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A NOVEL MIXED INTEGER PROGRAMMING FORMULATION AND PROGRESSIVELY STOCHASTIC SEARCH FOR CAPACITATED lot sizing

Journal of Systems Science and Systems Engineering 2011年第2期20卷 173-192页

作者： Tao WU Defu ZHANG Yan HE Department of Industrial and Systems Engineering University of Wisconsin-Madison Madison Department of Computer Science Xiamen University 361005 China State Key Laboratory of Mechanical Transmission Chongqing University Chongqing 400030 China

The capacitated multi-level lot sizing problem is to schedule a number of different items with a bill-of-materials structure over a horizon of finite periods. To advance techniques of solving this class of problems, this paper proposes a new mixed integer programming formulation. Theoretical proofs and computational tests are provided to show that this formulation is able to provide better linear programming relaxation lower bounds than a previously-proposed strong mixed integer programming formulation. Based on the new strong formulation, a progressively stochastic search approach is proposed for solving the problem. Computational results showed that the approach generates high quality solutions, especially for problems of large sizes.

关键词： Capacitated multi-level lot sizing optimization mixed integer programming facility location

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lot sizing in Production Scheduling at a Personal Protection Equipment Company

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American Journal of Operations Research 2016年第5期6卷 378-386页

作者： José Roberto Dale Luche Rodolfo Egon Perhs Production Department Faculty of Engineering UNESP Guaratinguetá Brazil

This work presents an optimization model to support decisions during production planning and control in the personal protective equipment (PPE) industry (in particular, gloves). A case study was carried out at a Brazilian company with the aim of increasing productivity and improving customer service with respect to meeting deadlines. In this case study, the mixed integer linear programming model of Luche (2009) was revisited. A new model for single-stage lot sizing was applied to the production scheduling of gloves. Optimizing this scheduling was not a simple task because of the scale of the equipment setup time, the diversity of the products and the deadlines for the orders. The model was implemented in GAMS IDE and solved by CPLEX 12. The model and the associated heuristic produce better solutions than those currently used by the company.

关键词： lot sizing Production Planning Personal Protective Equipment

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A LAGRANGIAN RELAXATION APPROACH FOR SUPPLY CHAIN PLANNING WITH ORDER/SETUP COSTS AND CAPACITY CONSTRAINTS

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Systems Science and Systems Engineering 2003年第1期12卷 98-110页

作者： Haoxun CHEN Chengbin CHUIndustrial System Optimization Laboratory Technology University of Troyes, France Industrial System Optimization Laboratory Technology University of Troyes France

A heuristic approach is developed for supply chain planning modeled as multi-item multi-level capacitated lot sizing problems. The heuristic combines Lagrangian relaxation (LR) with local search. Different from existing LR approaches that relax capacity constraints and/or inventory balance constraints, our approach only relaxes the technical constraints that each 0-1 setup variable must take value 1 if its corresponding continuous variable is positive. The relaxed problem is approximately solved by using the simplex algorithm for linear programming, while Lagrange multipliers are updated by using a surrogate subgradient method that ensures the convergence of the dual problem in case of the approximate resolution of the relaxed problem. At each iteration, a feasible solution of the original problem is constructed from the solution of the relaxed problem. The feasible solution is further improved by a local search that changes the values of two setup variables at each time. By taking the advantages of a special structure of the lot-sizing problem, the local search can be implemented by using a modified simplex algorithm, which significantly reduces its computation time. Numerical experiments show that our approach can find very good solutions for problems of realistic sizes in a short computation time and is more effective than an existing commercial optimization code.

关键词： Supply chain planning lot sizing lagrangian relaxation local search linear programming simplex algorithm

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Inventory and sales decisions in a vendor–buyer system with imperfect items and learning in inspection

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Journal of Control and Decision 2021年第4期8卷 453-463页

作者： Wakhid Ahmad Jauhari Diah Ayu Purnasari Cucuk Nur Rosyidi Department of Industrial Engineering Universitas Sebelas MaretSurakartaIndonesia

In this study,we propose a joint economic lot-sizing model to include learning process along with errors in inspection and full backordering *** aim to study pricing and inventory decisions in a two-level supply chain involving a single vendor and a single buyer in which the demand is sensitive to price and company’s advertisement *** mathematical inventory model is developed analytically and solved using a proposed *** objective of the model is to maximise joint total profit by simultaneously determining optimal shipment size,number of deliveries,backorder quantity and product selling price.A numerical example is provided to show the application of the model and to investigate the impact of key parameter’s changes on model *** comparing the integrated/centralised model to the independent/decentralised model,we note that the integrated/centralised model provides better profit to the system,along with lower selling price and smaller amount of backorder.

关键词： lot sizing inventory model supply chain learning inspection error sensitive demand full backorder

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