scholarly journals Alternative Mathematical Models and Solution Approaches for Lot-Sizing and Scheduling Problems in the Brewery Industry: Analyzing Two Different Situations

2017 ◽  
Vol 2017 ◽  
pp. 1-18
Author(s):  
Tamara A. Baldo ◽  
Reinaldo Morabito ◽  
Maristela O. Santos ◽  
Luis Guimarães
Keyword(s):  
Lot Sizing ◽  
Mixed Integer ◽  
Scheduling Problems ◽  
Heuristic Solution ◽  
Planning And Scheduling ◽  
Technology Investment ◽  
Production Planning And Scheduling ◽  
Mip Models ◽  
Solution Methods ◽  
Result Analysis

This research proposes new approaches to deal with the production planning and scheduling problem in brewery facilities. Two real situations found in factories are addressed, which differ by considering (or not) the setup operations in tanks that provide liquid for bottling lines. Depending on the technology involved in the production process, the number of tank swaps is relevant (Case A) or it can be neglected (Case B). For both scenarios, new MIP (Mixed Integer Programming) formulations and heuristic solution methods based on these formulations are proposed. In order to evaluate the approach for Case A, we compare the results of a previous study with the results obtained in this paper. For the solution methods and the result analysis of Case B, we propose adaptations of Case A approaches yielding an alternative MIP formulation to represent it. Therefore, the main contributions of this article are twofold: (i) to propose alternative MIP models and solution methods for the problem in Case A, providing better results than previously reported, and (ii) to propose new MIP models and solution methods for Case B, analyzing and comparing the results and benefits for Case B considering the technology investment required.

Production Planning Considering Transfer Lot Size

2010 ◽  
Vol 44-47 ◽  
pp. 552-556
Author(s):  
Zhi Cong Zhang ◽  
Kai Shun Hu ◽  
Hui Yu Huang ◽  
Shuai Li
Keyword(s):  
Production Planning ◽  
Performance Measures ◽  
Lot Sizing ◽  
Mixed Integer ◽  
Production Plan ◽  
Lot Size ◽  
Planning And Scheduling ◽  
Production Planning And Scheduling ◽  
Lot Sizing Problem ◽  
Plan Change

Traditional methods conduct production planning and scheduling separately and solve transfer lot sizing problem between these two steps. Unfortunately, this may result in infeasibility in planning and scheduling. We take into account transfer lot size in production planning to obtain the consistency and to eliminate the gap between planning and real production. We present the detailed Transfer Lot-Based Model with mixed integer programming. Experiments show that performance measures of a production plan change remarkably with increasing of transfer lot size.

scholarly journals Extended Model Formulation of the Proportional Lot-Sizing and Scheduling Problem with Lost Demand Costs

2011 ◽  
Vol 5 (1) ◽  
pp. 49-56
Author(s):  
Waldemar Kaczmarczyk
Keyword(s):  
Lot Sizing ◽  
Valid Inequalities ◽  
Mixed Integer ◽  
Extended Model ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Model Formulation ◽  
Mip Models ◽  
Planning Problems ◽  
Lot Sizing And Scheduling

We consider mixed-integer linear programming (MIP) models of production planning problems known as the small bucket lot-sizing and scheduling problems. We present an application of a class of valid inequalities to the case with lost demand (stock-out) costs. Presented results of numerical experiments made for the the Proportional Lot-sizing and Scheduling Problem (PLSP) confirm benefits of such extended model formulation.

scholarly journals Coordinated Production Planning and Scheduling Problem in a Foundry

2017 ◽  
Vol 17 (3) ◽  
pp. 133-138
Author(s):  
A. Stawowy ◽  
J. Duda
Keyword(s):  
Production Planning ◽  
Programming Model ◽  
Mixed Integer ◽  
Medium Size ◽  
Scheduling Problem ◽  
Planning And Scheduling ◽  
Alloy Casting ◽  
Production Planning And Scheduling ◽  
Multiple Cores ◽  
Molding Shop

Abstract In the paper, we present a coordinated production planning and scheduling problem for three major shops in a typical alloy casting foundry, i.e. a melting shop, molding shop with automatic line and a core shop. The castings, prepared from different metal, have different weight and different number of cores. Although core preparation does not required as strict coordination with molding plan as metal preparation in furnaces, some cores may have limited shelf life, depending on the material used, or at least it is usually not the best organizational practice to prepare them long in advance. Core shop have limited capacity, so the cores for castings that require multiple cores should be prepared earlier. We present a mixed integer programming model for the coordinated production planning and scheduling problem of the shops. Then we propose a simple Lagrangian relaxation heuristic and evolutionary based heuristic to solve the coordinated problem. The applicability of the proposed solution in industrial practice is verified on large instances of the problem with the data simulating actual production parameters in one of the medium size foundry.

scholarly journals Application of Interval Arithmetic to Production Planning in a Foundry

2017 ◽  
Vol 17 (1) ◽  
pp. 41-44
Author(s):  
J. Duda ◽  
A. Stawowy
Keyword(s):  
Production Planning ◽  
Interval Arithmetic ◽  
Lot Sizing ◽  
Accurate Information ◽  
Test Problems ◽  
Planning And Scheduling ◽  
Production Planning And Scheduling ◽  
Scheduling Model ◽  
Novel Approach ◽  
Lot Sizing And Scheduling

Abstract A novel approach for treating the uncertainty about the real levels of finished products during production planning and scheduling process is presented in the paper. Interval arithmetic is used to describe uncertainty concerning the production that was planned to cover potential defective products, but meets customer’s quality requirement and can be delivered as fully valuable products. Interval lot sizing and scheduling model to solve this problem is proposed, then a dedicated version of genetic algorithm that is able to deal with interval arithmetic is used to solve the test problems taken from a real-world example described in the literature. The achieved results are compared with a standard approach in which no uncertainty about real production of valuable castings is considered. It has been shown that interval arithmetic can be a valuable method for modeling uncertainty, and proposed approach can provide more accurate information to the planners allowing them to take more tailored decisions.

scholarly journals Production planning and scheduling problem of continuous parallel lines with demand uncertainty and different production capacities

2020 ◽  
Vol 7 (6) ◽  
pp. 761-774
Author(s):  
Kailash Changdeorao Bhosale ◽  
Padmakar Jagannath Pawar
Keyword(s):  
Production Planning ◽  
Demand Uncertainty ◽  
Clustering Algorithm ◽  
Real Life ◽  
Initial Population ◽  
Planning Problem ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Planning And Scheduling ◽  
Production Planning And Scheduling

Abstract Production planning and scheduling problems are highly interdependent as scheduling provides optimum allocation of resources and planning is an optimum utilization of these allocated resources to serve multiple customers. Researchers have solved production planning and scheduling problems by the sequential method. But, in this case, the solution obtained by the production planning problem may not be feasible for scheduling method. Hence, production planning and scheduling problems must be solved simultaneously. Therefore, in this work, a mathematical model is developed to integrate production planning and scheduling problems. The solution to this integrated planning and scheduling problem is attempted by using a discrete artificial bee colony (DABC) algorithm. To speed up the DABC algorithm, a k-means clustering algorithm is used in the initial population generation phase. This k-means clustering algorithm will help to converge the algorithm in lesser time. A real-life case study of a soap manufacturing industry is presented to demonstrate the effectiveness of the proposed approach. An objective function to minimize overall cost, which comprises the processing cost, material cost, utility cost, and changeover cost, is considered. The results obtained by using DABC algorithm are compared with those obtained by CPLEX software. There is a saving of ₹2 23 324 for weeks 1–4 in overall cost compared with the results obtained by using CPLEX software.

Presolve Reductions in Mixed Integer Programming

2020 ◽  
Vol 32 (2) ◽  
pp. 473-506 ◽  
Author(s):  
Tobias Achterberg ◽  
Robert E. Bixby ◽  
Zonghao Gu ◽  
Edward Rothberg ◽  
Dieter Weninger
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Mixed Integer ◽  
Scheduling Problems ◽  
Planning And Scheduling ◽  
Integer Programs ◽  
Mixed Integer Programs ◽  
Key Factor ◽  
The Difference ◽  
Feasible Solutions

Mixed integer programming has become a very powerful tool for modeling and solving real-world planning and scheduling problems, with the breadth of applications appearing to be almost unlimited. A critical component in the solution of these mixed integer programs is a set of routines commonly referred to as presolve. Presolve can be viewed as a collection of preprocessing techniques that reduce the size of and, more importantly, improve the “strength” of the given model formulation, that is, the degree to which the constraints of the formulation accurately describe the underlying polyhedron of integer-feasible solutions. As our computational results will show, presolve is a key factor in the speed with which we can solve mixed integer programs and is often the difference between a model being intractable and solvable, in some cases easily solvable. In this paper we describe the presolve functionality in the Gurobi commercial mixed integer programming code. This includes an overview, or taxonomy of the different methods that are employed, as well as more-detailed descriptions of several of the techniques, with some of them appearing, to our knowledge, for the first time in the literature.

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