The impacts of retailers' regret aversion on a random multi-period supply chain network

Yan Zhou; Chi Kin Chan; Kar Hung Wong

doi:10.3934/jimo.2021086

Article Contents

2022, Volume 18, Issue 4: 2651-2675. Doi: 10.3934/jimo.2021086

This issue Previous Article The loss-averse newsvendor problem with quantity-oriented reference point under CVaR criterion Next Article Optimal return and rebate mechanism based on demand sensitivity to reference price

The impacts of retailers' regret aversion on a random multi-period supply chain network

1.
Department of Management Science and Engineering, Qingdao University, Qingdao, Shandong 266071, China
2.
Hong Kong Statistical Society, Hong Kong, China
3.
School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa

^* Corresponding author
^* Corresponding author

Received: July 31, 2020

Revised: February 28, 2021

Published: July 2022

The first author is supported by the National Natural Science Foundation of China under grant 71901129 71771129

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Abstract

Most current studies on the equilibrium decision-makings of a supply chain network (SCN) consider only completely rational retailers who always try to maximize their expected profits under the situations that demands are random. However, many evidences show that a retailer wants to choose the decision-making involving random demand which provides him with minimum regret. In this paper, we consider the impacts of retailers' anticipated regret aversion and experiential regret aversion on the equilibrium decision-makings of a random SCN with multiple production periods. Due to the random demand, the decision-makings of retailers are influenced not only by their anticipated regret, but also by their experiential regret after they have encountered bad or good experiences during past periods. The equilibrium conditions of the model are established. A numerical example is solved to illustrate the benefit of retailers obtained by considering their regret-averse behaviors. Moreover, it is found that retailers should consider their anticipated regret aversion or experiential regret aversion according to different situations of the demand markets.

Correction: The third author's affiliation, previously "School of Computational and Applied Mathematics," is now called "School of Computer Science and Applied Mathematics."

Keywords:

Mathematics Subject Classification: Primary: 90B06, 90C33; Secondary: 90C46.

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Figure 1. The structure of SCN for $ T $ production periods

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Figure 2. The regret function $ R(\Delta v_j(t)) $ with different regret aversion coefficient $ \delta $

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Figure 3. The profit, regret and utility of all the decision makers in the rise situation of Example 1

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Figure 4. The profit, regret and utility of all the decision makers in the depleted situation of Example 1

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Table 1. The equilibrium in the rise situation of Example 1

$ i=1,2 $, $ j=1,2 $	regret-neutral	anticipated regret-averse
	$ k_j(t) $	$ k_j(t) $
	$ 0 $	$ 0.2 $	$ 0.4 $	$ 0.6 $	$ 0.8 $
$ \hat{q}_i^*(t),t=1 $	1.8633	1.6578	1.4318	1.1823	0.9097
$ \hat{q}_i^*(t),t=2 $	1.5945	1.4185	1.2248	1.0108	0.7769
$ \hat{q}_i^*(t),t=3 $	1.4934	1.3291	1.148	0.9476	0.728
$ I_i^*(t),t=1 $	0.5254	0.4672	0.4026	0.3309	0.2523
$ I_i^*(t),t=2 $	0.4356	0.3887	0.3364	0.2779	0.213
$ q_{ij}^*(t),t=1 $	0.6692	0.5938	0.5125	0.4237	0.3272
$ q_{ij}^*(t),t=2 $	0.8424	0.7469	0.6431	0.5297	0.4064
$ q_{ij}^*(t),t=3 $	0.9648	0.8571	0.7396	0.6102	0.4686
$ \rho_{j}^*(t),t=1 $	35.8181	40.1667	46.2534	55.4406	70.7135
$ \rho_{j}^*(t),t=2 $	40.228	45.183	52.1475	62.7221	80.4573
$ \rho_{j}^*(t),t=3 $	45.2266	50.7262	58.4607	70.2238	90.025

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Table 2. The equilibrium in the depleted situation of Example 1

$ i=1,2 $, $ j=1,2 $	regret-neutral	anticipated regret
	$ k_j(t) $	$ k_j(t) $
	$ 0 $	$ 0.2 $	$ 0.4 $	$ 0.6 $	$ 0.8 $
$ \hat{q}_i^*(t),t=1 $	2.1408	1.899	1.634	1.3421	1.0253
$ \hat{q}_i^*(t),t=2 $	1.6228	1.4407	1.2413	1.0214	0.7833
$ \hat{q}_i^*(t),t=3 $	1.253	1.1216	0.9755	0.813	0.6293
$ I_i^*(t),t=1 $	0.0457	0.044	0.0421	0.0395	0.0381
$ I_i^*(t),t=2 $	0	0	0	0	0.0055
$ q_{ij}^*(t),t=1 $	1.0476	0.9261	0.7939	0.6492	0.492
$ q_{ij}^*(t),t=2 $	0.8344	0.7408	0.6395	0.5282	0.4062
$ q_{ij}^*(t),t=3 $	0.6275	0.559	0.4851	0.404	0.3157
$ \rho_{j}^*(t),t=1 $	42.1631	47.4737	54.9998	66.5564	86.286
$ \rho_{j}^*(t),t=2 $	40.6374	45.5225	52.3862	62.818	80.423
$ \rho_{j}^*(t),t=3 $	37.6092	42.0773	48.2821	57.565	72.7609

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Table 3. The equilibrium decisions, profit, regret and utility in experiential regret-averse model of Example 1

$ i=1,2 $	in the rise situation			in the depleted situation
$ j=1,2 $	anticipated	experiential regret		anticipated	experiential regret
	$ \tau=0\% $	$ \tau=10\% $	$ \tau=20\% $	$ \tau=0\% $	$ \tau=10\% $	$ \tau=20\% $
$ \hat{q}_i^*(t),t=1 $	1.1823	1.111	1.0317	1.3421	1.3922	1.4385
$ \hat{q}_i^*(t),t=2 $	1.0108	0.9324	0.8457	1.0214	1.0765	1.1285
$ \hat{q}_i^*(t),t=3 $	0.9476	0.8502	0.744	0.813	0.8763	0.9326
$ I_i^*(t),t=1 $	0.3309	0.2645	0.1918	0.0395	0.0863	0.1325
$ I_i^*(t),t=2 $	0.2779	0.2087	0.135	0	0.0302	0.0597
$ q_{ij}^*(t),t=1 $	0.4237	0.4215	0.4187	0.6492	0.6506	0.6505
$ q_{ij}^*(t),t=2 $	0.5297	0.4921	0.4497	0.5282	0.564	0.5983
$ q_{ij}^*(t),t=3 $	0.6102	0.5269	0.4374	0.404	0.4509	0.4941
$ \rho_{j}^*(t),t=1 $	55.4406	56.6548	58.0501	66.5564	65.7988	65.2914
$ \rho_{j}^*(t),t=2 $	62.7221	67.4657	73.9462	62.818	59.1709	56.155
$ \rho_{j}^*(t),t=3 $	70.2238	79.7648	93.8077	57.565	52.5551	48.7155
$ \Sigma M_{i}(t) $	12.1586	10.1711	8.2357	11.8539	13.1645	14.4529
$ \Sigma E(\pi_{j}(t)) $	105.2413	110.8787	116.4356	105.4868	101.6604	97.9989
$ \Sigma E(R_j) $	48.8578	48.3116	47.7065	48.959	49.2566	49.5897
$ E(U_{j}) $	75.9265	78.371	80.7928	76.1115	74.4315	72.8693
Total profit	234.7998	242.0996	249.3426	234.6814	229.6498	224.9036

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