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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]

Abstract: Disruptions and random supplies have been important sources of uncertainty that should be considered in the design and control of supply chains. There have been many real world examples in which a single catastrophic event has simultaneously degraded the capabilities of several suppliers leading to considerable erosion of profits and goodwill for a company. However, the literature on analytical models that account for the dependence nature of disruptions and its impact on supply chain performance is sparse. In this paper, we consider an m-manufacturer, 1-retailer, newsvendor inventory system with stochastically dependent manufacturing capacities, caused by random disruptions that may simultaneously inflict damages to the capacities of the manufacturers. We develop the structural/analytical properties of key performance measures and optimal inventory policies for the multi-source and assembly inventory systems. We show that stochastic dependence in disruptions can have opposite effects on system performance in the multi-source and assembly systems. While risk diversification is preferred in the multi-source system, risk concentration is preferred in the assembly system. Our results also suggest that, if the retailer ignores the effect of dependent disruptions, then in the multi-source structure, it would underestimate the cost, overestimate the fill rate, and order more units than the optimum; however, in the assembly structure, the opposite would happen. We perform a comprehensive numerical study to validate our analytical results and generate useful managerial and operational insights for effective risk management of supply chains in the presence of dependent supply uncertainty. [Copyright &y& Elsevier]