This note gives a simple proof that in a (r, q) system the average outstanding backorders andthe average stockouts per unit time are jointly convex in the two control variables q and r.
Bid-prices are becoming an increasingly popular method for controlling the sale of inventory in revenue management applications. In this form of control, threshold—or "bid"—prices are set for the resources or units of inventory (seats on flight legs, hotel rooms on specific dates, etc.) and a product (a seat in a fare class on an itinerary or room for a sequence of dates) is sold only if the offered fare exceeds the sum of the threshold prices of all the resources needed to supply the product.
In this paper we address periodic base-stock policies for stochastic economic lot scheduling problems. These represent manufacturing settings in which multiple items compete for the availability of a common capacity source, in the presence of setup times and/or costs, incurred when switching between items, and in the presence of uncertainty regarding demand patterns, production, and setup times. Under periodic base-stock policies, items are produced according to a given periodic item-sequence.
We consider a distribution system consisting of a single warehouse and many geographically dispersed retailers. Each retailer faces demands for a single item which arise a deterministic, retailer specific rate. The retailers' stock is replenished by a fleet of vehicles of limited capacity, departing and returning to the warehouse and combining deliveries into efficient routes. The cost of any given route consists of a fixed component and a component which is proportional with the total distance driven. Inventory costs are proportional with the stock levels.
The accelerated pace of technological change has led to rapid obsolescence of productive capacity in electronics and other industries. Managers must consider the impact of future technologies while making acquisition and replacement decisions in such environments. We consider a problem where a sequence of technological breakthroughs are anticipated but their magnitude and timing are uncertain. A firm, operating in such an environment, must decide how much capacity of the current technology to acquire to meet future demand growth.
This paper studies the trade-off between inventory levels and the delivery leadtime offered to customers in achieving a target level of service. It addresses the question of how much a delivery leadtime can be reduced, per unit increase of inventory, at a fixed fill rate. We show that for a class of assemble-to-order models with stochastic demands and production intervals there is a simple linear trade-off between inventory and delivery leadtime, in a limiting sense, at high fill rates.
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We present diÆculties with realizing the capacity of queueing networks with batch servers under well known scheduling disciplines. We intro duce a family of scheduling p olicies called discrete-review p olicies, which not only guarantee capacity realization for queueing networks with batch servers, but also contain among them p olicies that allow us to realize desired b ehavior on \ uid" scale, including asymptotically optimal p olicies.
We analyze a multistage inventory system with limited production capacity facing stochastic demands. Each node follows a periodic-review base-stock policy for echelon inventory: in each period, each node attempts to produce enough material to restore cumulative down-stream inventory to a fixed target level. We develop approximations to the key measures of interest (average inventories, average backorders, and service levels) by simultaneously letting the mean demand approach the system's bottleneck capacity and letting the base-stock level for finished goods increase without bound.