Service outsourcing under different supply chain p

Authors: Junsong Bian Kin Keung Lai Zhongsheng Hua

Publish Date: 2016/05/23

Volume: 248, Issue: 1-2, Pages: 123-142

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Abstract

This paper studies the impact of service outsourcing under three supply chain power structures manufacturerStackelberg verticalNash and retailerStackelberg supply chains We first investigate price and service decisions by comparing the integrated channel and the decentralized channel with service outsourcing It is found that a lower retail price or a higher service level could occur in the decentralized channel with service outsourcing compared to those in the integrated channel but they never occur simultaneously Next we examine the manufacturer’s channel strategies and demonstrate that service outsourcing can always help the manufacturer earn more profit from the decentralized channel than from the integrated channel in the manufacturerStackelberg and retailerStackelberg markets as long as the retailer’s service investment is sufficiently efficient However in the verticalNash supply chain this occurs only when the manufacturer is inefficient and the retailer is efficient enough in service provision Finally comparisons of channel efficiency and numerical analysis are providedThe Hessian matrix of the profit function Pi C with respect to pC and sC is given by H 1 =left beginarrayll 2beta gamma gamma lambda M endarray right Since 2beta 0 and lambda M 0 so if 2lambda M beta gamma 20 profit function Pi C is strictly jointly concave with respect to pC and sCProfit function Pi RM with respect to uM and sM has a Hessian matrix H 2 =left beginarrayll 2beta gamma gamma lambda R endarray right Similar to Lemma 1 it is easy to check if 2lambda R beta gamma 20 holds then H 2 is strictly jointly concave in uM and sMif lambda M frac3gamma 24beta then either fracgamma 22beta lambda R le frac23lambda M or lambda R frac23lambda M holds corresponding to Delta sNge 0 or Delta sN0 respectivelyNext we prove the case for verticalNash market First comparing pN and pC we have Delta pN=pNpC=frac2lambda R alpha 3lambda R beta gamma 2fraclambda M alpha 2lambda M beta gamma 2=fracleft lambda M lambda R beta 2lambda R gamma 2+lambda M gamma 2 right alpha left 2lambda M beta gamma 2 right left 3lambda R beta gamma 2 right Delta pN0 if left 2gamma 2lambda M beta right lambda R lambda M gamma 2 which is always satisfied when lambda M ge frac2gamma 2beta Note that inequalitylambda R fracgamma 22beta must hold to guarantee the retailer’s participation If fracgamma 22beta lambda M le frac2gamma 23beta then fraclambda M gamma 22gamma 2lambda M beta le fracgamma 22beta lambda R which leads to pNpC Finally if frac2gamma 23beta lambda M frac2gamma 2beta pN can either be higher or lower than pC depending on whether fracgamma 22beta lambda R fraclambda M gamma 22gamma 2lambda M beta or lambda R ge fraclambda M gamma 22gamma 2lambda M beta holds ie pNleft beginarrayl le endarray right pC for left beginarrayl lambda R ge fraclambda M gamma 22gamma 2lambda M beta fracgamma 22beta lambda R fraclambda M gamma 22gamma 2lambda M beta endarray right

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