf{x^*})\ $
    0402315258.5853
    1000362214250.1422
    200037231623-32.983
    300039241821-421.655
    400041252020-1674.67
    500043252218-1975.9
    800045282315-3452.9
    1000043272513-3987.0
    3000041252612-5436.9
    5000043272711-6475.8
     | Show Table
    DownLoad: CSV
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