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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]

A deterministic continuous-time continuous-state inventory model is studied. In the absence of intervention, the level of stock evolves by a process governed by a differential equation. The inventory level is monitored continuously, and can be adjusted upwards at any time. The decision maker can order from several suppliers, each of which charges a different ordering and purchasing cost. The problem of selecting the supplier and the size of the order to minimize the total inventory cost over an infinite planning horizon is formulated as the solution of a quasi-variational inequality (QVI). It is shown that the QVI has a unique solution. This corresponds to a generalized (s, S) policy under amenable conditions, which have been characterized in an earlier work by the present authors. Under the complementary conditions a new type of optimal control policy emerges. This leads to the concept of a hyper-generalized (s, S) policy. The theory behind a policy of this type is exposed. [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]