An inventory management problem

Inventory management is a key problem in several industries, (car renting, storehouse space renting, etc.). It consists of managing a given fleet of equipment in order to satisfy requests to use it. When requests exceed the stock of available equipment, a decision has to be made, either to subcontract some requests to another provider or to purchase new pieces of equipment. The main difficulty lies in the fact that a subcontracted request must be subcontracted for all the duration of the request. For example, if a subcontracted car is rented to a given customer, this customer will keep the subcontracted car for all the duration of the rental. In this paper, we propose a set of benchmark problem instances, derived from real-world inventory management problems.