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A novel robust decomposition algorithm for a profit-oriented production routing problem with backordering, uncertain prices, and service level constraints

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ANNALS OF OPERATIONS RESEARCH 2024年 1-39页

作者： Zouadi, Tarik Chargui, Kaoutar Zhani, Najlae Charles, Vincent Sreedharan, V. Raja Int Univ Rabat Rabat Business Sch BEAR Lab Technopolis Shore Rocade 11100 Sala Al Jadida Morocco Queens Univ Belfast Queens Business Sch Belfast BT9 5EE North Ireland Cardiff Metropolitan Univ Cardiff Sch Management 200 Western AveLlandaff Campus Cardiff CF5 2YB Wales Cardiff Metropolitan Univ Cardiff Sch Management Cardiff Wales Woxsen Univ Sch Business Sangareddy Telangana India

The Production Routing Problem (PRP) seeks optimal production and distribution planning that minimises costs and fulfils customer orders. Yet, existing literature often overlooks the potential impact on profitability. Achieving optimal profit does not necessarily imply meeting all customer orders. The cost-to-profit ratio should be considered when serving customer orders, as there are circumstances where it might be more profitable to cancel or backorder certain orders. Thus, this paper proposes, for the first time, a novel extension of PRP that maximises profit where demand is price-sensitive and allows order cancellation and backorders under service level targets. From on-field observations, price is inherently subject to uncertainty;thus, we propose a robust mathematical model for the problem that optimises the worst-case profit. To solve the problem, the paper proposes a decomposition algorithm that splits the problem into a master problem and a set of subproblems, enhanced by valid inequalities and warming up lower bounds to alleviate the model complexity. Through a series of computational tests, we prove the ability of the proposed algorithm to tighten the optimality gaps and alleviate computational time. An additional economic study is conducted to investigate how parameter variation affects profit and how sensitive it is to service level targets.

关键词： Production routing problem Profit maximisation Backordering decomposition algorithm Service level Robust optimisation

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A decomposition algorithm for Solving a Three Level Large Scale linear Programming Problem

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APPLIED MATHEMATICS & INFORMATION SCIENCES 2014年第5期8卷 2217-2223页

作者： Sultan, T. I. Emam, O. E. Abohany, A. A. Helwan Univ Fac Comp Sci & Informat Dept Informat Syst Cairo Egypt Telecom Egypt Director Elect Document Management Syst Human Resources Behalf Cairo Egypt

This paper presents a three level large scale linear programming problem in which the objective functions at every level are to be maximized. A three level programming problem can be thought as a static version of the Stackelberg strategy. An algorithm for solving a three planner model and a solution method for treating this problem are suggested. At each level we attempt to optimize its problem separately as a large scale programming problem using Dantzig and Wolfe decomposition method. Therefore, we handle the optimization process through a series of sub problems that can be solved independently. Finally, a numerical example is given to clarify the main results developed in this paper.

关键词： Large scale problems linear programming three-level programming decomposition algorithm

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Resilient network design of two supply chains under price competition: game theoretic and decomposition algorithm approach

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OPERATIONAL RESEARCH 2022年第1期22卷 825-857页

作者： Taleizadeh, Ata Allah Ghavamifar, Ali Khosrojerdi, Amir Univ Tehran Coll Engn Sch Ind Engn Tehran Iran

This paper utilizes a Stackelberg game approach for designing resilient supply chains under price competition and facilities disruption. The impact of using resilience strategies, namely holding extra inventory at distribution centers and considering reliable distribution centers, was investigated on the supply chains competition. A two-phase bi-level mixed integer programming approach is utilized to model the assumed problem, and a decomposition-based approach is utilized to solve the resultant model. Then, the performance of the presented model and solution approach is examined through numerical experiments. Finally, some discussions are presented with a number of examples, and managerial insights are suggested for the conditions similar to the assumed problem. Our analysis focuses on exploring the advantages of considering resilience strategies in the competitive supply chain netwrok design problems.

关键词： Pricing Resilience Disruption risks decomposition algorithm

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A decomposition algorithm for the development of multilateral strategies for environmental protection

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OR SPEKTRUM 1998年第4期20卷 269-277页

作者： Wietschel, M Ardone, A Fichtner, W Rentz, O Univ Karlsruhe Inst Industriebetriebslehre & Ind Prod D-76187 Karlsruhe Germany

In the convention on climate change as well as in other environmental protocols a co-operation between states for emission reduction is foreseen. Therefore, a investor receives a emission credit by reducing the emissions in a partner state. To integrate international co-operation approaches into national strategies, the national energy and material flow models are linked using a decomposition algorithm. In an iterative process, the marginal costs for CO2 reduction in the Federal Republic of Germany, which constitute the demand price for common projects, and the marginal costs for CO2 reduction in the host countries, which constitute the supply price, are brought to an equilibrium. The analyses have shown that co-operation approaches potentially result in significant decreases in the total expenditures for emission reduction in the Federal Republic of Germany.

关键词： energy-emission-model decomposition algorithm CO2-reduction emission reduction strategies

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THEORETICAL PROPERTIES AND NUMERICAL TESTS OF AN EFFICIENT NON-LINEAR decomposition algorithm

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1980年第2期30卷 211-227页

作者： SANDBLOM, CL Associate Professor Department of Quantitative Methods Concordia University Montreal Canada

Kronsjö's nonlinear generalization (Ref. 1) of Benders' algorithm (Ref. 2) is reviewed. At each iteration, this algorithm produces upper and lower bounds to the true optimum, and the sequence of lower bounds is increasing. The algorithm is modified, so that the sequence of upper bounds is ε-decreasing as well. The two versions are tested numerically using an ALGOL program originally written by Wong (Ref. 3), incorporating the SUMT method (Fiacco and McCormick, Refs. 4 and 5). The two versions are compared against each other, and the problem of the optimal degree of decomposition is considered. Finally, an attempt is made to express the computer time required to solve the test problems as a function of master problem size, number of subproblems, and average subproblem size.

关键词： Nonlinear programming decomposition algorithm convexity convergence SUMT algorithm

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A new decomposition algorithm for complex voting gates processing in qualitative fault tree analysis

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART O-JOURNAL OF RISK AND RELIABILITY 2015年第6期229卷 568-575页

作者： Wang, Jin Chen, Shanqi Wang, Fang Hu, Liqin Univ Sci & Technol China Hefei 230027 Anhui Peoples R China

Fault tree analysis technique is one of the main methods of reliability analysis. In a fault tree, voting gate, namely k out of n (k/n) gate, is one of the standard Boolean logic constructs which can represent AND, OR and NOT gates. It is traditionally expanded into a combination of AND and OR gates, but such expansion results in combinatorial explosion problem in determining minimal cut sets of the fault tree for even a not very big n, especially when the voting gate inputs are complex sub-trees rather than basic events. In this article, a new decomposition algorithm based on expanded combination formula which can decompose the voting gates more quickly while the space and time complexity is lower than the traditional expansion was proposed. The results of experiments on fault trees with voting gates showed that this algorithm was more efficient than the traditional expansion method and the recursive decomposition method.

关键词： decomposition algorithm voting gates fault tree analysis minimal cut sets qualitative analysis

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A rolling horizon-based decomposition algorithm for the railway network train timetabling problem

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INTERNATIONAL JOURNAL OF RAIL TRANSPORTATION 2013年第3期1卷 129-160页

作者： Peng, Qiyuan Zhao, Jun Wen, Chao Southwest Jiaotong Univ Sch Transportat & Logist Chengdu 610031 Sichuan Peoples R China Natl United Engn Lab Integrated & Intelligent Transportat Chengdu 610031 Peoples R China Key Lab Comprehens Transportat Sichuan Prov Chengdu Sichuan Peoples R China

This article presents the train timetabling problem in the complex railway network (including single-track line, double-track line, mixed-track line and terminal) and a solution algorithm. The problem is to determine the arrival, departure or through time of each train at each station on its predetermined route to satisfy several operational and safety requirements and minimise multiple objectives corresponding to train and engine time. The problem is formulated as a large-scale mixed integer nonlinear programming model with multiple objectives to simultaneously minimise the total train travel time, the total train connection time and the total engine turnaround time with several practical constraints. The model can be easily modified to simulate different scenarios of train timetabling problems. By aggregating the objectives and simplifying some constraints, a rolling horizon-based decomposition algorithm is developed based on the unique structure of the railway network and the characteristic of the train timetable. The algorithm decomposes the network into several single lines and progressively adds the train timetable of a new line into the current partial network train timetable until a complete network train timetable is obtained. The rolling horizon method is designed to determine the train timetable of each single line in iterations. Each iteration is restricted into a subregion of the feasible region, and the feasible solution to that subregion is determined by a timetable evaluation procedure and a boundary detection procedure. Lastly, computational test on real-world data shows that the presented approach can produce high-quality solutions for large-scale problems within a reasonable computation time.

关键词： railway scheduling train timetabling problem optimisation model decomposition algorithm rolling horizon method

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A. decomposition algorithm for surface electrode-array electromyogram -: A noninvasive, three-step approach to analyze surface EMG signals

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IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE 2005年第4期24卷 63-72页

作者： García, GA Okuno, R Akazawa, K Osaka Univ Dept Bioinformat Engn Grad Sch Informat Sci & Technol Suita Osaka 5650871 Japan

The purpose of the present study was to fully and reliably decompose surface electromyograms (s-EMGs) into their constitutive motor action unit potential trains (MUAPTs) at higher levels of contraction than that possible by using established methods. An algorithm for s-EMG signals decomposition based on preprocessing filters, independent component analysis (ICA), and on a template-matching technique was developed. In this study, it was demonstrated how ICA can be used successfully for solving overlaps of MUAPs. In each iteration of the algorithm, the action potentials of one motor unit (MU) could generally be separated from the others. Subsequently, using a template-matching technique, we were able to identify the action potential train of the selected MU. Results show that the algorithm satisfactorily decomposed the s-EMGs into their constitutive MUAPTs up to 30, 50, and even 60% maximum voluntary contraction (MVC). The results are in agreement with the generally accepted behavior of MUs firing rates.

关键词： electromyography filters independent component analysis medical signal processing action unit potential trains decomposition algorithm firing rates maximum voluntary contraction preprocessing filters surface electrode-array FIRING RATE Action Potentials Filters Electromyogram medical signal processing

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A decomposition algorithm for Mean-Variance Economic Model Predictive Control of Stochastic Linear Systems

A Decomposition Algorithm for Mean-Variance Economic Model P...

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IEEE International Symposium on Intelligent Control (ISIC)

作者： Sokoler, Leo Emil Dammann, Bernd Madsen, Henrik Jorgensen, John Bagterp Tech Univ Denmark Dept Appl Math & Comp Sci DK-2800 Lyngby Denmark DONG Energy DK-2820 Gentofte Denmark

ISBN: (纸本)9781479974061

This paper presents a decomposition algorithm for solving the optimal control problem (OCP) that arises in Mean-Variance Economic Model Predictive Control of stochastic linear systems. The algorithm applies the alternating direction method of multipliers to a reformulation of the OCP that decomposes into small independent subproblems. We test the decomposition algorithm using a simple power management case study, in which the OCP is formulated as a convex quadratic program. Simulations show that the decomposition algorithm scales linearly in the number of uncertainty scenarios. Moreover, a parallel implementation of the algorithm is several orders of magnitude faster than state-of-the-art convex quadratic programming algorithms, provided that the number of uncertainty scenarios is large.

关键词： convex programming linear systems optimal control parallel algorithms predictive control quadratic programming stochastic systems OCP reformulation convex quadratic programming algorithms decomposition algorithm mean-variance economic model predictive control multipliers alternating direction method optimal control problem parallel algorithm power management stochastic linear systems subproblems Linear programming Linear systems Optimization Prediction algorithms Trajectory Uncertainty Vectors Linear system Parallel algorithms Predictive control quadratic programming Optimal control Prediction algorithms convex programming stochastic systems linear programming trajectory Open circuit potential decomposition Economic Models

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A decomposition algorithm for the optimisation of hybrid dynamic processes

A decomposition algorithm for the optimisation of hybrid dyn...

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European Symposium on Computer Aided Process Engineering-9 (Escape-9)

作者： Avraam, MP Shah, N Pantelides, CC Univ London Imperial Coll Sci Technol & Med Ctr Proc Syst Engn London SW7 2BY England

This paper presents a decomposition algorithm for the dynamic optimisation of hybrid processes described by general state-transition networks (Pantelides, 1995). In each state, the transient system behaviour is described by a different set of differential and algebraic equations (DAEs). Transitions occur from one state to another whenever certain logical conditions are satisfied. A complete discretisation procedure is employed to convert the original infinite dimensional dynamic optimisation problem into a large mixed integer nonlinear programming (MINLP) problem. We then utilise a novel outer approximation/augmented penalty/equality relaxation algorithm, comprising a continuous nonlinear programming (NLP) subproblem and a mixed integer linear programming (MILP) master problem. The MILP master problem determines the sequence of state transitions the system goes through and the NLP subproblem solves the dynamic optimization problem for the given sequence. In contrast to our previous work (Avraam et al., 1998), here we describe a much more efficient approach based on a reduced NLP containing only the active state-period combinations determined by the MILP master problem. The computational efficiency of this approach is illustrated.

关键词： state transition networks optimisation decomposition algorithm

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