Improvements for Inventory Models with Generalized Interarrival Times

Single-machine, single-product inventory models with generalized interarrival times have lacked a fully rigorous and computationally efficient optimization framework because a sign error in earlier derivations produced ad hoc feasibility restrictions and overly broad search domains. This study presents a corrected derivation that proves the strict convexity of the minimum-cost objective and establishes the existence and uniqueness of an interior optimum without auxiliary conditions, therefore consolidating previously fragmented results into a single theorem. Building on these structural properties, the maximum-profit formulation is reduced to a one-dimensional program with natural finite bounds that tightly bracket the optimizer, replacing earlier paired bounds defined on an effectively unbounded domain. Numerical results for a canonical benchmark show that the tightened admissible interval recovers the same optimum with fewer function evaluations, thereby improving computational efficiency and implementation robustness. The paper therefore contributes a corrected optimality theory, a problem-native one-dimensional reformulation of the profit model, and a more reproducible computational procedure for capacity-constrained single-machine systems under generalized interarrival times.