Existence and derivation of forecast horizons in a dynamic lot size model with nondecreasing holding costs

The authors are concerned with a discrete-time undiscounted dynamic lot size model in which demand and the production setup cost are constant for an initial few periods and the holding cost of inventory is an arbitrary nondecreasing function assumed to be stationary (i.e., explicitly independent of time) in the same initial few periods. They show that there exists a finite forecast horizon in the present model and obtain an explicit formula for it. In addition, the authors obtain fairly general conditions under which the existence of a solution horizon in the model implies the existence of a forecast horizon. They also derive an explicit formula for the minimal solution horizon. These results extend the earlier ones obtained for the dynamic lot size model with linearly increasing holding costs.