A matheuristic for complex pricing problems: An application to rentable resources

We consider the problem of a service provider who offers resources (such as equipment or accommodation) for rent that are substitutable and renewable over time. The provider aims to set static, yet time-dependent prices to maximize revenue while adhering to business-specific pricing rules. As customers arrive consecutively, they base their rental decisions on their willingness to pay, the prices set by the provider, and resource availability, leading to dynamic substitution.

To solve the problem, we propose a mixed-integer linear program (MIP) for a given stream of customers and different price constraints. The problem is difficult to solve because it requires modeling customers’ choices and resource availability over the course of time and also includes many prices that are closely intertwined by price constraints, constituting a complex pricing system. When developing heuristics, applying construction or improvement approaches becomes difficult because knowing all prices is necessary to evaluate a customer stream. Therefore, we develop a matheuristic based on the destroy/repair paradigm. To regain feasibility in the repair step, our approach uses a sub-MIP, which can easily consider different price constraints. As a benchmark, we also implement an enumeration-based approach.

We conduct a comprehensive computational study that covers 198 different instance classes of realistic size considering various price constraints. The study findings indicate that the new MIP-based heuristic outperforms the enumeration-based approach and a standard solver when applied to the initial MIP formulation.