Auction-Based Capacity Allocation in Two Parallel Machines with Inclusive Processing Set Restrictions

Abstract

We consider the scarce capacity allocation problem in two parallel machines with inclusive processing set restrictions. Our focus is to design an auction mechanism to allocate the production capacity among several selfish customers effectively and efficiently. In our iterative ascending auction mechanism, we need to design jointly two things: who wins what and who pays what. First, we propose an adaptive ascending pricing policy to ensure that bidding by truthful processing requirements and keeping on bidding until the ask prices reach his real revenue is a dominant strategy for each customer. Second, we establish a facility owner’s profit maximization model to determine the capacity allocation in two parallel machines with inclusive processing set restrictions; it is an NP hard problem; we also develop a heuristic based on the Lagrangian relaxation technology to obtain the suboptimal solutions. Our computational analysis shows that the auction mechanism can achieve more than 87% of the global system value.