We consider a multi-item lot-sizing problem with joint set-up costs and constant capacities. Apart from the usual per unit production and storage costs for each item, a set-up cost is incurred for each batch of production, where a batch consists of up toC units of anymix of the items. In addition, an upper bound on the number of batches may be imposed. Under widely applicable conditions on the ...

We consider a single stage production-inventory system whose production and demand rates are modulated by an environment process modeled as a finite state Continuous Time Markov Chain (CTMC). When the inventory level reaches zero, an order is placed from an external supplier, and it arrives instantaneously. We derive an Economic Order Quantity (EOQ ) policy that minimizes the long-run average c...

We present a fully polynomial time approximation scheme (FPTAS) for a capacitated economic lot-sizing problem with a monotone cost structure. An FPTAS delivers a solution with a given relative error ε in time polynomial in the problem size and in 1/ε. Such a scheme was developed by van Hoesel and Wagelmans [8] for a capacitated economic lot-sizing problem with monotone concave (convex) producti...

We study the integrated inventory distribution problem which is concerned with multiperiod inventory holding, backlogging, and vehicle routing decisions for a set of customers who receive units of a single item from a depot with infinite supply. We consider an environment in which the demand at each customer is deterministic and relatively small compared to the vehicle capacity, and the custome...

Markov-modulated processes have been used in stochastic inventory models with setup costs for modeling demand under the innuence of uncertain environmental factors, such as uctuating economic and market conditions. The analyses of these models have been carried out in the literature only under the assumption that unsatissed demand is fully backlogged. The lost sales situation occurs in many ret...