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Joint optimization of lot-sizing and pricing with backlogging

COMPUTERS & INDUSTRIAL ENGINEERING 2022年 167卷

作者： Liu, Ming Tang, Hao Chu, Feng Zheng, Feifeng Chu, Chengbin Tongji Univ Sch Econ & Management Shanghai Peoples R China Univ Paris Saclay Univ Evry IBISC Evry France Donghua Univ Glorious Sun Sch Business & Management Shanghai Peoples R China Univ Gustave Eiffel ESIEE Paris F-93162 Noisy Le Grand France Lab GRETTIA COSYS F-93162 Noisy Le Grand France

Lot-sizing and pricing are two important manufacturing decisions that impact together the profit of a company. Existing works address the joint lot-sizing and pricing problem without backlogging, although it is a usual strategy that permits to satisfy customer demand with delay. In this work, we study a new multi-product joint lot-sizing and pricing problem with backlogging and limited production capacity. The objective is to maximize the total company profit over a finite planning horizon. For the problem, a mixed integer nonlinear programming (MINLP) formulation is given. Then, several optimality properties are provided and a tighter MINLP model is established based on these properties. According to the NP-hard nature and non-linearity of the model, a model based heuristic that focuses on efficiently solving small-sized instances is proposed and a genetic algorithm (GA) with new progressive repair strategy is developed to address large-sized instances. Managerial insights are drawn based an illustrative example. Numerical experiments are conducted on 64 benchmark based instances and 105 randomly generated instances with up to 10 products and 12 periods, which validates the MINLP formulation and shows the efficiency of the proposed solution methods.

关键词： Lot-sizing Pricing Backlogging Optimality property mixed integer nonlinear programming Genetic algorithm

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Sustainable reverse logistics optimization with triple bottom line approach: An integration of disassembly line balancing

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JOURNAL OF CLEANER PRODUCTION 2020年 270卷 122475-122475页

作者： Budak, Aysenur Gebze Tech Univ Ind Engn Dept Gebze Turkey

The objective of this study is to develop the sustainable reverse logistics network with integration of disassembly line balancing to examine decisions in view of Triple Bottom Line. The Triple Bottom Line approach is a framework that considers three strategies which are economic, environmental, and social. Disassembly has great importance in reverse logistics operations. Therefore, disassembly line balancing approach has been integrated into sustainable reverse logistics network problem for the first time. A Multi period Multi-Objective mixed integer nonlinear programming model is proposed and solved with Improved Augmented Epsilon Constraint (AUGMECON-2) technique. Pareto optimal solution set is obtained. In order to demonstrate the applicability of the suggested model, developed solution procedure has been applied on end of life mobile phone recycling network. Objectives are indicated as social impact maximization, economic and environmental effect minimization. This study is applied for a three-year time period. Disassembly processes are also taken into account. The model respectively determines: (i) optimal quantity of WEEE between the facilities and inventory amounts, (ii) the number of workstations in disassembly centers (iii) the number of facilities that will be opened (iv) optimal task assignments to workstations in disassembly centers. Sensitivity analysis is proposed to examine the impact of incremental changes in WEEE amounts on the sustainable reverse logistics network. According to each scenario the number of changes in facilities, objective function values and tasks assigned to workstations are specified. This developed model could offer managers to take strategic decisions in recycling processes with regard to environmental and social impact and help to gain managerial insights as well. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Sustainable reverse logistics mixed integer nonlinear programming Multi objective optimization Triple bottom line Disassembly line balancing

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Combining Mathematical programming and SysML for Automated Component Sizing of Hydraulic Systems

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JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING 2012年第4期12卷 41006-41006页

作者： Shah, Aditya A. Paredis, Christiaan J. J. Burkhart, Roger Schaefer, Dirk Deere & Co Dubuque IA 52001 USA Georgia Inst Technol George W Woodruff Sch Mech Engn Atlanta GA 30332 USA Deere & Co Moline IL 61265 USA Georgia Inst Technol George W Woodruff Sch Mech Engn Savannah GA 31407 USA

In this paper, we present a framework for automated component sizing to extend a designer's ability to evaluate a particular configuration during the architecture exploration phase of a design process. Component sizing is a hard problem to solve, both from a computational and modeling aspect. This is because of competing objectives, requirements from multiple disciplines, and the need to find a good solution quickly for the architecture being considered. In current approaches, designers rely on heuristics and iterate over the multiple objectives and requirements until a satisfactory solution is found. To improve on this state of practice, we introduce advances in the following two areas: (a) solving the problem efficiently so that all of the imposed requirements are satisfied simultaneously and the solution obtained is mathematically optimal and (b) modeling a component sizing problem in a manner that is convenient to designers. An acausal, algebraic, equation-based, declarative modeling approach using mathematical programming (GAMS) is taken to solve these problems more efficiently. The object management group systems modeling language (OMG SysML (TM)) is used to model component sizing problems in order to facilitate problem formulation, model reuse and automatic generation of low-level code that can be solved using GAMS and its solvers. This framework is demonstrated by applying it to an example of a hydraulic log splitter. Based on this initial example, we discuss two advantages of this framework-total time taken in solving multiple scenarios for a given configuration and the graphical representation of a problem in SysML. [DOI: 10.1115/1.4007764]

关键词： Component sizing constraint satisfaction problems systems modeling language SysML mixed integer nonlinear programming CSP model transformations algebraic equations GAMS BARON

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Facility Location-Network Design Problem: Reliability and Investment Budget Constraint

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JOURNAL OF URBAN PLANNING AND DEVELOPMENT 2014年第3期140卷 04014005-04014005页

作者： Shishebori, Davood Jabalameli, Mohammad Saeed Jabbarzadeh, Armin Iran Univ Sci & Technol Dept Ind Engn Tehran Iran

The simultaneous consideration of combined facility location and network design is an attractive empirical topic for locating public and private facilities and for reducing transportation costs. Moreover, applying a reliable facility location problem is one of the most effective ways to protect against occasional failures of the system, because of considering unexpected failures and possible customer reassignment when locating facilities. Accordingly, this study concerns a reliable combined facility location-network design problem regarding the investment budget constraint and proposes a mixed integer nonlinear programming formulation to model this constraint. The proposed model is linearized by suitable techniques. Also, a practical case study subject to sustainable design in urban health care development is presented in detail to illustrate the application of the proposed mathematical model. Finally, a sensitivity analysis is conducted to provide insights into the behavior of the proposed model in response to the changes of key parameters of the problem. (C) 2014 American Society of Civil Engineers.

关键词： Facility location Network design Urban transportation planning Facility reliability Investment budget constraint Health care Case study mixed integer nonlinear programming

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Incremental design of water symbiosis networks with prior knowledge: The case of an industrial park in Kenya

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SCIENCE OF THE TOTAL ENVIRONMENT 2021年 751卷 141706-141706页

作者： Ramin, Elham Bestuzheva, Ksenia Gargalo, Carina L. Ramin, Danial Schneider, Carina Ramin, Pedram Flores-Alsina, Xavier Andersen, Maj M. Gernaey, Krist V. Tech Univ Denmark Dept Chem & Biochem Engn Lyngby Denmark Konrad Zuse Ctr Comp Sci & Appl Math Berlin ZIB Berlin Germany CNR Inst Intelligent Ind Technol & Syst Adv Mfg Milan Italy Tech Univ Denmark Dept Environm Engn Lyngby Denmark Univ Copenhagen Dept Geosci & Nat Resource Management Copenhagen Denmark

Industrial parks have a high potential for recycling and reusing resources such as water across companies by creating symbiosis networks. In this study, we introduce a mathematical optimization framework for the design of water network integration in industrial parks formulated as a large-scale standard mixed-integer non-linear programming (MINLP) problem. The novelty of our approach relies on i) developing a multi-level incremental optimization framework for water network synthesis, ii) including prior knowledge of water demand growth and projected water scarcity to evaluate the significance of water-saving solutions, iii) incorporating a comprehensive formulation of the water network synthesis problem including multiple pollutants and different treatment units and iv) performing a multi-objective optimization of the network including freshwater savings and relative cost of the network. The significance of the proposed optimization framework is illustrated by applying it to an existing industrial park in a water-scarce region in Kenya. Firstly, we illustrated the benefits of including prior knowledge to prevent an over-design of the network at the early stages. In the case study, we achieved a more flexible and expandable water network with 36% lower unit cost at the early stage and 15% lower unit cost at later stages for overall maximum freshwater savings of 25%. Secondly, multi-objective analysis suggests an optimum freshwater savings of 14% to reduce the unit cost of the network by half. Moreover, the significance of symbiosis networks is highlighted by showing that intra-company connections can only achieve a maximum freshwater savings of 17% with significantly higher unit cost (+45%). Finally, we showed that the values of symbiosis connectivity index in the Pareto front correspond to higher freshwater savings, indicating the significant role of the symbiosis network in the industrial park under study. This is the first study, where all the above elements have

关键词： Wastewater treatment Water scarcity Membranes Circular economy mixed integer nonlinear programming Water network integration

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COMPARISON BETWEEN FIVE MINLP SOLVERS AND NEW RESULTS RELATED TO TRIGONOMETRIC FUNCTIONS

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FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2022年第10期30卷 2240249-2240249页

作者： Alkhalifa, Loay Qassim Univ Dept Math Coll Arts & Sci Ar Rass 51921 Saudi Arabia

Due to the rapid development of algorithms and techniques that are used to deal with mixed integer nonlinear programming (MINLP) problems, many global MINLP solvers were introduced. In this paper, computational experiments were done to compare between the performances of five of these solvers. Some of these solvers do not support trigonometric functions. Therefore, piecewise linear approximation (PLA) is applied to problems having these function so the solvers can deal with these problems. Additional computational tests were performed on to show how PLA can be useful, even to some powerful global solvers.

关键词： mixed integer nonlinear programming Piecewise Linear Approximation Branch and Bound Outer Approximation

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Near-optimal time series sampling based on the reduced Hessian

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AICHE JOURNAL 2020年第7期66卷 e16248-e16248页

作者： Chen, Weifeng Biegler, Lorenz T. Zhejiang Univ Technol Coll Informat Engn Hangzhou Peoples R China Carnegie Mellon Univ Dept Chem Engn Ctr Adv Proc Decis Making 5000 Forbes Ave Pittsburgh PA 15213 USA

A model-based experimental design strategy is developed to select a minimal set of measured points from a time series of experiments. Based on reduced Hessian information embedded within a mixed integer nonlinear program, an optimal time series is determined that leads to well-fitted models, with ratios of parameter standard deviation to estimated value within acceptable bounds. Demonstrated on three examples, the proposed approach is effective and efficient especially for time-consuming and expensive measurements.

关键词： experimental design mixed integer nonlinear programming nonlinear optimization parameter estimation

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Mathematical programming Methods for Pressure Management in Water Distribution Systems

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Procedia Engineering 2015年 119卷 937-946页

作者： Filippo Pecci Edo Abraham Ivan Stoianov InfraSense Labs Department of Civil and Environmental Engineering Imperial College London South Kensington Campus London SW7 2AZ UK.

In this paper, we survey mathematical programming methods for the management of pressure in water distribution systems through optimal placement and operation of control valves. The optimization framework addresses the minimization of average zone pressure under multiple demand scenarios, enforcing hydraulic equations as nonlinear constraints. Binary variables are used to model the placement of valves. The derived nonlinear optimization problem is a non-convex MINLP. We implement and evaluate a direct MINLP solver and two different reformulation methods for MINLPs that solve sequences of regular NLPs. Moreover, we investigate the solutions under different design and operation loading conditions.

关键词： Water distribution systems valve placement mathematical optimization mixed integer nonlinear programming pressure management.

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Optimal policies for finite horizon model with time-varying demand rate, non-instantaneous deterioration and backlogging

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE-OPERATIONS & LOGISTICS 2023年第1期10卷 Article: 2041128页

作者： Almathkour, Fatmah Benkherouf, Lakdere Kuwait Univ Coll Sci Dept Stat & Operat Res POB 5969 Kuwait 13060 Kuwait

This paper is concerned with the problem of finding an optimal replenishment policy for a finite planning horizon inventory model with time-varying demand, non-instantaneous deteriorating items and backlogging. This is formulated as a problem of solving some mixed integer non-linear program whose optimal solution delivers the frequency of orders as well as the timing of orders. The phenomena of non-instantaneous deterioration introduce a non-smoothness in the objective function which makes direct application of existing results, in the literature, not possible to the present model. A complete mathematical analysis of the problem is undertaken to overcome the non-smoothness of the objective and derive the optimal inventory policy. Uniqueness of the policy is shown under some technical conditions. Numerical results are presented for illustration.

关键词： Inventory model finite time horizon optimal schedule mixed integer nonlinear programming submodular function

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A Decision-Making Model to Determine Dynamic Facility Locations for a Disaster Logistic Planning Problem Using Deep Learning

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ALGORITHMS 2023年第10期16卷 468-468页

作者： Tanti, Lili Efendi, Syahril Lydia, Maya Silvi Mawengkang, Herman Univ Sumatera Utara Fac Comp Sci & Informat Technol Medan 20155 Indonesia Univ Sumatera Utara Fac Math & Sci Medan 20155 Indonesia

Disaster logistics management is vital in planning and organizing humanitarian assistance distribution. The planning problem faces challenges, such as coordinating the allocation and distribution of essential resources while considering the severity of the disaster, population density, and accessibility. This study proposes an optimized disaster relief management model, including distribution center placement, demand point prediction, prohibited route mapping, and efficient relief goods distribution. A dynamic model predicts the location of post-disaster distribution centers using the K-Means method based on impacted demand points' positions. Artificial Neural Networks (ANN) aid in predicting assistance requests around formed distribution centers. The forbidden route model maps permitted and prohibited routes while considering constraints to enhance relief supply distribution efficacy. The objective function aims to minimize both cost and time in post-disaster aid distribution. The model deep location routing problem (DLRP) effectively handles mixed nonlinear multi-objective programming, choosing the best forbidden routes. The combination of these models provides a comprehensive framework for optimizing disaster relief management, resulting in more effective and responsive disaster handling. Numerical examples show the model's effectiveness in solving complex humanitarian logistics problems with lower computation time, which is crucial for quick decision making during disasters.

关键词： artificial neural network deep learning K-means location routing problem mixed integer nonlinear programming

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