Sequencing Capacity Expansion Projects in Continuous Time

We consider a problem of sequencing capacity expansion projects with a continuous demand function specified over a given time horizon. Each type of expansion project has a specified integer capacity and an associated cost which is nonincreasing with respect to the time at which the project is brought on stream. The problem is to determine the sequence of expansions to provide sufficient capacity to meet demand at minimum cost. A formulation is presented and its relaxation leads to a shortest route problem. The sequencing problem is solved using a branch and bound procedure with Lagrangean relaxation providing bounds. A particularly effective heuristic is also developed. Computational results are given.