scholarly journals Mathematical modeling to optimize production planning and scheduling in a small foundry with multiple alternating furnaces

2021 ◽  
Vol 16 (04) ◽  
pp. 82-114
Author(s):  
Michael Ferreira Bertulucci ◽  
Giovanna Abreu Alves ◽  
Victor Claudio Bento de Camargo
Keyword(s):  
Mathematical Modeling ◽  
Lot Sizing ◽  
Load Capacity ◽  
Mixed Integer ◽  
Suitable Model ◽  
Extended Model ◽  
Lot Size ◽  
Planning And Scheduling ◽  
Actual Application ◽  
Lot Sizing And Scheduling

Purpose - This study presents an extension to a model in the literature for lot-sizing and scheduling in a small foundry with multiple alternate furnaces. The purpose of the model is to minimize delays and inventory costs. In addition, it determines the best use of the load capacity in the furnaces. Theoretical framework – Lot-sizing in foundries in the marketplace is a subject of academic interest due to its applicability and mathematical and computational complexity. Many papers address the production problem in foundries with a single furnace, however, few papers address the possibility of multiple furnaces. Design/methodology/approach - Mathematical modeling was used to represent the lot-sizing and scheduling problem in a small foundry. Data from the company's order books were collected and model validation questionnaires were applied. Findings - The extended model was able to generate good production plans at different planning horizons, with better performance than the current methods obtained by the company. Originality/value - the extension of the model contributes to the literature by addressing the existence of multiple non-simultaneous furnaces, a feature that has not been greatly explored. A comparison with other models is performed to indicate the most suitable model for actual application. Keywords: Alloys scheduling. Foundry. Lot size. Mixed integer programming.

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.

Optimization Methods for Lot-Sizing Problem in an Automated Foundry

2013 ◽  
Vol 58 (3) ◽  
pp. 863-866 ◽  
Author(s):  
J. Duda ◽  
A. Stawowy
Keyword(s):  
Production Planning ◽  
Lot Sizing ◽  
Planning Horizon ◽  
Optimization Methods ◽  
Mixed Integer ◽  
Planning Problem ◽  
Lot Size ◽  
Mip Model ◽  
Production Planning Problem ◽  
Problem Instances

Abstract In the paper we studied a production planning problem in a mid-size foundry that provides tailor-made cast products in small lots for a large number of clients. Assuming that a production bottleneck is the furnace, a mixed-integer programming (MIP) model is proposed to determine the lot size of the items and the required alloys to be produced during each period of the finite planning horizon that is subdivided into smaller periods. As using an advanced commercial MIP solvers may be impractical for more complex and large problem instances, we proposed and compared a few computational intelligence heuristics i.e. tabu search, genetic algorithm and differential evolution. The examination showed that heuristic approaches can provide a good compromise between speed and quality of solutions and can be used in real-world production planning.

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 Optimizing Inventory Replenishment for Seasonal Demand with Discrete Delivery Times

2021 ◽  
Vol 11 (23) ◽  
pp. 11210
Author(s):  
Mohammed Alnahhal ◽  
Diane Ahrens ◽  
Bashir Salah
Keyword(s):  
Lot Sizing ◽  
Planning Horizon ◽  
Service Level ◽  
Mixed Integer ◽  
Lot Size ◽  
Dynamic Planning ◽  
Holding Costs ◽  
Delivery Times ◽  
Mip Model ◽  
Total Inventory

This study investigates replenishment planning in the case of discrete delivery time, where demand is seasonal. The study is motivated by a case study of a soft drinks company in Germany, where data concerning demand are obtained for a whole year. The investigation focused on one type of apple juice that experiences a peak in demand during the summer. The lot-sizing problem reduces the ordering and the total inventory holding costs using a mixed-integer programming (MIP) model. Both the lot size and cycle time are variable over the planning horizon. To obtain results faster, a dynamic programming (DP) model was developed, and run using R software. The model was run every week to update the plan according to the current inventory size. The DP model was run on a personal computer 35 times to represent dynamic planning. The CPU time was only a few seconds. Results showed that initial planning is difficult to follow, especially after week 30, and the service level was only 92%. Dynamic planning reached a higher service level of 100%. This study is the first to investigate discrete delivery times, opening the door for further investigations in the future in other industries.

scholarly journals Joint lot sizing and scheduling of a multi-product multi-period supply chain

2019 ◽  
Vol 10 (5) ◽  
pp. 1516
Author(s):  
Ahmed Othman El-meehy ◽  
Amin K. El-Kharbotly ◽  
Mohammed M. El-Beheiry
Keyword(s):  
Supply Chain ◽  
Lot Sizing ◽  
Raw Materials ◽  
Supply Chain Design ◽  
Raw Material ◽  
Design Parameters ◽  
Distribution Centers ◽  
Lot Size ◽  
Holding Cost ◽  
Lot Sizing And Scheduling

The joint lot sizing and scheduling problem can be considered as an evolvement of the joint economic lot size problem which has drawn researchers’ interests for decades. The objective of this paper is to find the effect of a capacitated multi-period supply chain design parameters on joint lot sizing and scheduling decisions for different holding and penalty costs. The supply chain deals with two raw materials suppliers. The production facility produces two products which are shipped to customers through distribution centers. A mathematical model is developed to determine optimum quantities of purchased raw materials, production schedule (MPS), delivered quantities and raw material and products inventory for predetermined number of periods. The model is solved to maximize total supply chain profits. Results showed that at high capacity and low holding cost, the supply chain tends to produce only one product each period, for limited capacity and high value of holding cost, the supply chain may produce the two products together each period.

scholarly journals Study on column generation for the lot-sizing and scheduling problem with sequencedependent setup time

2018 ◽  
Vol 189 ◽  
pp. 06002
Author(s):  
Dandan Zhang ◽  
Canrong Zhang
Keyword(s):  
Lot Sizing ◽  
Setup Time ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Optimal Solutions ◽  
Sequence Dependent ◽  
Sequence Dependent Setup Time ◽  
Capacitated Lot Sizing ◽  
Sequence Dependent Setup ◽  
Lot Sizing And Scheduling

The capacitated lot-sizing and scheduling problem with sequence-dependent setup time and carryover setup state is a challenge problem in the semiconductor assembly and test manufacturing. For the problem, a new mixed integer programming model is proposed, followed by exploring its relative efficiency in obtaining optimal solutions and linearly relaxed optimal solutions. On account of the sequence-dependent setup time and the carryover of setup states, a per-machine Danzig Wolfe decomposition is proposed. We then build a statistical estimation model to describe correlation between the optimal solutions and two lower bounds including the linear relaxation solutions, and the pricing sub-problem solutions of Danzig Wolfe decomposition, which gives insight on the optimal values about information regarding whether or not the setup variables in the optimal solution take the value of 1, and the information is further used in the branch and select procedure. Numerical experiments are conducted to test the performance of the algorithm.

General lot-sizing and scheduling for perishable food products

2020 ◽  
Vol 54 (3) ◽  
pp. 913-931 ◽  
Author(s):  
Zohreh Alipour ◽  
Fariborz Jolai ◽  
Ehsan Monabbati ◽  
Nima Zaerpour
Keyword(s):  
Lot Sizing ◽  
Food Products ◽  
Production Costs ◽  
Mixed Integer ◽  
Computational Time ◽  
Scheduling Problem ◽  
Solution Quality ◽  
Perishable Product ◽  
Tactical Decision ◽  
Lot Sizing And Scheduling

General lot-sizing and scheduling is a well-studied problem in the literature, but for perishable or time-sensitive products is less investigated. Also, most of studies on perishable product supply chains focus on strategic and tactical decision levels rather than operational decision level and integrated operational and tactical decision levels. We focus on a general lot-sizing and scheduling problem faced by perishable food products. The lifespan and shelf life are two important key features of perishable products that are considered in the problem. This problem can be described as a multi-product, multi-parallel line, multi-period general lot-sizing and scheduling problem with sequence dependent change over time. The objective function is sum of production costs, inventory holding costs, waste costs, and lifespan related cost function. We apply two mixed-integer programming based heuristics to solve generated instances. The heuristics are compared in terms of solution quality and computational time. Also, the sensitivity analysis is presented to analyze the effects of parameters’ changes.

scholarly journals Optimization models for a lot sizing and scheduling problem on parallel production lines that share scarce resources

2021 ◽  
Author(s):  
Willy Alves de Oliveira Soler ◽  
Maristela Oliveira Santos ◽  
Maria do Socorro Nogueira Rangel
Keyword(s):  
Lot Sizing ◽  
Computational Study ◽  
Mixed Integer ◽  
Optimization Models ◽  
Scheduling Problem ◽  
Production Lines ◽  
Commodity Flow ◽  
Scarce Resources ◽  
Computational Performance ◽  
Lot Sizing And Scheduling

The purpose of this paper is to propose mathematical models to represent a lot sizing and scheduling problem on multiple production lines that share scarce resources and to investigate the computational performance of the proposed models. The main feature that differentiates this problem from others in the literature is that the decision on which lines to organize should be taken considering the availability of the necessary resources. The optimization criterion is the minimization of the costs incurred in the production process (inventory, backlogging, organization of production lines, and sequence-dependent setup costs). Nine mixed integer optimization models to represent the problem are given and, also, the results of an extensive computational study carried out using a set of instances from the literature. The computational study indicates that an efficient formulation, able to provide high quality solutions for large sized instances, can be obtained from a classical model by making the binary production variables explicit, using the facility location reformulation as well as the single commodity flow constraints to eliminate subsequences. Moreover, from the results, it is also clear that the consideration of scarce resources makes the problem significantly more difficult than the traditional one.

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