Problem description

A company produces liquid nitrogen and liquid oxygen (we will call them LIN and LOX in the remainder) and needs to plan production for the next N periods, identified as shifts of 8 hours each. Although the resource procurement is rather trivial (these two elements compose most of the troposphere), the process of obtaining these two liquid gases requires a vast amount of electricity, both for refrigerating the stored liquid gases and for powering the plant.

Given that the energy cost is the largest component of the production cost, power suppliers offer several types of energy supply contracts; one of these is known as Interruptible Load Contracts (or ILC for short) and allows the power supplier to interrupt, with a short notice (a few minutes), the provision of electricity to a large customer such as a plant for a limited period of time; most likely the power supplier will take advantage of this in times of high electricity demand, such as hot summer days. However, the ILC requires that there be no more than K interruptions throughout the planning horizon.

We are dealing therefore with a production planning problem under uncertainty in the power supply. We are given in input the production and inventory cost, the maximum production, the inventory capacity, the initial inventory, the demand in LIN and LOX for each period, and the maximum number K of interruptions. The problem consists of finding the amount of LIN and LOX to be produced every day so that the demands are satisfied irrespective of the interruptions that may occur within the clause of the contract.

This optimization problem requires the application of Robust Optimization for one reason among several: among the customers of this company there are hospitals, for which the fulfilment of the demand of LOX is imperative.