Pull and push contracts in a decentralised assembly system with random component yields

Abstract

This study investigates how random component yields can influence pricing and production decisions under pull and push contracts. We consider a decentralised assembly system where a manufacturer procures complementary components from two suppliers with random yields. We first characterise the centralised equilibrium decision as a benchmark and then analyse the equilibrium solutions in a decentralised assembly system under each contract. We find that neither contract is always superior to the other in terms of system profit. Under a push contract, suppliers always achieve the first mover advantage with higher payoff. However, the first mover advantage does not hold for the manufacturer under a pull contract. We further conduct sensitivity analysis to study the impact of random component yields and retail price on equilibrium solutions under each contract. Interestingly, the wholesale prices charged by suppliers always increase with supply yield uncertainty under a pull contract, but decrease under a push contract. In contrast with the centralised solution, the equilibrium quantities in the decentralised solution decrease with supply yield uncertainty under both pull and push contracts. We then extend our model to a general case with multiple suppliers. The system payoff decreases with the number of suppliers, and the main results derived in two suppliers setting still hold in the system with multiple suppliers.

Keywords:

• assembly systems
• random yield
• pull contract
• push contract
• game theory

Disclosure statement

No potential conflict of interest was reported by the authors.

Acknowledgements

The authors sincerely thank the editor and two anonymous reviewers for their insightful comments and suggestions. This research is partially supported by the National Natural Science Foundation of China under the grant nos. 91746110, 71372019, 91746208, 71521002; the National Science Fund of China for Distinguished Young Scholars under the grant no. 71625003; the Special Items Fund of Beijing Municipal Commission of Education.

Notes

1. Note that the concavity of payoff can only be ensured when Q > 1, where p > 3(c₁ + c₂). See proof of Lemma 1 in the Appendix 1 for details.