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arXiv 2021年

作者： LipińSki, Zbigniew Wojtkowski, Maciej P. University of Opole Opole Poland The University of Arizona TucsonAZ85721 United States

linear second order recursive sequences with arbitrary initial conditions are studied. For sequences with the same parameters a ring and a group is attached, and isomorphisms and homomorphisms are established for related parameters. In the group, called the sequence group, sequences are identified if they differ by a scalar factor, but not if they differ by a shift, which is the case for the Laxton group. Prime divisors of sequences are studied with the help of the sequence group mod p, which is always cyclic of order p ± 1. Even and odd numbered subsequences are given independent status through the introduction of one rational parameter in place of two integer parameters. This step brings significant simplifications in the algebra. All elements of finite order in Laxton groups and sequence groups are described effectively. A necessary condition is established for a prime p to be a divisor of a sequence: the norm (determinant) of the respective element of the ring must be a square mod p. This leads to an uppers estimate of the set of divisors by a set of prime density 1/2. Numerical experiments show that the actual density is typically close to 0.35. A conjecture is formulated that the sets of prime divisors of the even and odd numbered elements are independent for a large family of *** Codes 11B37, 11B39 © 2021, CC BY-NC-ND.

关键词： mixed-integer linear programming

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Location model for a remanufacturing reverse logistics network based on adaptive genetic algorithm

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SIMULATION-TRANSACTIONS OF THE SOCIETY FOR MODELING AND SIMULATION INTERNATIONAL 2019年第11期95卷 1069-1084页

作者： Yan, Rui Yan, Bo Univ Calif Los Angeles Dept Math Los Angeles CA 90024 USA South China Univ Technol Sch Econ & Commerce Guangzhou Guangdong Peoples R China

Energy saving and environmental protection are important issues of today. Concerning the environmental and social need to increase the utilization of used products, this paper introduces two remanufacturing reverse logistics (RL) network models, namely, the open-loop model and the closed-loop model. In an open-loop RL system, used products are recovered by outside firms, while in a closed-loop RL system, they are returned to their original producers. The open-loop model features a location selection with two layers. For this model, a mixed-integer linear program (MILP) is built to minimize the total costs of the open-loop RL system, including the fixed cost, the freight between nodes, the operation cost of storage and remanufacturing centers, the penalty cost of unmet or remaining demand quantity, and the government-provided subsidy given to the enterprises that protect the environment. This MILP is solved using an adaptive genetic algorithm with MATLAB simulation. For a closed-loop RL network model, a special demand function considering the relationship between new and remanufactured products is developed. Remanufacturing rate, environmental awareness, service demand elasticity, value-added services, and their impacts on total profit of the closed-loop supply chain are analyzed. The closed-loop RL network model is proved effective through the analysis of a numerical example.

关键词： Reverse logistics remanufacturing adaptive genetic algorithm mixed-integer linear programming

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Surgical case scheduling with sterilising activity constraints

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2019年第10期57卷 2984-3002页

作者： Al Hasan, Hasan Gueret, Christelle Lemoine, David Rivreau, David Univ Angers LARIS Angers France IMT Atlantique LS2N Nantes France Univ Catholique Ouest LARIS Angers France

In this paper, we study a real scheduling problem which consists in scheduling a set of elective surgical cases requiring surgical instruments and tools in several operating rooms. The objectives are to minimise the overtime of the surgical unit staff, the number of operating rooms used and the number of instruments processed in emergency in the sterilising unit while respecting the current level of service represented by the total number of patients operated per month at the orthopaedic surgery unit. This research was performed in collaboration with the University Hospital of Angers in France (CHU Angers), which has also provided historical data for the experiments. We propose a mixed integer linear programming model for the problem which is solved in a lexicographic fashion. We also propose a robust formulation to deal with the uncertain surgery durations. Both the deterministic and robust formulations are then compared over a set of instances provided by the CHU. The solutions obtained are competitive in terms of number of operating rooms and significantly improve those implemented operationally at the CHU in terms of overtime and emergencies at the sterilising unit.

关键词： operating rooms in health services elective surgeries planning sterilisation unit scheduling mixed-integer linear programming robust optimisation

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Scheduling identical jobs on uniform machines with a conflict graph

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COMPUTERS & OPERATIONS RESEARCH 2019年 111卷 357-366页

作者： Mallek, Amin Bendraouche, Mohamed Boudhar, Mourad USTHB Univ RECITS Lab Fac Math BP 32 El Alia Algiers Algeria Saad Dahleb Univ Fac Sci Route Soumaa BlidaBP Blida 270 Blida Algeria

This paper addresses the problem of scheduling n identical jobs on a set of m parallel uniform machines. The jobs are subjected to conflicting constraints modelled by an undirected graph G, in which adjacent jobs are not allowed to be processed on the same machine. Minimising the maximum completion time in the schedule (makespan C-max) is known to be NP-hard. We prove that when G is restricted to complete bipartite graphs the problem remains NP-hard for arbitrary number of machines, however, if m is fixed an optimal solution can be obtained in polynomial time. To solve the general case of the problem, we propose mixed-integer linear programming (MILP) formulations alongside with lower bounds and heuristic approaches. Furthermore, computational experiments are carried out to measure the performance of the proposed methods. (C) 2019 Published by Elsevier Ltd.

关键词： Scheduling Identical jobs Incompatible jobs Uniform machines Conflict graph mixed-integer linear programming

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Corridor level cooperative trajectory optimization with connected and automated vehicles

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2019年 105卷 405-421页

作者： Yu, Chunhui Feng, Yiheng Liu, Henry X. Ma, Wanjing Yang, Xiaoguang Tongji Univ Minist Educ Key Lab Rd & Traff Engn 4800 Caoan Rd Shanghai Peoples R China UMTRI 2901 Baxter Rd Ann Arbor MI 48109 USA Univ Michigan Dept Civil & Environm Engn 2320 GG Brown2350 Hayward St Ann Arbor MI 48109 USA

Trajectory planning for connected and automated vehicles (CAVs) has been studied at both isolated intersections and multiple intersections under the fully CAV environment in the literature. However, most of the existing studies only model limited interactions of vehicle trajectories at the microscopic level, without considering the coordination between vehicle trajectories. This study proposes a mixed-integer linear programming (MILP) model to cooperatively optimize the trajectories of CAVs along a corridor for system optimality. The car-following and lane-changing behaviors of each vehicle along the entire path are optimized together. The trajectories of all vehicles along the corridor are coordinated for system optimality in terms of total vehicle delay. All vehicle movements (i.e., left-turning, through, and right-turning) are considered at each intersection. The ingress lanes are not associated with any specific movement and can be used for all vehicle movements, which provides much more flexibility. Vehicles are controlled to pass through intersections without traffic signals. Due to varying traffic conditions, the planning horizon is adaptively adjusted in the implementation procedure of the proposed model to find a balance between solution feasibility and computational burden. Numerical studies validate the advantages of the proposed CAV-based control over the coordinated fixed-time control at different demand levels in terms of vehicle delay and throughput. The analyses of the safety time gaps for collision avoidance within intersection areas show the promising benefits of traffic management under the fully CAV environment.

关键词： Connected and automated vehicle Trajectory optimization and coordination Corridor mixed-integer linear programming

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Optimal design of an oil pipeline with a large-slope section

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ENGINEERING OPTIMIZATION 2019年第9期51卷 1480-1494页

作者： Wang, Bohong Yuan, Meng Yan, Yamin Yang, Ke Zhang, Haoran Liang, Yongtu China Univ Petr Natl Engn Lab Pipeline Safety MOE Key Lab Petr Engn Beijing Peoples R China China Univ Petr Beijing Key Lab Urban Oil & Gas Distribut Technol Beijing Peoples R China Univ Tokyo Ctr Spatial Informat Sci Chiba Japan

One of the important issues in the operation of a long-distance oil pipeline in a large-slope area is pressure control, especially for the section after the turning point. In this study, a method to optimally design an oil pipeline with a large-slope section is proposed. The method is based on a stochastic mixed-integer linear programming model with minimal total cost as the objective function to determine the size of the pipeline, the location, the operational plan of pump stations and the location of pressure reduction stations. Hydraulic calculations and different types of oil product are considered. The uncertainty in flow rates of the pipeline is studied by the proposed stochastic programming approach. This method is applied to a real case of designing an oil product pipeline in a large-slope area.

关键词： Oil pipeline large slope design pressure control mixed-integer linear programming

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A Benders' decomposition algorithm with combinatorial cuts for the multi-manned assembly line balancing problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第3期278卷 796-808页

作者： Michels, Adalberto Sato Lopes, Thiago Cantos Stall Sikora, Celso Gustavo Magatao, Leandro Fed Univ Technol Parana UTFPR Grad Program Elect & Comp Engn CPGEI Curitiba Parana Brazil Univ Hamburg Hamburg Business Sch Inst Operat Res Hamburg Germany

Multi-manned assembly lines are commonly found in industries that manufacture large-size products (e.g. automotive industry), in which multiple workers are assigned to the same station in order to perform different operations simultaneously on the same product. Although the balancing problem of multi manned assembly lines had been modelled before, the previously presented exact mathematical formulations are only able to solve few small-size instances, while larger cases are solved by heuristics or metaheuristics that do not guarantee optimality. This work presents a new mixed-integer linear programming model with strong symmetry break constraints and decomposes the original problem into a new Benders' Decomposition Algorithm to solve large instances optimally. The proposed model minimises the total number of workers along the line and the number of opened stations as weighted primary and secondary objectives, respectively. Besides, feasibility cuts and symmetry break constraints based on combinatorial Benders' cuts and model's parameters are applied as lazy constraints to reduce search-space by eliminating infeasible sets of allocations. Tests on a literature dataset have shown that the proposed mathematical model outperforms previously developed formulations in both solution quality and computational processing time for small-size instances. Moreover, the proposed Benders' Decomposition Algorithm yielded 117 optimal results out of a 131-instances dataset. Compared to previously presented methods, this translates to 19 and 25 new best solutions reached for medium and large-size instances, respectively, of which 19 and 23 are optimal solutions. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Combinatorial optimisation Multi-manned assembly line balancing Benders' decomposition Combinatorial Benders' cuts mixed-integer linear programming

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Three methods for robust grading

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期272卷 364-371页

作者： Burer, Samuel Piccialli, Veronica Dept Management Sci S346 Pappajohn Business Bldg Iowa City IA 52242 USA Univ Roma Tor Vergata Dipartimento Ingn Civile & Ingn Informat Via Politecn 1 I-00133 Rome Italy

We propose three strategies by which a professor of a university course can assign final letter grades taking into account the natural uncertainty in students' individual assignment and final numerical grades. The first strategy formalizes a common technique that identifies large gaps in the final numerical grades. For the second and third strategies, we introduce the notion of a borderline student, that is, a student who is close to, but below, the breakpoint for the next highest letter grade. Using mixed-integer linear programming and a tailor-made branch-and-bound algorithm, we choose the letter-grade breakpoints to minimize the number of borderline students. In particular, the second strategy treats the uncertainty implicitly and minimizes the number of borderline students, while the third strategy uses a robust-optimization approach to minimize the maximum number of borderline students that could occur based on an explicit uncertainty set. We compare the three strategies on realistic instances and identify overall trends as well as some interesting exceptions. While no strategy appears best in all cases, each can be computed in a reasonable amount of time for a moderately sized course. Moreover, they collectively provide the professor important insight into how uncertainty affects the assignment of final letter grades. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Robust optimization mixed-integer linear programming Branch-and-bound Grading Higher education

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A bi-objective model for design and analysis of sustainable intermodal transportation systems: a case study of Turkey

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2019年第19期57卷 6146-6161页

作者： Resat, Hamdi Giray Turkay, Metin Izmir Univ Econ Dept Ind Engn TR-35330 Izmir Turkey Koc Univ Dept Ind Engn TR-34450 Istanbul Turkey

This paper presents a mixed-integer linear optimisation model to analyse the intermodal transportation systems in the Turkish transportation industry. The solution approach includes mathematical modelling, data analysis from real-life cases and solving the resulting mathematical programming problem to minimise total transportation cost and carbon dioxide emissions by using two different exact solution methods in order to find the optimal solutions. The novel approach of this paper generates Pareto solutions quickly and allows the decision makers to identify sustainable solutions by using a newly developed solution methodology for bi-objective mixed-integer linear problems in real-life cases.

关键词： Logistics sustainability mixed-integer linear programming bi-objective optimisation

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Improving Energy Efficiency in Discrete Parts Manufacturing System Using an Ultra-Flexible Job Shop Scheduling Algorithm

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INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING-GREEN TECHNOLOGY 2019年第2期6卷 349-365页

作者： Liu, Ning Zhang, Y. F. Lu, Wen Feng Natl Univ Singapore Dept Mech Engn 9 Engn Dr 1 Singapore 117576 Singapore

Improving energy efficiency has been one of main objectives in modern manufacturing enterprises. Various approaches aiming at efficient energy management have been proposed/developed, among which minimizing energy consumption by energy-sensible production scheduling techniques has emerged as a promising one. However, reported workshop models are quite simple and unrealistic. This paper studies a more realistic workshop model called ultra-flexible job shop (uFJS). In an uFJS, the sequence among operations for a job can be changed within certain constraints. To formulate this energy-efficient scheduling problem, a mixed-integer linear programming model was developed. To deal with large-sized problems, a specially designed genetic algorithm (GA) was subsequently proposed and implemented. Numerical results showed the proposed GA worked with decent effectiveness and efficiency. Finally, several comparative studies are carried out to further demonstrate its efficacy in terms of energy efficiency improvement. The advantage of the uFJS as compared to other relative simple workshop models is also shown. By considering the flexibility in operation sequencing in each job, the uFJS effectively integrates process planning and scheduling in discrete parts manufacturing system, thus providing a much larger solution space for more energy-efficient solutions. It therefore provides an excellent platform for decision-makers when developing energy-efficient techniques and strategies

关键词： Energy efficiency Discrete parts manufacturing system Production scheduling Ultra-flexible job shop mixed-integer linear programming Genetic algorithm

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