Needless to say that the combined lot sizing and cutting stock problem is very relevant in a wide range of manufacturing industries. This paper presents an algorithmic solution approach to overcome the difficulty in solving non-linear integer formulation of the problem. The algorithm is based on the traditional approach where the lot sizing is determined for each period, and then the best cutti...

We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities subsume existing inequalities for this problem, and they are facet-defining under certain conditions. In addition, we show that they give the convex hull descr...

The semiconductor manufacturing process usually consists of four main production stages: wafer fabrication, probe, assembly, and final test. This paper considers the lot-sizing and scheduling problem in the assembly stages. A hierarchical solution approach is outlined with focus on the first of three suggested phases, namely the bottleneck lot-sizing and scheduling phase. The approach integrate...

The multi-stage lot-sizing problem with production capacities (MLSP-PC) deals with a supply chain that consists of a manufacturer with stationary production capacity and intermediaries (distribution centers or wholesalers) and a retailer to face deterministic demand. An optimal supply chain plan for the MLSP-PC specifies when and how many units each organization of the supply chain has to produ...

We consider a variant of the single item lot sizing problem where the product, when stored, suffers from a proportional loss, and in which the product demand is affected by uncertainty. This setting is particularly relevant in the energy sector, where the demands must be satisfied in a timely manner and storage losses are, often, unavoidable. We propose a two-stage robust optimization approach ...

This study presents mixed integer programming (MIP) models for production lot-sizing problems with distribution costs using unit load devices such as pallets and containers. Problems that integrate production lot-sizing decisions and loading of the products in vehicles (bins) are also modelled, in which constraints such as weight limits, volume restrictions or the value of the cargo loaded in t...

In this paper, we consider the well-known constant-batch lot-sizing problem, which we refer to as the single module capacitated lot-sizing (SMLS) problem, and multi-module capacitated lot-sizing (MMLS) problem. We provide sufficient conditions under which the (k, l, S, I) inequalities of Pochet and Wolsey (Math of OR 18: 767-785, 1993), the mixed (k, l, S, I) inequalities, derived using mixing ...

Multi-period single-item lot sizing problem under stochastic environment has been tackled by few researchers and remains in need of further studies. It is mathematically intractable due to its complex structure. In this paper, an optimum lot-sizing policy based on minimum total relevant cost under price and demand uncertainties was studied by using various artificial neural networks trained wit...

NP{hard cases of the single{item capacitated lot{sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge, until now no polynomial approximation method is known which produces solutions with a relative deviati...

Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed-integer programming formulation and Lagrangian relaxation solution procedur...