We address a stochastic single item production system in a make-to-stock environment with partial knowledge on future demand resulting from customers ordering in advance of their actual needs. The problem consists of determining the optimal size of a production lot to replenish inventory, so that delivery promises are met on time at the expense of minimal average costs. For this problem an opti...

Consider a two-level inventory system consisting of one supplier and one retailer. The retailer faces a Poisson demand with a known rate and applies base stock (one-for-one ordering) policy. That is, his inventory position is set to a pre-determined level, so the demand pattern is transferred exactly to the supplier. The supplier has an inventory system and a service unit with exponentially dis...

We study an Inventory Routing Problem in which the supplier has a limited production capacity and the stochastic demand of the retailers is satisfied with procurement of transportation services. The aim is to minimize the total expected cost over a planning horizon, given by the sum of the inventory cost at the supplier, the inventory cost at the retailers, the penalty cost for stock-out at the...

A wide class of single-product, dynamic inventory problems with convex cost functions and a finite horizon is investigated as a stochastic programming problem. When demands have finite discrete distribution functions, we show that the problem can be substantially reduced in size to a linear program with upper-bounded variables. Moreover,, we show that the reduced problem has a network represent...

In this paper, we consider an inventory problem with two demand classes having different priorities. The appropriate policy of rationing the available stock, i.e. reserving some stock for meeting prospective future demand of preferred customers at the expense of deliberately losing some of the currently materialized demand of lower demand class(es), relies on the estimation of the future demand...

We present three problems motivated by order fulfillment in online retailing. First, we focus on one warehouse or fulfillment center. To optimize the storage space and labor, an e-tailer splits the warehouse into two regions with different storage densities. One is for picking customer orders and the other to hold a reserve stock that replenishes the picking area. Consequently, the warehouse is...

Consider a single commodity inventory system in which the demand is modelled by a sequence of i.i.d. random variables that can take negative values. Such problems have been studied in the literature under the name cash management and relate to the variations of the on-hand cash balances of financial institutions. The possibility of a negative demand also models product returns in inventory syst...

Variability, in general, has a deteriorating effect on the performance of stochastic inventory systems. In particular, previous results indicate that demand variability causes a performance degradation in terms of inventory related costs when production capacity is unlimited. In order to investigate the effects of demand variability in capacitated production settings, we analyse a make-to-stock...

In the reverse supply chain inventory theory, inventory models are concerned with the demand of reusable parts, stock replenishment, ordering cycle, delivery lead time, number of disassembled products, ordering costs. The particularity of these models consists in the occurrence of high uncertainties of the quantity and quality of the returned products and resulting parts. To overcome the proble...