A Lagrangian relaxation approach to a coupled lot-sizing and cutting stock problem

Industrial production processes involving both lot-sizing and cutting stock problems are common in many industrial settings. However, they are usually treated in a separate way, which could lead to costly production plans. In this paper, a coupled mathematical model is formulated and a heuristic method based on Lagrangian relaxation is proposed. Computational results prove its effectiveness. (C) 2009 Elsevier B.V. All rights reserved.

A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

A coupling cutting stock-lot sizing problem in the paper industry

An important production programming problem arises in paper industries coupling multiple machine scheduling with cutting stocks. Concerning machine scheduling: how can the production of the quantity of large rolls of paper of different types be determined. These rolls are cut to meet demand of items. Scheduling that minimizes setups and production costs may produce rolls which may increase waste in the cutting process. On the other hand, the best number of rolls in the point of view of minimizing waste may lead to high setup costs. In this paper, coupled modeling and heuristic methods are proposed. Computational experiments are presented.

Population structure of the migratory fish Prochilodus lineatus (Characiformes) from rio Grande basin (Brazil), an area fragmented by dams

1. Prochilodus lineatus (Prochilodontidae, Characiformes) is a migratory species of great economic importance both in fisheries and aquaculture that is found throughout the Jacui, Paraiba do Sul, Parana, Paraguay and Uruguay river basins in South America. Earlier population studies of P. lineatus in the rio Grande basin (Parana basin) indicated the existence of a single population; however, the range of this species has been fragmented by the construction of several dams. Such dams modified the environmental conditions and could have constrained the reproductive migration of P. lineatus, possibly leading to changes in the population genetic structure. 2. In order to evaluate how genetic diversity is allocated in the rio Grande basin, 141 specimens of P. lineatus from eight collection sites were analysed using polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) with 15 restriction enzymes. 3. Forty-six haplotypes were detected, and 70% of them are restricted. The mean genetic variability indexes (h = 0.7721 and pi = 1.6%) were similar to those found in natural populations with a large effective size. Fst and Exact Test values indicated a lack of structuring among the samples, and the model of isolation by distance was tested and rejected. 4. The haplotype network indicated that this population of P. lineatus has been maintained as a single variable stock with some differences in the genetic composition (haplotypes) between samples. Indications of population expansion were detected, and this finding was supported by neutrality tests and mismatch distribution analyses. 5. The present study focused on regions between dams to serve as a parameter for further evaluations of genetic variability and the putative impact of dams and repopulation programmes in natural populations of P. lineatus. Copyright (C) 2011 John Wiley & Sons, Ltd.

Lot sizing and furnace scheduling in small foundries

A lot sizing and scheduling problem prevalent in small market-driven foundries is studied. There are two related decision levels: (I the furnace scheduling of metal alloy production, and (2) moulding machine planning which specifies the type and size of production lots. A mixed integer programming (MIP) formulation of the problem is proposed, but is impractical to solve in reasonable computing time for non-small instances. As a result, a faster relax-and-fix (RF) approach is developed that can also be used on a rolling horizon basis where only immediate-term schedules are implemented. As well as a MIP method to solve the basic RF approach, three variants of a local search method are also developed and tested using instances based on the literature. Finally, foundry-based tests with a real-order book resulted in a very substantial reduction of delivery delays and finished inventory, better use of capacity, and much faster schedule definition compared to the foundry`s own practice. (c) 2006 Elsevier Ltd. All rights reserved.