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Non-permutation flowshop scheduling with dual resources

EXPERT SYSTEMS WITH APPLICATIONS 2013年第13期40卷 5061-5076页

作者： Mehravaran, Yasaman Logendran, Rasaratnam Oregon State Univ Sch Mech Ind & Mfg Engn Corvallis OR 97331 USA

Typically, in order to process jobs in a flowshop both machines and labor are required. However, in traditional scheduling problems, labor is assumed to be plentiful and only machine is considered to be a constraint. This assumption could be due to the lower cost of labor compared to machines or the complexity of dual-resource constrained problems. In this paper a mathematical model is developed to minimize the work-in-process inventory while maximizing the service level in a flowshop with dual resources. The model focuses on optimizing a non-permutation flowshop. There are different skill levels considered for labor and the setup times on machines are sequence-dependent. Jobs are allowed to skip one or more stages in the flowshop. Job release and machine availability times are considered to be dynamic. The problem is solved in two layers. The outer layer is a search algorithm to find the schedule of jobs on the machine (traditional flowshop scheduling problem) and the inner layer is a three-step heuristic to find a schedule of jobs on labor in accordance to the machine schedule. Three different search algorithms are developed to solve the proposed NP-hard problem. First algorithm can solve a permutation flowshop while the other two are developed to solve a non-permutation flowshop. The comparison between the optimal solution and the search algorithms in small examples shows a good performance of the algorithms with an average deviation of only 2.00%. An experimental design analyzes the effectiveness and efficiency of the algorithms statistically. The results show that non-permutation algorithms perform better than the permutation algorithm, although the former are less efficient. The effectiveness and efficiency in all three algorithms have an inverse relation. To the best of our knowledge, this research is the first of its kind to provide a comprehensive mathematical model for dual resource flowshop scheduling problem. (c) 2013 Elsevier Ltd. All rights reserved.

关键词： Scheduling Dual resources mixed-integer programming Non-permutation flowshop Sequence-dependent setup time

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Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming

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AICHE JOURNAL 2013年第9期59卷 3276-3295页

作者： Grossmann, Ignacio E. Trespalacios, Francisco Carnegie Mellon Univ Dept Chem Engn Ctr Adv Proc Decis Making Pittsburgh PA 15213 USA

Discrete-continuous optimization problems are commonly modeled in algebraic form as mixed-integer linear or nonlinear programming models. Since these models can be formulated in different ways, leading either to solvable or nonsolvable problems, there is a need for a systematic modeling framework that provides a fundamental understanding on the nature of these models. This work presents a modeling framework, generalized disjunctive programming (GDP), which represents problems in terms of Boolean and continuous variables, allowing the representation of constraints as algebraic equations, disjunctions and logic propositions. An overview is provided of major research results that have emerged in this area. Basic concepts are emphasized as well as the major classes of formulations that can be derived. These are illustrated with a number of examples in the area of process systems engineering. As will be shown, GDP provides a structured way for systematically deriving mixed-integer optimization models that exhibit strong continuous relaxations, which often translates into shorter computational times. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 3276-3295, 2013

关键词： optimization mixed-integer programming logic-based optimization

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Optimizing designs and operations of a single network or multiple interdependent infrastructures under stochastic arc disruption

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COMPUTERS & OPERATIONS RESEARCH 2013年第11期40卷 2677-2688页

作者： Shen, Siqian Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA

In this paper, we consider an infrastructure as a network with supply, transshipment, and demand nodes. A subset of potential arcs can be constructed between node pairs for conveying service flows. The paper studies two optimization models under stochastic arc disruption. Model 1 focuses on a single network with small-scale failures, and repairs arcs for quick service restoration. Model 2 considers multiple interdependent infrastructures under large-scale disruptions, and mitigates cascading failures by selectively disconnecting failed components. We formulate both models as scenario-based stochastic mixed-integer programs, in which the first-stage problem builds arcs, and the second-stage problem optimizes recourse operations for restoring service or mitigating losses. The goal is to minimize the total cost of infrastructure design and recovery operations. We develop cutting-plane algorithms and several heuristic approaches for solving the two models. Model 1 is tested on an IEEE 118-bus system. Model 2 is tested on systems consisting of the 118-bus system, a 20-node network, and/or a 50-node network, with randomly generated interdependency sets in three different topological forms (i.e., chain, tree, and cycle). The computational results demonstrate that (i) decomposition and cutting-plane algorithms effectively solve Model 1, and (ii) heuristic approaches dramatically decrease the CPU time for Model 2, but yield worse bounds when cardinalities of interdependency sets increase. Future research includes developing special algorithms for optimizing Model 2 for complex multiple infrastructures with special topological forms of system interdependency. (c) 2013 Elsevier Ltd. All rights reserved.

关键词： Critical infrastructure analysis System interdependency Stochastic optimization mixed-integer programming Cutting-plane algorithms Power systems

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Theoretical and Computational Advances for Network Diversion

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NETWORKS 2013年第3期62卷 225-242页

作者： Cullenbine, Christopher A. Wood, R. Kevin Newman, Alexandra M. Colorado Sch Mines Div Econ & Business Golden CO 80401 USA Colorado Sch Mines Div Econ & Business Golden CO 80401 USA Naval Postgrad Sch Dept Operat Res Monterey CA 93943 USA

The network-diversion problem (ND) is defined on a directedor undirected graph G = (V,E) having non-negative edge weights, a source vertex s, a sink vertex t, and a diversion edge e. This problem, with intelligence-gathering and war-fighting applications, seeks a minimum-weight, minimal s-t cut ECE in G such that eEC. We present (a) a new NP-completeness proof for ND on directed graphs, (b) the first polynomial-time solution algorithm for a special graph topology, (c) an improved mixed-integer programming formulation (MIP), and (d) useful valid inequalities for that MIP. The proof strengthens known results by showing, for instance, that ND is strongly NP-complete on a directed graph even when e is incident from s or into t, but not both, and even when G is acyclic;a corollary shows the NP-completeness of a vertex-deletion version of ND on undirected graphs. The polynomial-time algorithm solves ND on s-t planar graphs. Compared to a MIP from the literature, the new MIP, coupled with valid inequalities, reduces the average duality gap by 10-50% on certain classes of test problems. It can also reduce solution times by an order of magnitude. We successfully solve unweighted problems with roughly 90,000 vertices and 360,000 edges and weighted problems with roughly 10,000 vertices and 40,000 edges. (c) 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 000(00), 000-000 2013

关键词： network diversion minimum cut complexity mixed-integer programming valid inequality

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Optimising lot sizing with nonlinear production rates in a multi-product single-machine environment

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2013年第12期51卷 3561-3573页

作者： Neidigh, Robert O. Harrison, Terry P. Shippensburg Univ Shippensburg PA 17257 USA Penn State Univ University Pk PA 16802 USA

We model a nonlinear production process at CTS Reeves, a manufacturing firm in Carlisle, PA, using a linear approximation model and heuristic methods to find a near optimal solution to determining lot sizes when learning effects are present. In a nonlinear manufacturing process, the average time to produce a part varies based upon the lot size, and typically, the average time to produce a part decreases as the lot size increases owing to a learning effect. Our linear approximation model uses discrete time periods to represent production lots. The amount of production is known for any discrete period, and as the length of the period increases, the production amounts increase at the nonlinear rate. The discrete time periods enable a production schedule to be determined that minimises production and holding costs. We build upon our prior method, which successfully addressed the single-product, single-machine environment. In this work, we expand the method to the multiple product and single machine environment. Our method constructs a feasible production schedule with total production and holding costs close to those in the optimal linear approximation model. The viability of the heuristic method is verified with testing on 50, 100, 200, 500, 1500, and 3000 period models.

关键词： mathematical programming production scheduling non-linear production rates mixed-integer programming learning effect

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MIP formulation and heuristics for multi-stage capacitated lot-sizing and scheduling problem with availability constraints

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JOURNAL OF MANUFACTURING SYSTEMS 2013年第2期32卷 392-401页

作者： Ramezanian, Reza Saidi-Mehrabad, Mohammad Fattahi, Parviz Iran Univ Sci & Technol Dept Ind Engn Tehran Iran Bu Ali Sina Univ Dept Ind Engn Hamadan Iran

In this paper, the problem of lot-sizing and scheduling of multiple product types in a capacitated flow shop with availability constraints for multi-period planning horizon is considered. In many real production systems, machines may be unavailable due to breakdowns or preventive maintenance activities, thus integrating lot-sizing and scheduling with maintenance planning is necessary to model real manufacturing conditions. Two variants are considered to deal with the maintenance activities. In the first, the starting times of maintenance tasks are fixed, whereas in the second one, maintenance must be carried out in a given time window. A new mixed-integer programming (MIP) model is proposed to formulate the problem with sequence-dependent setups and availability constraints. The objective is to find a production and preventive maintenance schedule that minimizes production, holding and setup costs. Three MIP-based heuristics with rolling horizon framework are developed to generate the integrated plan. Computational experiments are performed on randomly generated instances to show the efficiency of the heuristics. To evaluate the validity of the solution methods, problems with different scales have been studied and the results are compared with the lower bound. Computational experiments demonstrate that the performed methods have good-quality results for the test problems. (C) 2013 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

关键词： Dynamic lot-sizing and scheduling Flow shop Availability constraint Sequence-dependent setup mixed-integer programming MIP-based heuristic

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WORST-CASE LOAD IN PLASTIC LIMIT ANALYSIS OF FRAME STRUCTURES

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JOURNAL OF MECHANICS OF MATERIALS AND STRUCTURES 2013年第8-10期8卷 415-439页

作者： Kanno, Yoshihiro Univ Tokyo Grad Sch Informat Sci & Technol Dept Math Informat Bunkyo Ku Tokyo 1138656 Japan

This paper addresses the plastic limit analysis of a frame structure under uncertainty in the external load. Given a bounded set in which an external load can vary, we attempt to find the worst load that minimizes the limit load factor. It is shown that this problem can be formulated as a mixed-integer linear programming problem. The global optimal solution of this optimization problem can be found by using an existing algorithm, e.g., a branch-and-cut method. Guaranteed convergence to a global optimal solution is important because it implies that the proposed method yields neither overestimation nor underestimation in this uncertainty analysis problem. Two numerical examples illustrate that the worst scenario problem can be solved with modest computational effort. They also show that not only does the limit load factor depend on the level of uncertainty in the external load, but the collapse mode as well.

关键词： robustness uncertainty worst scenario detection plastic limit analysis global optimization mixed-integer programming

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A mixed-integer programming formulation for the general capacitated lot-sizing problem

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COMPUTERS & CHEMICAL ENGINEERING 2008年第1-2期32卷 244-259页

作者： Sung, Charles Maravelias, Christos T. Univ Wisconsin Dept Biol & Chem Engn Madison WI 53706 USA

A new mixed-integer programming (MIP) formulation is presented for the production planning of single-stage multi-product processes. The problem is formulated as a multi-item capacitated lot-sizing problem in which (a) multiple items can be produced in each planning period, (b) sequence-independent set-ups can carry over from previous periods, (c) set-ups can cross over planning period boundaries, and (d) set-ups can be longer than one period. The formulation is extended to model time periods of non-uniform length, idle time, parallel units, families of products, backlogged demand, and lost sales. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： production planning multi-item capacitated lot sizing mixed-integer programming set-up carry over set-up cross over

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Multi-choice stochastic transportation problem involving extreme value distribution

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APPLIED MATHEMATICAL MODELLING 2013年第4期37卷 2230-2240页

作者： Mahapatra, Deshabrata Roy Roy, Sankar Kumar Biswal, Mahendra Prasad Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 W Bengal India Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

In this paper a multi choice stochastic transportation problem is considered where the supply and demand parameters of the constraints follow extreme value distribution. Some of the cost coefficients of the objective function are multi-choice type. At first all the probabilistic constraints are transformed into deterministic constraints. Further using the binary variables, multi-choice type cost coefficients are handled. Then the transformed problem is considered as a deterministic multi-choice transportation problem. Finally, a numerical example is presented to illustrate the solution procedure. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Multi-choice programming Stochastic programming Extreme value distribution Transportation problem Transformation technique mixed-integer programming

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An assembly decomposition model for subassembly planning considering imperfect inspection to reduce assembly defect rates

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JOURNAL OF MANUFACTURING SYSTEMS 2013年第3期32卷 412-416页

作者： Ko, Jeonghan Nazarian, Ehsan Wang, Hui Abell, Jeffrey Ajou Univ Dept Ind Engn Suwon 443749 Gyeonggi Do South Korea Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA Univ Nebraska Lincoln NE 68588 USA Gen Motors Global Res Dev Mfg Syst Res Lab Warren MI 48090 USA

The assembly decomposition is to divide the assembly to subassemblies that are to be joined in the final assembly processes. The assembly decomposition decision strongly affects the effectiveness of a product assembly in terms of quality, sequence and supplier selection. This paper presents an assembly-decomposition model to improve product quality. mixed-integer programming is used to partition the liaison graph of a product assembly. The mixed-integer programming model takes into account the defect rates in components and assembly tasks. The defect rate of the final assembly product is to be minimized considering type II errors in subassembly inspection. A numerical example is presented to demonstrate the methodology, and this numerical study shows that assembly decomposition strongly affects the final assembly defect rate. The developed assembly decomposition method is expected to enhance the decision making in assembly planning. (C) 2012 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

关键词： Assembly Decomposition Decision making Design Disassembly Quality mixed-integer programming

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