On the Properties of Yield Distributions in Random Yield Problems: Conditions, Class of Distributions and Relevant Applications. Issue 7 (17th April 2018)

• Record Type: Journal Article
• Authors: Kouvelis, Panos; Xiao, Guang; Yang, Nan
• Is Part Of: Production and operations management. Volume 27:Issue 7(2018)
• Page Start: 1291
• Page End: 1302
• Publication Date: 2018-04-17
• Subjects: random yield -- price and quantity decisions -- price elasticity functions; Production management -- Periodicals; 658.505
• DOI: 10.1111/poms.12869
• Languages: English
• ISSNs: 1059-1478

Abstract

Abstract : In this study, we propose two technical assumptions to ensure the unimodality of the objective functions in two classes of price and quantity decision problems with one procurement opportunity under supply random yield and deterministic demand in a price‐setting environment. The first class of problems involves a decentralized supply chain/assembly system under different configurations, and the second class focuses on a single firm's price and quantity decisions under different contracts, payment schemes and supplier portfolios. We provide appealing economic interpretations and easy‐to‐verify sufficient conditions for our proposed technical assumptions. We show that both assumptions are preserved under truncation and positive scale, and satisfied by most commonly used continuous yield distributions. Moreover, similar to the role that the increasing generalized failure rate (IGFR) property plays in analyzing operations problems with demand uncertainty, our Assumption 1 plays a fundamental role in regulating the behaviors of the objective functions for both classes of random yield problems. Assumption 2 is more general than both Assumption 1 and the IGFR property and is used to analyze the second class of problems. Finally, we discuss the difference between random yield and random demand problems, and explain the rationale for the need of different technical assumptions.