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11 – 20 of over 2000
Article
Publication date: 12 June 2009

Ralf Östermark

To discuss a new parallel algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.

Abstract

Purpose

To discuss a new parallel algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.

Design/methodology/approach

The platform combines features from classical non‐linear optimization methodology with novel innovations in computational techniques. The system constructs discrete search zones around noninteger discrete‐valued variables at local solutions, which simplifies the local optimization problems and reduces the search process significantly. In complicated problems fast feasibility restoration may be achieved through concentrated Hessians. The system is programmed in strict ANSI C and can be run either stand alone or as a support library for other programs. File I/O is designed to recognize possible usage in both single and parallel processor environments. The system has been tested on Alpha, Sun and Linux mainframes and parallel IBM and Cray XT4 supercomputer environments. The constrained problem can, for example, be solved through a sequence of first order Taylor approximations of the non‐linear constraints and feasibility restoration utilizing Hessian information of the Lagrangian of the MINLP problem, or by invoking a nonlinear solver like SQP directly in the branch and bound tree. minlp_machine( ) has been tested as a support library to genetic hybrid algorithm (GHA). The GHA(minlp_machine) platform can be used to accelerate the performance of any linear or non‐linear node solver. The paper introduces a novel multicomputer partitioning of the discrete search space of genuine MINLP‐problems.

Findings

The system is successfully tested on a small sample of representative MINLP problems. The paper demonstrates that – through concurrent nonlinear branch and bound search – minlp_machine( ) outperforms some recent competing approaches with respect to the number of nodes in the branch and bound tree. Through parallel processing, the computational complexity of the local optimization problems is reduced considerably, an important aspect for practical applications.

Originality/value

This paper shows that binary‐valued MINLP‐problems will reduce to a vector of ordinary non‐linear programming on a suitably sized mesh. Correspondingly, INLP‐ and ILP‐problems will require no quasi‐Newton steps or simplex iterations on a compatible mesh.

Details

Kybernetes, vol. 38 no. 6
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 15 February 2008

Amy H.I. Lee and He‐Yau Kang

This paper seeks to construct a model for inventory management for multiple periods. The model considers not only the usual parameters, but also price quantity discount, storage…

1394

Abstract

Purpose

This paper seeks to construct a model for inventory management for multiple periods. The model considers not only the usual parameters, but also price quantity discount, storage and batch size constraints.

Design/methodology/approach

Mixed 0‐1 integer programming is applied to solve the multi‐period inventory problem and to determine an appropriate inventory level for each period. The total cost of materials in the system is minimized and the optimal purchase amount in each period is determined.

Findings

The proposed model is applied in colour filter inventory management in thin film transistor‐liquid crystal display (TFT‐LCD) manufacturing because colour filter replenishment has the characteristics of price quantity discount, large product size, batch‐sized purchase and forbidden shortage in the plant. Sensitivity analysis of major parameters of the model is also performed to depict the effects of these parameters on the solutions.

Practical implications

The proposed model can be tailored and applied to other inventory management problems.

Originality/value

Although many mathematical models are available for inventory management, this study considers some special characteristics that might be present in real practice. TFT‐LCD manufacturing is one of the most prosperous industries in Taiwan, and colour‐filter inventory management is essential for TFT‐LCD manufacturers for achieving competitive edge. The proposed model in this study can be applied to fulfil the goal.

Details

Kybernetes, vol. 37 no. 1
Type: Research Article
ISSN: 0368-492X

Keywords

Book part
Publication date: 5 May 2017

Robert J. Stawicki

Folding cartons are used in myriad consumer products. For some products, such as hair dye kits, a very high-resolution printing is required. This is typically done using a…

Abstract

Folding cartons are used in myriad consumer products. For some products, such as hair dye kits, a very high-resolution printing is required. This is typically done using a technology known as Gravure printing. Gravure printing utilizes engraved cylinders which are very expensive. As a result, the printer often combines multiple products on one set of cylinders to minimize the total number of cylinders used. Since the demand between products varies, this can result in overproduction of the low demand products. This chapter presents an integer programming formulation that assigns products across multiple sets of cylinders in order to minimize this overproduction. Sample problems, their solutions and solution times are presented.

Details

Applications of Management Science
Type: Book
ISBN: 978-1-78714-282-4

Keywords

Book part
Publication date: 3 February 2015

Ammar Y. Alqahtani and Surendra M. Gupta

Economic incentives, government regulations, and customer perspective on environmental consciousness (EC) are driving more and more companies into product recovery business, which…

Abstract

Economic incentives, government regulations, and customer perspective on environmental consciousness (EC) are driving more and more companies into product recovery business, which forms the basis for a reverse supply chain. A reverse supply chain consists a series of activities that involves retrieving used products from consumers and remanufacturing (closed-loop) or recycling (open-loop) them to recover their leftover market value. Much work has been done in the areas of designing forward and reverse supply chains; however, not many models deal with the transshipment of products in multiperiods. Linear physical programming (LPP) is a newly developed method whose most significant advantage is that it allows a decision-maker to express his/her preferences for values of criteria for decision-making in terms of ranges of different degrees of desirability but not in traditional form of weights as in techniques such as analytic hierarchy process, which is criticized for its unbalanced scale of judgment and failure to precisely handle the inherent uncertainty and vagueness in carrying out pair-wise comparisons. In this chapter, two multiperiod models are proposed for a remanufacturing system, which is an element of a Reverse Supply Chain (RSC), and illustrated with numerical examples. The first model is solved using mixed integer linear programming (MILP), while the second model is solved using linear physical programming. The proposed models deliver the optimal transportation quantities of remanufactured products for N-periods within the reverse supply chain.

Details

Applications of Management Science
Type: Book
ISBN: 978-1-78441-211-1

Keywords

Article
Publication date: 1 September 1997

S.O. Duffuaa and K.S. Al‐Sultan

Addresses the problem of maintenance planning and scheduling and reviews pertinent literature. Discusses the characteristics and the complexity of the problem. Advocates…

2594

Abstract

Addresses the problem of maintenance planning and scheduling and reviews pertinent literature. Discusses the characteristics and the complexity of the problem. Advocates mathematical programming approaches for addressing the maintenance scheduling problem. Gives examples to demonstrate the utility of these approaches. Proposes expansion of the state‐of‐the‐art maintenance management information system to utilize the mathematical programming approaches and to have better control over the maintenance scheduling problem.

Details

Journal of Quality in Maintenance Engineering, vol. 3 no. 3
Type: Research Article
ISSN: 1355-2511

Keywords

Article
Publication date: 2 March 2012

Esther Claudine Bitye Mvondo, Yves Cherruault and Jean‐Claude Mazza

The purpose of this paper is to use α‐dense curves for solving Boolean equations, 0‐1 integer programming problems such as the shortest path problem or the knapsack problem.

Abstract

Purpose

The purpose of this paper is to use α‐dense curves for solving Boolean equations, 0‐1 integer programming problems such as the shortest path problem or the knapsack problem.

Design/methodology/approach

The paper's aim is to present the applications in Boolean algebra and 0‐1 integer programming of a new method based on α‐dense curves first developed at the beginning of the 1980s by Yves Cherruault and Arthur Guillez. The α‐dense curves generalize the space filling curves (Peanocurves,…) and fractal curves. The main idea consists in expressing n variables by means of a single one.

Findings

Apply the method to Boolean algebra and 0‐1 integer programming.

Originality/value

The paper presents a new method based on α‐dense curves for solving Boolean equations and 0‐1 integer programming problems.

Article
Publication date: 28 September 2010

Wen‐Jinn Chen

In practical environments, machines subject to maintenance are prevalent in many production systems. This paper aims to find a schedule that minimizes the completion time (or…

Abstract

Purpose

In practical environments, machines subject to maintenance are prevalent in many production systems. This paper aims to find a schedule that minimizes the completion time (or equivalently, the total setup time) subject to maintenance and due dates.

Design/methodology/approach

An efficient heuristic is presented to provide the near‐optimal solution for the problem. The performance of the heuristic is evaluated by comparing its solution with the optimal solution obtained from the integer linear programming model.

Findings

In many production systems, the sequence‐dependent setup time of a job cannot be ignored when a switch between two different jobs occurs. The paper studies the sequence‐dependent setup time problem with periodic maintenance, where several maintenances are required. Computational results show that problems with larger time interval and smaller maintaining time can produce a smaller completion time.

Practical implications

Here an efficient heuristic is developed to provide the near‐optimal schedule for the problem. The proposed integer linear programming model is also presented to provide the optimal schedule. However, the proposed heuristic and the integer linear programming model developed in the paper are appropriate for those companies where maintenance is performed periodically and the sequence‐dependent setup times of their jobs are required.

Originality/value

The paper presents the heuristic and the integer linear programming model to deal with sequencing and maintenance problems.

Details

Journal of Quality in Maintenance Engineering, vol. 16 no. 4
Type: Research Article
ISSN: 1355-2511

Keywords

Article
Publication date: 26 January 2024

Mohsen Rajabzadeh, Seyed Meysam Mousavi and Farzad Azimi

This paper investigates a problem in a reverse logistics (RLs) network to decide whether to dispose of unsold goods in primary stores or re-commercialize them in outlet centers…

Abstract

Purpose

This paper investigates a problem in a reverse logistics (RLs) network to decide whether to dispose of unsold goods in primary stores or re-commercialize them in outlet centers. By deducting the costs associated with each policy from its revenue, this study aims to maximize the profit from managing unsold goods.

Design/methodology/approach

A new mixed-integer linear programming model has been developed to address the problem, which considers the selling prices of products in primary and secondary stores and the costs of transportation, cross-docking and returning unwanted items. As a result of uncertain nature of the cost and time parameters, gray numbers are used to deal with it. In addition, an innovative uncertain solution approach for gray programming problems is presented that considers objective function satisfaction level as an indicator of optimism.

Findings

According to the results, higher costs, including transportation, cross-docking and return costs, make sending goods to outlet centers unprofitable and more goods are disposed of in primary stores. Prices in primary and secondary stores heavily influence the number of discarded goods. Higher prices in primary stores result in more disposed of goods, while higher prices in secondary stores result in fewer. As a result of the proposed method, the objective function satisfaction level can be viewed as a measure of optimism.

Originality/value

An integral contribution of this study is developing a new mixed-integer linear programming model for selecting the appropriate goods for re-commercialization and choosing the best outlet center based on the products' price and total profit. Another novelty of the proposed model is considering the matching percentage of boxes with secondary stores’ desired product lists and the probability of returning goods due to non-compliance with delivery dates. Moreover, a new uncertain solution approach is developed to solve mathematical programming problems with gray parameters.

Details

Kybernetes, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 1 February 2001

A.P. Giddings, T.G. Bailey and J.T. Moore

Response surface methodology (RSM) is used for optimality analysis of the cost coefficients in mixed integer linear programming. This optimality analysis goes beyond traditional…

1879

Abstract

Response surface methodology (RSM) is used for optimality analysis of the cost coefficients in mixed integer linear programming. This optimality analysis goes beyond traditional sensitivity and parametric analysis in allowing investigation of the optimal objective function value response over pre‐specified ranges on multiple problem parameters. Design of experiments and least squares regression are used to indicate which cost coefficients have the greatest impact on the optimal total cost surface over the specified coefficient ranges. The mixed integer linear programming problems of interest are the large‐scale facility location and allocation problems in supply chain optimization. A system that automates this process for supply chain optimization at PFS Logistics Consulting is discussed and an example is presented.

Details

International Journal of Physical Distribution & Logistics Management, vol. 31 no. 1
Type: Research Article
ISSN: 0960-0035

Keywords

Article
Publication date: 1 July 2001

Mingyuan Chen

Inventory control models deal with production planning in order to minimize inventory and shortage cost, while cellular manufacturing analysis mainly addresses how machines should…

2052

Abstract

Inventory control models deal with production planning in order to minimize inventory and shortage cost, while cellular manufacturing analysis mainly addresses how machines should be grouped and parts be produced. A mathematical programming model is developed using an integrated approach for production and inventory planning in a cellular manufacturing environment. The mathematical programming model minimizes inter‐cell material handling cost, finished‐good inventory cost and system set‐up cost. The non‐linear mixed integer programming model cannot be directly solved for real size practical problems due to its NP‐complexity. A decomposition‐based heuristic algorithm was then developed to efficiently solve the integrated planning and control problem. Numerical examples are provided to test and illustrate the model and the solution method presented in this paper.

Details

Integrated Manufacturing Systems, vol. 12 no. 4
Type: Research Article
ISSN: 0957-6061

Keywords

11 – 20 of over 2000