An auction mechanism for capacity allocation in identical parallel machines with time window constraints

We study the scarce production capacity allocation problem in a decentralised decision-making environment. We focus on the design of an auction mechanism for effective allocation of scarce capacity, without private information. In our problem setting, the firm's machine environment is identical parallel machines, and each customer order must be processed within a time window. Here, resource scarcity depends not only on capacity, but also on the customer orders' time window constraints. Hence, we propose an ascending auction with a discriminatory pricing scheme for customers, to identify the real processing requirements of the customer orders and resolve resource conflicts. In our auction, the winner determination problem is NP-complete, we develop a heuristic to solve this problem using the Lagrangian relaxation technique. The computational study shows that our auction mechanism achieves over 93% of the global optimal value. [Submitted 20 April 2021; Accepted 6 May 2022]