The single-item stochastic lot-sizing problem is to find an inventory replenishment policy in the presence of discrete stochastic demands under periodic review and finite time horizon. A closely related problem is the single-period newsvendor model. It is well known that the newsvendor problem admits a closed formula for the optimal order quantity whenever the revenue and salvage values are lin...

We study two different lot-sizing problems with time windows that have been proposed recently. For the case of production time windows, in which each client specific order must be produced within a given time interval, we derive tight extended formulations for both the constant capacity and uncapacitated problems with Wagner-Whitin (non-speculative) costs. For the variant with nonspecific order...

In this paper we propose exact solution methods for a bilevel uncapacitated lot-sizing problem with backlogs. This is an extension of the classical uncapacitated lot-sizing problem with backlogs, in which two autonomous and self-interested decision makers constitute a twoechelon supply chain. The leader buys items from the follower in order to meet external demand at lowest cost. The follower a...

In this paper we investigate the complexity of the economic lot-sizing problem with remanufacturing (ELSR) options. Whereas in the classical economic lot-sizing problem demand can only be satisfied by production, in the ELSR problem demand can also be satisfied by remanufacturing returned items. Although the ELSR problem can be solved efficiently for some special cases, we show that the problem...

In the present paper, we discuss one of the many processes arising in the context of supply chain management, namely production planning. We focus on one type of production planning models called capacitated lot sizing models. These models appear to be well suited for the usually rather in exible production resources found in the process industries. We review the literature on single-level sing...

Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by many researchers. Considering the quantity discount in purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In this paper, stochastic dynamic...

The Inventory Routing Problem (IRP) involves the distribution of one or more products from a supplier to a set of customers over a discrete planning horizon. The version treated here, the so-called Vendor Managed Inventory Routing Problem (VMIRP), is the Inventory Routing problem arising when the replenishment policy is decided a priori. We consider two replenishment policies. The first is know...

In a previous paper (Araujo et al. 2007), the authors proposed a lot sizing and sequencing model for a production process where a key material is prepared and then transformed into different final items. The lot sizing decisions concern not only the production of final items, but also that of the prepared material in order to take account of their sequence-dependent setup costs and times. The n...

the aim of this paper is to study a multi-product, multi-period production systems in a hybrid flow shop so that lot-sizing and scheduling will be detemined simultaneously. a new mixed-integer programming model is proposed to formulate the studied problem. the objective function in this investigation includes the total cost of production, inventory and external supply. in the case of not satisf...