Inventory and Supply Chain Management with Forecast Updates is concerned with the problems of inventory and supply chain decision making with information updating over time. The models considered include inventory decisions with multiple sources and delivery modes, supply-contract design and evaluation, contracts with exercise price, volume-flexible contracts allowing for spot-market purchase decisions, and competitive supply chains. Real problems are formulated into tractable mathematical models, which allow for an analysis of various approaches, and provide insights for better supply chain management. The book provides a unified treatment of these models, presents a critique of the existing results, and points out potential research directions. Attention is focused on solutions – that is, inventory decisions prior and subsequent to information updates and the impact of the quality of information on these decisions.

Ce chapitre concerne les files d’attente variables dans le temps, avec abandon des clients et salles d’attente finies. Une approche en chaîne de Markov à deux échelles temporelles est utilisée. Les écarts modérés et les écarts importants sont pris en compte lorsque la séparation des échelles de temps est en vigueur. Dans l’étude, une expression générale de la fonction de taux est fournie. Un exemple numérique est également inclus pour illustrer le calcul de la fonction de taux. DOI : 10.51926/ISTE.9001.ch10

This paper presents an extension of earlier research on hierarchical control of stochastic manufacturing systems with long-run average cost in which a positive inventory deterioration/cancellation rate for each product is assumed. Here we drop the assumption of the positive inventory deterioration/cancellation rate for each product, and give an asymptotic analysis of the manufacturing systems as the rates of change of the machine states approach infinity. We obtain a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. We use a near optimal control of the limiting problem to construct nearly asymptotically optimal open-loop piecewise deterministic controls for the original problem.

We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.

Information delays exist when the most recent inventory information available to the Inventory Manager (IM) is dated. In other words, the IM observes only the inventory level that belongs to an earlier period. Such situations are not uncommon, and they arise when it takes a while to process the demand data and pass the results to the IM. In this paper, we establish that the average cost optimal policy is of state-dependent basestock type with respect to the reference inventory position. We show that the optimal base stock depends on the age and the magnitude of the latest observed delay. We illustrate the results by solving an example with delays of 0 and 1, for which we are able to obtain formulas/bounds for the basestock levels.

We present a periodic review inventory model with multiple delivery modes. While base-stock policies are optimal for one or two consecutive delivery modes, they are not so otherwise. For multiple consecutive delivery modes, we show that only the fastest two modes have optimal base stocks, and provide a simple counterexample to show that the remaining ones do not. We investigate why the base-stock policy is or is not optimal in different situations. This note is an abridged version of Q. Feng, S. P. Sethi, H. Yan and H. Zhang, Optimality and nonoptimality of the base-stock policy in inventory problems with multiple delivery modes, Journal of Industrial and Management Optimization, Vol. 2, No. 1, 2006, pp. 19-42.

We consider a production planning problem for a general jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are modeled as Markov chains. The objective is to choose the rates of production of the final products and intermediate parts on the various machines over time in order to meet the demand for the system's production at the minimum long-run average cost of production and surplus. The problem is formulated as a stochastic dynamic program. We prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the so-called potential function. Finally, we construct a potential function in the special case of a jobshop producing only one final product.

Recently, the production control problem in stochastic manufacturing systems has generated a great deal of interest. The goal is to obtain production rates to minimize total expected surplus and production cost. This paper reviews the research devoted to minimum average cost production planning problems in stochastic manufacturing systems. Manufacturing systems involve a single or parallel failure-prone machines producing a number of different products, random production capacity, and constant demands.

This paper studies a supply chain consisting of two suppliers and one retailer in a spot market, where the retailer uses the newsvendor solution as its purchase policy, and suppliers compete for the retailer's purchase. Since each supplier's bidding strategy affects the other's profit, a game theory approach is used to identify optimal bidding strategies. We prove the existence and uniqueness of a Nash solution. It is also shown that the competition between the supplier leads to a lower market clearing price, and as a result, the retailer benefits from it. Finally, we demonstrate the applicability of the obtained results by deriving optimal bidding strategies for power generator plants in the deregulated California energy market.

This paper is concerned with optimal production planning on a single failure-prone flexible machine that produces N distinct part types. The machine is flexible in the sense that no setup is required for switching from production of one part type to another. We consider the problem of controlling production rates to minimize the expected long-run average cost of product surpluses over time. We assume constant unit holding and shortage costs and constant demand rates for the part types. Moreover, the costs are assumed to be the same for all products. We provide an explicit optimal solution for the problem.