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

Yanju Zhou; Zhen Shen; Renren Ying; Xuanhua Xu

doi:10.3934/jimo.2017069

Article Contents

2018, Volume 14, Issue 2: 687-705. Doi: 10.3934/jimo.2017069

This issue Previous Article Lyapunov method for stability of descriptor second-order and high-order systems Next Article An adaptive trust region algorithm for large-residual nonsmooth least squares problems

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

1.
School of Business, Central South University, Changsha 410083, China
2.
School of Architecture Engineering, Jiangxi Modern Polytechnic College, Nanchang 330095, China

* Corresponding author: shenzhen@csu.edu.cn
* Corresponding author: shenzhen@csu.edu.cn

Received: November 30, 2015

Revised: November 30, 2016

Early access: May 2017

Published: March 2018

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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Abstract

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.

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

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Figure 1. The Time Line of the Event

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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}\ $
200	123.69	400	63.72	200	57.44	400	59.79

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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^})\ $
0	271	281	427	429	3283.9
1000	270	278	426	428	2475.8
2000	265	273	421	427	1347.2
3000	270	268	413	427	643.9
4000	298	280	410	403	-235.7
5000	315	285	460	305	-785.4
8000	335	290	459	303	-1436.7
10000	333	285	457	302	-2578.8
30000	331	283	455	301	-3521.6
50000	333	288	454	300	-4076.4

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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^})\ $
0	40	23	15	25	8.5853
1000	36	22	14	25	0.1422
2000	37	23	16	23	-32.983
3000	39	24	18	21	-421.655
4000	41	25	20	20	-1674.67
5000	43	25	22	18	-1975.9
8000	45	28	23	15	-3452.9
10000	43	27	25	13	-3987.0
30000	41	25	26	12	-5436.9
50000	43	27	27	11	-6475.8

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