This paper considers a stochastic dynamic inventory problem involving a single item, linear cost structures, and finite distributions (but not necessarily independent) for the stochastic cost and demand parameters. We develop primal and dual algorithms for a multi-stage stochastic linear programming formulation for the problem. The complexity of the proposed algorithms is shown to be within O(N...

This paper considers a stochastic dynamic inventory problem involving a single item, linear cost structures, and finite distributions (but not necessarily independent) for the stochastic cost and demand parameters. We develop primal and dual algorithms for a multi-stage stochastic linear programming formulation for the problem. The complexity of the proposed algorithms is shown to be within O(N...

In this paper we formulate a two-stage stochastic quadratic optimization problem, that models a production planning problem of multiple products, over several time periods, with uncertain demands. This model considers quadratic inventory holding and demand backlogging recourse costs, which model the saturation phenomenon inherent to the increase of the inventory and/or backlogged demand levels....

Intuition may lead to the hypothesis that in stochastic inventory systems a higher demand variability results in larger variances and in an increase of total expected system costs. In a recent paper, Song [5] formally proved this assertion to hold for a certain class of inventory models (including the Newsboy Problem), given a particular definition of variability. Here we use stochastic dominan...

Introduction. We study a class of capacitated stochastic lot-sizing inventory control problems with stochastic, non-stationary and correlated demands that evolve over time. Economies of scale and capacity constraints exist in many practical scenarios. However, models with fixed ordering costs and capacity constraints are typically computationally intractable, and even the structure of the optim...

The single-item stochastic inventory control problem is to find an inventory replenishment policy in the presence of independent discrete stochastic demands under periodic review and finite time horizon. In this paper, we prove that this problem is intractable and for any 2 > 0, we design an algorithm with running time polynomial in the size of the problem input and in 1/2, that finds a policy ...