Mechanism design in project procurement auctions with cost uncertainty and failure risk

Xiaohu Qian; Min Huang; Wai-Ki Ching; Loo Hay Lee; Xingwei Wang

doi:10.3934/jimo.2018036

Article Contents

2019, Volume 15, Issue 1: 131-157. Doi: 10.3934/jimo.2018036

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Mechanism design in project procurement auctions with cost uncertainty and failure risk

1.
College of Information Science and Engineering, Northeastern University, Shenyang 110819, China
2.
Research Institute of Business Analytics & Supply Chain Management, College of Management, Shenzhen University, Shenzhen 518060, China
3.
College of Information Science and Engineering, Northeastern University, State Key Laboratory of Synthetical Automation, for Process Industries (Northeastern University), Shenyang, Liaoning 110819, China
4.
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
5.
Department of Industrial and Systems Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
6.
College of Software, Northeastern University, Shenyang, Liaoning 110819, China

^* Corresponding author: M. Huang
^* Corresponding author: M. Huang

Received: April 2017

Revised: September 2017

Early access: April 2018

Published: January 2019

This work has been sponsored by Distinguished Young Scholars Award of NSFC Grant #71325002; Major International Joint Research Project of NSFC Grant #71620107003; Foundation for Innovative Research Groups of NSFC Grant #61621004; the 111 Project Grant #B16009; Fundamental Research Funds for State Key Laboratory of Synthetical Automation for Process Industries Grant #2013ZCX11; Research Funds of Shenzhen University Grant #2018059

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Abstract

Project procurement has two important attributes: cost uncertainty and failure risk. Due to the incomplete feature of such attributes, a novel mechanism incorporating contingent payments and cost sharing contracts is proposed for the buyer. Constructing models of bid decisions for risk averse and risk neutral suppliers, respectively, closed-form solutions of optimal bid prices are derived. By investigating the properties of bid prices in a first-score sealed-bid reverse auction, we find that when the degree of risk aversion or the variance of unpredictable cost is sufficiently small, bid prices of risk averse suppliers could be lower than those of risk neutral suppliers. Yet risk averse suppliers always bid higher than risk neutral suppliers in a second-score sealed-bid reverse auction. An interesting result verified by numerical experiments is that the classical revenue equivalence theorem no longer holds for the proposed mechanism if suppliers involve risk averse behavior. In this case, the buyer's best choice is to adopt a first-score sealed-bid reverse auction. We also provide decision support for the buyer to achieve optimal expected profit.

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

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Figure 1. Timing of events

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Figure 2. Comparison of ex ante expected payments of the buyer when facing risk averse suppliers in FSRA and SSRA

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Figure 3. Comparison of ex ante expected payments of the buyer when facing risk averse and risk neutral suppliers in FSRA

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Figure 4. Impact of parameters on β and ∆ for the buyer when facing risk averse suppliers in FSRA

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