Product recovery has received greater attention in recent years mainly due to increased environmental awareness of consumers and stricter environmental regulations imposed by governments. In product recovery, disassem...
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Product recovery has received greater attention in recent years mainly due to increased environmental awareness of consumers and stricter environmental regulations imposed by governments. In product recovery, disassembly of the product into its constituent parts is the most significant activity and generally performed on a disassembly line. During disassembly, a complete or partial disassembly of the product may be preferred. In complete disassembly, all parts must be disassembled, while partial disassembly allows to disassemble a subset of parts (e. g., the ones with relatively high revenues). This study deals with a partial disassembly line balancing and sequencing (PDLBS) problem considering revenues of parts to be disassembled, general workstation cost, additional cost of workstation(s) with hazardous parts, and cost of direction changes. For the PDLBS problem, a generic mixed integer programming (MIP) model, with the aim of maximizing total profit, is developed. To strengthen the MIP formulation, two sets of valid inequalities are proposed. The computational results show that the MIP model with valid inequalities is able to provide optimal solutions for the PDLBS problems with up to 30 tasks. To obtain near-optimal solutions for large-sized problems, a MIP-based solution approach is proposed. The proposed approach decomposes the entire MIP model into selection and assignment (SA) and sequencing (SEQ) models. The SA model is an exact relaxation of the MIP model (with valid inequalities) obtained by removing all the sequencing variables and constraints. Hence, SA model also produces an efficient upper bound for the PDLBS problem. The SEQ model, accordingly, aims to find an optimal sequence of tasks subject to the fixed selection and assignment of tasks provided by the SA model. The computational results show that the proposed MIP-based solution approach provides efficient solutions with small optimality gaps for large-sized problems.
Unit commitment problem is a complex decision-making process which involves the scheduling of generators over a set of time periods to satisfy system load demand, water demand, system reliability, operational, and sec...
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Unit commitment problem is a complex decision-making process which involves the scheduling of generators over a set of time periods to satisfy system load demand, water demand, system reliability, operational, and security constraints. Mathematically, this is a nonlinear, nonconvex, high dimensional, and large-scale optimization problem over mixedinteger variables. Additionally, for a short-term unit commitment problem such as hourly or daily scheduling of generators, the operator needs to run the model in realtime. The operator should have immediate access to information concerning which units should be operated when emergency situations arise or how to schedule around planned maintenance of units. mixed integer programming (MIP) model is developed to solve the unit commitment problem. The MIP model developed in this study consists of three sub-models: PLANT-DY-W, PLANT-GO-W, and PLANT-ST-W. It provides generation control tool that regulates the hydropower system while improving powerplants efficiency. Also, it automates and improves the unit schedule process for the powerplants. To demonstrate the capabilities of the unit commitment models a case study was carried out on a hydropower system in Lower Colorado River Basin.
This article proposes a mixedinteger linear programming (MILP)-based algorithm to estimate faults locations, types, and fault current magnitudes in unbalanced three-phase distribution networks. The proposed method re...
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This article proposes a mixedinteger linear programming (MILP)-based algorithm to estimate faults locations, types, and fault current magnitudes in unbalanced three-phase distribution networks. The proposed method requires voltage phasors prior to and during fault conditions. The measurements are collected by microPMUs at the end of the branches along with the bus impedance matrix. To assess the proposed technique's performance in fault location and current identification, different types of faults scenarios are considered. Balanced and unbalanced faults are examined on the IEEE 37-bus, the IEEE 123-bus, and 134-node real-life feeders. Efficiency of the proposed method is investigated on ungrounded systems, reduced microPMU number, different fault resistances, inaccurate bus impedance matrix, distributed generation penetration, and noisy measurement data. High accuracy rate is achieved by the proposed method in identifying fault locations, types, and current magnitudes.
A graph is an interval graph if its vertex set corresponds to a family of intervals on the real line, called a model, such that two distinct vertices are adjacent in the graph if and only if their corresponding interv...
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A graph is an interval graph if its vertex set corresponds to a family of intervals on the real line, called a model, such that two distinct vertices are adjacent in the graph if and only if their corresponding intervals intersect each other. The minimum number of interval lengths that suffices to represent a model of a given interval graph is its interval count. The use of mathematical optimization techniques for solving interval count problems was first explored by Joos et al.[1]. In more detail, given a bipartition of vertices into classes of lengths, the authors propose an efficient linear programming based algorithm for solving the interval count two problem. However, so far, no mathematical formulation exists in the literature for general interval count. As a contribution in that direction, we introduce a mixed integer programming formulation for the exact value of interval count, parameterized by the largest interval length. Additionally, we also propose a quadratic formulation for a valid upper bound on interval count. Solution algorithms for these formulations were tested on interval count instances found in the literature. As an outcome of these experiments, the algorithm for the upper bound formulation was shown to run much faster than its exact solution counterpart. Furthermore, the upper bounds thus obtained were frequently certified as optimal by the exact algorithm.
This paper addresses the question of decomposing an infinite family of rational polyhedra in an integer fashion. It is shown that there is a finite subset of this family that generates the entire family. Moreover, an ...
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This paper addresses the question of decomposing an infinite family of rational polyhedra in an integer fashion. It is shown that there is a finite subset of this family that generates the entire family. Moreover, an integer analogue of Caratheodory's theorem carries over to this general setting. The integer decomposition of a family of polyhedra has some applications in integer and mixed integer programming, including a test set approach to mixed integer programming.
For many decades, solving the optimal architectural layout design is unattainable for the reasonable problem sizes. Architects have to settle foil acceptable layouts instead of the favourable optimal solution. With to...
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ISBN:
(纸本)1402034601
For many decades, solving the optimal architectural layout design is unattainable for the reasonable problem sizes. Architects have to settle foil acceptable layouts instead of the favourable optimal solution. With today technologies, various optimization techniques have been used to alleviate the optimal search according to diversified goals. This paper formulates the optimal architectural layout design as the multiobjective mixed integer programming model solved by the MIP solver. The main idea is to capture functional constraints, dimensional constraints and the objective function using only linear formulae with binary variables. Functional constraints are the connectivities, the unused grid cells, the fixed room location, the boundary and the fixed border location while dimension constraints are the non-intersecting, the overlapping, the length and the ratio constraints. The objective function is designed to minimize the absolute distance among rooms and maximize room spaces. Due to the nonlinearity of area computation, the linear approximation of width and height constraints have been utilized. Architects can control these different objectives within the model. By specifying the rigid restriction and the time limits, the problem can be solved within a reasonable amount of time.
Based on several existing literatures that use mixed integer programming (MIP) to solve parallel machine scheduling problems, this study tests and compares three MIP models. Each order has its own ready date, due date...
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ISBN:
(纸本)9781509036653
Based on several existing literatures that use mixed integer programming (MIP) to solve parallel machine scheduling problems, this study tests and compares three MIP models. Each order has its own ready date, due date and processing time. The completion time of the order cannot over the its due date. If not, penalties for tardiness will occur. Formulation 1 used in immediate-precedence variables [1]. Formulation 2 is an improved version of immediate-precedence variables original proposed by [2]. Formulation 3 used linear ordering variables[1]. The results reveal that Formulation 2 has better computational performance than other does.
This study aims to provide a systematic framework of the container selection and cargo loading problems, which are currently faced by a forwarding company in Hong Kong. The forwarding company first consolidates all go...
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ISBN:
(纸本)188933524X
This study aims to provide a systematic framework of the container selection and cargo loading problems, which are currently faced by a forwarding company in Hong Kong. The forwarding company first consolidates all goods that will be shipped to overseas markets into different types of cargos. Then the company is responsible for packing the cargos into containers, which arc rented from airlines a week in advance in order to obtain a cheap price from the airlines. The airlines can provide different types and numbers of containers. Therefore, the question of how to select containers from the airlines and how to pack cargos into the containers is a very important issue that the forwarding company faces every day. The decision-making process becomes complex because of the containers' volume and weight limits and the fact that the rental cost is the fixed cost for using the containers plus the variable cost that depend on the total weight that each container holds. The objective in this study is to minimize the total rental cost, which is the piece-wise function. We further change it into anther form, in which the piece-wise function can be expressed as a continue one. Therefore, a mixedinteger linear programming model is provided to determine the optimal container selection and cargo loading strategy. The application of the proposed model is illustrated by the practical problems from the forwarding company.
This study targets an examination proctor assignment problem where faculties and academic staffs are assigned to examinations as proctors in the regular examination period at our university. In previous work, the auth...
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This study targets an examination proctor assignment problem where faculties and academic staffs are assigned to examinations as proctors in the regular examination period at our university. In previous work, the author formulated fundamental mathematical model for the assignment task in a mixed integer programming form and developed a prototype system based on spreadsheet software to derive an optimal assignment. In this study, the proposed mathematical model is extended and revised to deal with the conditions in the assignment task. Some solutions are discussed to improve practicality for system users.
The objective of this study is to propose a mixed integer programming model which can help make-to-order (MTO) companies to make proper decisions in accepting or rejecting customers' orders. The proposed model can...
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ISBN:
(纸本)9780982148945
The objective of this study is to propose a mixed integer programming model which can help make-to-order (MTO) companies to make proper decisions in accepting or rejecting customers' orders. The proposed model can solve small capacity planning problems with the objective function of maximizing the profit, with the condition that the orders must be delivered on time. If the company accepts the orders, three decisions can be made within the planning horizon, which are to do the job by normal time, overtime, or to outsource it. A case study was conducted in a MTO company and the proposed model was solved by using ILOG Optimization programming Language (OPL). The reasonableness of the optimum solution shows that the model is applicable in practice.
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