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The inventory control problem with a finite horizon is concerned with the holding of a stock of a commodity in order to satisfy the demand for the commodity over a specified period. The objective is to find the number of procurements and the timing of these procurements that minimizes the cost of procuring and carrying the stock. It is shown that there are demand rates for which the archetypical problem with a fixed number of procurements has two minima. Consequently the problem of finding the number of procurements and the timing of these procurements has multiple solutions. Generalizations of the basic problem are also considered, demonstrating that a body of results concerning these models in the Management Science and Operations Research literature are false. The demand rates exhibited are smooth, positive and have a derivative with fixed sign. So the multiplicity cannot be attributed to a property that is abnormal with regard to applications. The proof is constructive and based on a detailed mathematical analysis of the problem with a demand rate that is piecewise linear, and mollification. [ABSTRACT FROM AUTHOR]

The subject is a deterministic continuous-time continuous-state inventory control model. Stock is replenished by ordering from one of a number of suppliers incurring a different cost per item and a different set-up cost. Taking the cost of procurement into account, the objective is to minimize the total discounted cost over an infinite planning horizon. The size of the order that is to be placed and the supplier with which it is to be placed are to be decided. Earlier studies of the problem have relied substantially on the assumption that the set-up cost of every supplier is strictly positive. Removing this restriction calls for a significant modification of the adopted approach. This is realized in the present study. It is shown that there is a stable unique optimal policy of a type that encompasses (s, S) and generalized (s, S) policies. Conditions that are necessary and sufficient for it to reduce to each of these types are established. The case of two suppliers is studied in detail, properties of the solution are investigated, numerical examples illustrating various aspects are included, and the connection with antecedent results is assessed. [ABSTRACT FROM AUTHOR]

This paper examines the problem of finding an optimal replenishment policy for a single product inventory model with a finite planning horizon. Changes in inventory level are caused by deterioration of the product and a demand which varies with time, and the inventory holder is permitted to delay payment to the supplier of the product. A consequence of the latter feature is that the objective function in the resulting mixed integer non-linear programming problem does not possess the smoothness required for the straightforward application of techniques to be found in the literature to date. The authors overcome this difficulty by reducing an appropriate technique to its core mathematical essentials. It is shown that the optimization problem with a fixed number of replenishment periods has a unique global optimal solution, and that the corresponding optimal value is a strictly convex function of this number. Numerical examples are presented, and managerial implications are discussed. [ABSTRACT FROM AUTHOR]

With q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under the assumption that the initial-data function is bounded and continuous. Results on the existence, uniqueness, and regularity of solutions are obtained. [Copyright &y& Elsevier]