Operational decisions for multi-period industrial gas pipeline networks under uncertainty

An industrial gas company (IGC) manages a large pipeline network consisting of several gas production plants and many customers. Natural gas is an input to the production process at each plant, and a different industrial gas (e.g., hydrogen or oxygen) is the plant output. Each day the company must propose 24 h in advance a “nomination value” for the amount of natural gas they plan to use at each plant over the next day. The nomination value goes to the natural gas provider who then offers a set price for the nominated amount. If the nomination amount underestimates actual usage, the IGC must purchase the extra gas at a (typically higher) spot market price. If the nomination value overestimates usage, the IGC sells extra gas at a (typically lower) spot market price. In this study, we develop a multi-period model to determine decisions for daily nomination values of natural gas for multiple plants as well as production and distribution decisions for a steady-state behaving industrial gas at distribution network, where the direction of the gas flow is not known at each pipe. The model considers demands from multiple customers to be uncertain and varying throughout the day. Daily planning requires a multi-period formulation that includes ramping constraints (physical constraints that limit how much a plant’s production can change over each period). The model also dictates that customer demands be met with high probability and that the physical constraints of the pipeline are met. The result is a challenging multi-period, chance constrained, nonlinear integer optimization problem. We propose an optimization-based heuristic approach to find a high-quality feasible solution for industry-sized problems. Also, we use a convex relaxation of the problem to obtain valid lower bound for the problem in order to obtain a measure of the near-optimality of the problem’s feasible solution found via the introduced heuristic approach. Numerical experiments show that the proposed heuristic is able to efficiently find near-optimal solutions for the problem instances in which using an exact solution approach is prohibitively time consuming.