The effect of repeating transactions on service supply chain performance under proprietary and agent modes

Xiangrong Song; Jianbin Li; Xiyang Hou; Zhuolin Yang

doi:10.3934/jimo.2022191

Article Contents

2023, Volume 19, Issue 8: 5690-5723. Doi: 10.3934/jimo.2022191

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The effect of repeating transactions on service supply chain performance under proprietary and agent modes

School of Management, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

^*Corresponding author: Xiyang Hou
^*Corresponding author: Xiyang Hou

Received: March 2022

Revised: September 2022

Early access: September 2022

Published: August 2023

This work was supported by NSFC (Nos. 71831007 and 72071085), HUST Double First-Class Funds for Humanities and Social Sciences (Digital Intelligence Decision Optimization Innovation Team, 2021WKFZZX008), and China Postdoctoral Science Foundation (No. 2021M701297)

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Abstract

In a service supply chain, the service capacity prepared before the final demand is realized can be used for multiple periods but may depreciate over time. This paper studies the impact of repeating transactions on the decisions and performances of the service supply chain under two operational modes: proprietary mode and agent mode. We show that under both modes, repeating transactions over and over again does increase the profits of platform service supply chain members. The number of periods and the depreciation rate of capacity influence the gap between decentralized and centralized supply chains only under agent mode but not under proprietary mode. In addition, compared with that under proprietary mode, agent mode yields a greater expected profit for the retailer and a lower expected profit for the supplier, and the increased expected profit of the retailer compensates for the expected profit loss of the supplier. Furthermore, we present a modified new proprietary mode and find that it can yield a greater expected profit for the whole supply chain under agent mode within certain regions. In the end, we extend our model to the situation in which the supply chain members pay for the service relevant cost.

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Mathematics Subject Classification: Primary: 90B06, 90B50; Secondary: 91A80.

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Figure 1. Comparisons under PM and AM with different depreciation rate $ \delta $

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Figure 2. The supplier's wholesale price and the retailer's commission rate change with $ n $ fixed $ b = 2 $

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Figure 3. The optimal retail prices and quantities of service capacity change with $ n $ fixed $ b = 2 $

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Table 1. List of notations

Notation	Definition
$ n: $	the number of periods
$ c: $	Supplier's unit preparation cost of the service capacity
$ c_s: $	Unit salary of professional talent each period
$ c_t: $	Unit service relevant cost from service capacity to customized product
$ p: $	Retail price, and $p^* (\overline{p}^{}, \widehat{p}^{})$ is the equilibrium solution under a centralized system (PM, AM, respectively)
$ w: $	Wholesale price, and $ \overline{w}^{*} $ is the equilibrium solution under PM
$ r: $	Commission rate, and $ \widehat{r}^{*} $ is the equilibrium solution under AM
$ k: $	The quantity of service capacity, and $k^* (\overline{k}^{}, \widehat{k}^{})$ is the equilibrium solution under a centralized system (PM, AM, respectively)
$ \delta: $	Depreciation rate of the service capacity per period
$ D(p,\epsilon): $	$ =y(p)\cdot\epsilon $, the random price-dependent demand in the multiplicative form
$ y(p): $	$=ap^{-b}$, an iso-elastic demand where $a$ represents the size of market and $b$ represents sensitivity of demand to price
$ \epsilon: $	Random factor of demand with probability density function $f(x)$ and cumulative distribution function $F(x)$
$ \Pi: $	Profit of the whole supply chain under a centralized system
$ \overline{\Pi}_{S}^{}, \widehat{\Pi}_{S}^{}: $	Expected profit of the supplier under PM and AM respectively
$ \overline{\Pi}_{R}^{}, \widehat{\Pi}_{R}^{}: $	Expected profit of the retailer under PM and AM respectively
$ t: $	A subscript representing the situation where the supply chain members pay for service relevant cost

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Table 2. Performance of the service supply chain under PM and AM

As the number of periods increases ($ n $, $ \uparrow $)	PM	AM	PM vs. AM
Per-period profit of the retailer	$ \uparrow $	$ \uparrow $	AM$ \ge $PM
Per-period profit of the supplier	$ \uparrow $	$ \uparrow $	AM$ \ge $PM
Total per-period profit	$ \uparrow $	$ \uparrow $	AM$ \ge $PM
Profit loss ratio	$ - $	$ \downarrow $	PM$ \ge $AM
Profit share of the supplier	$ - $	$ \downarrow $	PM$ \ge $AM

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