Dynamic capacity expansion problem with deferred expansion and age-dependent shortage cost

Deferring capacity expansion may be a cost effective decision when there is anticipation of cheaper capacity in the near future and/or the current demand is too low to justify an immediate expansion. This paper studies a finite-horizon capacity expansion problem (CEP) with deferred capacity expansion. The operating cost and the cost of holding unused capacity in each period depend on the time when the capacity is acquired, and the shortage cost depends on the time when the shortage occurred. Our model is a generalization of the Wagner–Whitin formulation of the CEP and an extension (with deferred expansion) of two other polynomially solvable CEPs in the literature. We explore structural properties of the problem and develop an efficient dynamic programming algorithm to solve the problem in polynomial time.