Effect of timing on reliability improvement and ordering decisions in a decentralized assembly system

In this study, we investigate a decentralized assembly system in which the suppliers are unreliable and have uncertain production capacities. We focus on the case in which a manufacturer deals with two suppliers that provide complementary products. We assume that the suppliers have the opportunity to improve their reliabilities through investments. The manufacturer determines her order quantities and the suppliers decide on their investment amounts in their capacities. The timing of the decisions has a substantial effect on the optimal behaviors of the players. We investigate the problem under four different settings based on the sequence of events: (1) simultaneous ordering and investment in which decisions are made concurrently, (2) ordering after observation of capacities in which the manufacturer orders after observing the suppliers' capacities, (3) ordering before realization of capacities in which the manufacturer orders after the suppliers' investment decisions, and (4) ordering before investments in which the suppliers invest after the manufacturer's ordering decision. We demonstrate the existence of a Pareto optimal equilibrium in the first two scenarios. In addition, we show that in the fourth scenario, there exists a unique Nash equilibrium in the suppliers' game. Based on the realized capacities of the suppliers, it may be beneficial for them to share their production information with the manufacturer. In addition, we indicate that using a sequential decision strategy can enhance the performances of the supply chain and the members. When the suppliers are the leaders, they implement investment inflation strategies to stimulate the manufacturer to place larger orders. When the manufacturer is the leader, she uses an order inflation strategy to increase the investment of the suppliers. Our numerical analysis revealed that in different situations, the players may prefer ordering before realization of capacities scenario or ordering before investments. Finally, we extended our results to a multiple-suppliers case in which the suppliers are identical.