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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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: (1) 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. © 2006 Elsevier Ltd. All rights reserved.

Heuristics and meta-heuristics for lot sizing and scheduling in the soft drinks industry: A comparison study

This chapter studies a two-level production planning problem where, on each level, a lot sizing and scheduling problem with parallel machines, capacity constraints and sequence-dependent setup costs and times must be solved. The problem can be found in soft drink companies where the production process involves two interdependent levels with decisions concerning raw material storage and soft drink bottling. Models and solution approaches proposed so far are surveyed and conceptually compared. Two different approaches have been selected to perform a series of computational comparisons: an evolutionary technique comprising a genetic algorithm and its memetic version, and a decomposition and relaxation approach. © 2008 Springer-Verlag Berlin Heidelberg.

Evaluating genetic algorithms with different population structures on a lot sizing and scheduling problem

This paper studies the use of different population structures in a Genetic Algorithm (GA) applied to lot sizing and scheduling problems. The population approaches are divided into two types: single-population and multi-population. The first type has a non-structured single population. The multi-population type presents non-structured and structured populations organized in binary and ternary trees. Each population approach is tested on lot sizing and scheduling problems found in soft drink companies. These problems have two interdependent levels with decisions concerning raw material storage and soft drink bottling. The challenge is to simultaneously determine the lot sizing and scheduling of raw materials in tanks and products in lines. Computational results are reported allowing determining the better population structure for the set of problem instances evaluated. Copyright 2008 ACM.

Tabu search to solve the Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem

This paper proposes a tabu search approach to solve the Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem (SITLSP). It is a real-world problem, often found in soft drink companies, where the production process has two integrated levels with decisions concerning raw material storage and soft drink bottling. Lot sizing and scheduling of raw materials in tanks and products in bottling lines must be simultaneously determined. Real data provided by a soft drink company is used to make comparisons with a previous genetic algorithm. Computational results have demonstrated that tabu search outperformed genetic algorithm in all instances. Copyright 2011 ACM.

A priori reformulations for joint rolling-horizon scheduling of materials processing and lot-sizing problem

In many production processes, a key material is prepared and then transformed into different final products. The lot sizing decisions concern not only the production of final products, but also that of material preparation in order to take account of their sequence-dependent setup costs and times. The amount of research in recent years indicates the relevance of this problem in various industrial settings. In this paper, facility location reformulation and strengthening constraints are newly applied to a previous lot-sizing model in order to improve solution quality and computing time. Three alternative metaheuristics are used to fix the setup variables, resulting in much improved performance over previous research, especially regarding the use of the metaheuristics for larger instances. © 2013 Elsevier Ltd. All rights reserved.

The integrated lot sizing and cutting stock problem in a furniture factory

This work studies the integrated lot sizing and cutting stock problem, where the goal is to capture the dependency that exists between two important decisions in the production process, in order to economize raw materials and also reduce production and inventory costs. The integrated lot sizing and cutting stock problem is studied in a small furniture factory that produces wardrobes, dressing tables and cupboards and the lot sizing and cutting stock decisions are taken by the production manager. A column-generation technique is used to solve a linear relaxation of the proposed model. The computational results, using real data from the factory, show that it is possible to reduce total inventory and raw material costs when integrated planning is used. © 2013 IFAC.

Production lot sizing and scheduling with non-triangular sequence-dependent setup times

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Reformulation and a Lagrangian heuristic for lot sizing problem on parallel machines

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Integrated cutting machine programming and lot sizing in furniture industry

In this paper a mathematical model that combines lot-sizing and cutting-stock problems applied to the furniture industry is presented. The model considers the usual decisions of the lot sizing problems, as well as operational decisions related to the cutting machine programming. Two sets of a priori generated cutting patterns are used, industry cutting patterns and a class of n-group cutting patterns. A strategy to improve the utilization of the cutting machine is also tested. An optimization package was used to solve the model and the computational results, using real data from a furniture factory, show that a small subset of n-group cutting patterns provides good results and that the cutting machine utilization can be improved by the proposed strategy.

Electric consumption in SHSs in rural communities of brazil and Peru and recommendations for sizing

The lack of data records of electric power consumption of smallphotovoltaic home systems, independently of the method used for sizing them, drives to consider the demand as a constant. However, the existing data reveal the variability of the consumption due to the influences of some social, cultural and psychosocial aspects of the human groups. This paper presents records of consumption data obtainedfrom several solar home systems (SHSs) in Brazil and Peru, and it discusses about the Gamma distribution function that can express to a great extent the behaviour of the demand. By this analysis it was verified that `a lot of people consume little and few people consume a lot`. In that sense, a few recommendations for sizing procedures that can be useful in the implantation of extensive programmes of rural electrification by SHSs are presented. Copyright (c) 2007 John Wiley & Sons, Ltd.

Asynchronous teams for joint lot-sizing and scheduling problem in flow shops

The integrated production scheduling and lot-sizing problem in a flow shop environment consists of establishing production lot sizes and allocating machines to process them within a planning horizon in a production line with machines arranged in series. The problem considers that demands must be met without backlogging, the capacity of the machines must be respected, and machine setups are sequence-dependent and preserved between periods of the planning horizon. The objective is to determine a production schedule to minimise the setup, production and inventory costs. A mathematical model from the literature is presented, as well as procedures for obtaining feasible solutions. However, some of the procedures have difficulty in obtaining feasible solutions for large-sized problem instances. In addition, we address the problem using different versions of the Asynchronous Team (A-Team) approach. The procedures were compared with literature heuristics based on Mixed Integer Programming. The proposed A-Team procedures outperformed the literature heuristics, especially for large instances. The developed methodologies and the results obtained are presented.

Three time-based scale formulations for the two-stage lot sizing and scheduling in process industries

In this paper, we propose three novel mathematical models for the two-stage lot-sizing and scheduling problems present in many process industries. The problem shares a continuous or quasi-continuous production feature upstream and a discrete manufacturing feature downstream, which must be synchronized. Different time-based scale representations are discussed. The first formulation encompasses a discrete-time representation. The second one is a hybrid continuous-discrete model. The last formulation is based on a continuous-time model representation. Computational tests with state-of-the-art MIP solver show that the discrete-time representation provides better feasible solutions in short running time. On the other hand, the hybrid model achieves better solutions for longer computational times and was able to prove optimality more often. The continuous-type model is the most flexible of the three for incorporating additional operational requirements, at a cost of having the worst computational performance. Journal of the Operational Research Society (2012) 63, 1613-1630. doi:10.1057/jors.2011.159 published online 7 March 2012

Models for capacitated lot-sizing problem with backlogging, setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.

TANK SIZING AND OPTIMIZING LOOP PLACEMENT IN A BRANCHED WATER DISTRIBUTION SYSTEM

More than eighteen percent of the world’s population lives without reliable access to clean water, forced to walk long distances to get small amounts of contaminated surface water. Carrying heavy loads of water long distances and ingesting contaminated water can lead to long-term health problems and even death. These problems affect the most vulnerable populations, women, children, and the elderly, more than anyone else. Water access is one of the most pressing issues in development today. Boajibu, a small village in Sierra Leone, where the author served in Peace Corps for two years, lacks access to clean water. Construction of a water distribution system was halted when a civil war broke out in 1992 and has not been continued since. The community currently relies on hand-dug and borehole wells that can become dirty during the dry season, which forces people to drink contaminated water or to travel a far distance to collect clean water. This report is intended to provide a design the system as it was meant to be built. The water system design was completed based on the taps present, interviews with local community leaders, local surveying, and points taken with a GPS. The design is a gravity-fed branched water system, supplied by a natural spring on a hill adjacent to Boajibu. The system’s source is a natural spring on a hill above Boajibu, but the flow rate of the spring is unknown. There has to be enough flow from the spring over a 24-hour period to meet the demands of the users on a daily basis, or what is called providing continuous flow. If the spring has less than this amount of flow, the system must provide intermittent flow, flow that is restricted to a few hours a day. A minimum flow rate of 2.1 liters per second was found to be necessary to provide continuous flow to the users of Boajibu. If this flow is not met, intermittent flow can be provided to the users. In order to aid the construction of a distribution system in the absence of someone with formal engineering training, a table was created detailing water storage tank sizing based on possible source flow rates. A builder can interpolate using the source flow rate found to get the tank size from the table. However, any flow rate below 2.1 liters per second cannot be used in the table. In this case, the builder should size the tank such that it can take in the water that will be supplied overnight, as all the water will be drained during the day because the users will demand more than the spring can supply through the night. In the developing world, there is often a problem collecting enough money to fund large infrastructure projects, such as a water distribution system. Often there is only enough money to add only one or two loops to a water distribution system. It is helpful to know where these one or two loops can be most effectively placed in the system. Various possible loops were designated for the Boajibu water distribution system and the Adaptive Greedy Heuristic Loop Addition Selection Algorithm (AGHLASA) was used to rank the effectiveness of the possible loops to construct. Loop 1 which was furthest upstream was selected because it benefitted the most people for the least cost. While loops which were further downstream were found to be less effective because they would benefit fewer people. Further studies should be conducted on the water use habits of the people of Boajibu to more accurately predict the demands that will be placed on the system. Further population surveying should also be conducted to predict population change over time so that the appropriate capacity can be built into the system to accommodate future growth. The flow at the spring should be measured using a V-notch weir and the system adjusted accordingly. Future studies can be completed adjusting the loop ranking method so that two users who may be using the water system for different lengths of time are not counted the same and vulnerable users are weighted more heavily than more robust users.