There has been a recent interest in cutting planes generated from two or more rows of the optimal simplex tableau. One can construct examples of integer programs for which a single cutting plane generated from two row...
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There has been a recent interest in cutting planes generated from two or more rows of the optimal simplex tableau. One can construct examples of integer programs for which a single cutting plane generated from two rows dominates the entire split closure. Motivated by these theoretical results, we study the effect of adding a family of cutting planes generated from two rows on a set of instances from the MIPLIB library. The conclusion of whether these cuts are competitive with Gomory mixed-integer cuts is very sensitive to the experimental setup. In particular, we consider the issue of reliability versus aggressiveness of the cut generators, an issue that is usually not addressed in the literature.
This paper addresses an actual production planning problem for a large seed corn production company. Various scenarios are included in different mathematical programming models in order to help the management make pro...
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This paper addresses an actual production planning problem for a large seed corn production company. Various scenarios are included in different mathematical programming models in order to help the management make production decisions. A linear programming package and a mixed-integer programming package are combined by a designed heuristic program to solve the problem. The solutions obtained and an accompanying sensitivity analysis provide the management with insight into the system's operation and potentials of cost savings.
Given a mixed-integer programming problem with two matrix constraints, it is possible to define a Lagrangean relaxation such that the relaxed problem decomposes additively into two subproblems, each having one of the ...
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Given a mixed-integer programming problem with two matrix constraints, it is possible to define a Lagrangean relaxation such that the relaxed problem decomposes additively into two subproblems, each having one of the two matrices of the original problem as its constraints. There is one Lagrangean multiplier per variable. We prove that the optimal value of this new Lagrangean dual dominates the optimal value of the Lagrangean dual obtained by relaxing one set of constraints and give a necessary condition for a strict improvement. We show on an example that the resulting bound improvement can be substantial. We show on a complex practical problem how Lagrangean decomposition may help uncover hidden special structures and thus yield better solution methodology.
In this article,an Enlarged Polygon/Polyhedron(ELP)method without binary variables is proposed to represent the Convex Polygonal/Polyhedral Obstacle Avoidance(CPOA)constraints in trajectory ***,the equivalent conditio...
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In this article,an Enlarged Polygon/Polyhedron(ELP)method without binary variables is proposed to represent the Convex Polygonal/Polyhedral Obstacle Avoidance(CPOA)constraints in trajectory ***,the equivalent condition of a point outside the convex set is given and proved ***,the ELP condition describing the CPOA constraints equivalently is given without introducing binary variables,and its geometric meaning is ***,the ELP method is used to transform the CPOA trajectory optimization problem into an optimal control problem without binary *** effectiveness and validity of ELP method are demonstrated through simulations with both simple linear dynamic model(unmanned aerial vehicle)and complex nonlinear dynamic model(hypersonic glide vehicle).Comparison indicates the computational time of ELP method is only 1%-20%of that of the traditional mixed-integer programming(MIP)method.
The advancement of autonomous technology makes electric-powered drones an excellent choice for flexible logistics services at the last mile delivery *** reach a balance between green transportation and competitive edg...
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The advancement of autonomous technology makes electric-powered drones an excellent choice for flexible logistics services at the last mile delivery *** reach a balance between green transportation and competitive edge,the collaborative routing of drones in the air and trucks on the ground is increasingly invested in the next generation of delivery,where it is particularly reasonable to consider customer time windows and time-dependent travel times as two typical time-related factors in daily *** this paper,we propose the Vehicle Routing Problem with Drones under Time constraints(VRPD-T)and focus on the time constraints involved in realistic scenarios during the delivery.A mixed-integer linear programming model has been developed to minimize the total delivery completion ***,to overcome the limitations of standard solvers in handling large-scale complex issues,a space-time hybrid heuristic-based algorithm has been developed to effectively identify a high-quality *** numerical results produced from randomly generated instances demonstrate the effectiveness of the proposed algorithm.
In this work, we present an exact approach for solving network design problems that is based on an iterative graph aggregation procedure. The scheme allows existing preinstalled capacities. Starting with an initial ag...
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In this work, we present an exact approach for solving network design problems that is based on an iterative graph aggregation procedure. The scheme allows existing preinstalled capacities. Starting with an initial aggregation, we solve a sequence of network design master problems over increasingly fine-grained representations of the original network. In each step, a subproblem is solved that either proves optimality of the solution or gives a directive where to refine the representation of the network in the subsequent iteration. The algorithm terminates with a globally optimal solution to the original problem. Our implementation uses a standard integerprogramming solver for solving the master problems as well as the subproblems. The computational results on random and realistic instances confirm the profitable use of the iterative aggregation technique. The computing time often reduces drastically when our method is compared to solving the original problem from scratch.
This paper concerns the development and implementation of a pilot Decision Support System for the bottleneck packaging facilities of a large dairy company. The planning and scheduling problem has been decomposed into ...
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This paper concerns the development and implementation of a pilot Decision Support System for the bottleneck packaging facilities of a large dairy company. The planning and scheduling problem has been decomposed into two levels: a tactical and operational control level. On the tactical level a feasible (daily) 'master production schedule' of the orderbook is determined. A mixedinteger Linear programming model is the basis for making this schedule. On the operational control level two sequencing subproblems have to be solved. For the solution of these subproblems well-known heuristics have been used.
This paper introduces a novel algorithm for selecting the optimal wafers for measurement given a set of selection rules. The algorithm is based on assigning a penalty to each of the sampling rules and then using a mix...
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This paper introduces a novel algorithm for selecting the optimal wafers for measurement given a set of selection rules. The algorithm is based on assigning a penalty to each of the sampling rules and then using a mixed-integer linear program to pick the wafers which minimize the sum of the penalties. By waiting until the metrology step to determine the best wafers to measure, a real-time decision can be made based on which wafers have previously been measured, the tools and chambers on which wafers were processed, and other user-specified selection criteria. The penalties can also be increased after a rule violation to ensure that each of the selection rules are satisfied at a finite frequency.
Purpose The objective of this research study is to formulate and develop a novel optimization model that enables planners of modular construction to minimize the total transportation and storage costs of prefabricated...
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Purpose The objective of this research study is to formulate and develop a novel optimization model that enables planners of modular construction to minimize the total transportation and storage costs of prefabricated modules in modular construction projects. Design/methodology/approach The model is developed by identifying relevant decision variables, formulating an objective function capable of minimizing the total transportation and storage costs and modelling relevant constraints. The model is implemented by providing all relevant planner-specified data and performing the model optimization computations using mixed-integer programming to generate the optimal solution. Findings A case study of hybrid modular construction of a healthcare facility is used to evaluate the model performance and demonstrate its capabilities in minimizing the total transportation and onsite storage costs of building prefabricated modules. Research limitations/implications The model can be most effective in optimizing transportation for prefabricated modules with rectangular shapes and might be less effective for modules with irregular shapes. Further research is needed to consider the shape of onsite storage area and its module arrangement. Practical implications The developed model supports construction planners in improving the cost effectiveness of modular construction projects by optimizing the transportation of prefabricated modules from factories to construction sites. Originality/value The original contributions of this research is selecting an optimal module truck assignment from a feasible set of trucks, identifying an optimal delivery day of each module as well as its location and orientation on the assigned truck and complying with relevant constraints including the non-overlap of modules on each truck, shipment weight distribution and aerodynamic drag reduction.
In order to reduce the negative impact of fuel-powered vehicles on the environment, the use of alternative-fuel vehicles (AFVs), which produce far less pollution than traditional fuel-powered vehicles, is being introd...
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In order to reduce the negative impact of fuel-powered vehicles on the environment, the use of alternative-fuel vehicles (AFVs), which produce far less pollution than traditional fuel-powered vehicles, is being introduced in many countries around the world. However, compared to the fuel-powered vehicles, AFVs such as electric vehicles require frequent recharging of their electrical energy storages (batteries), which results in a short vehicle driving range. Thus, AFV users who want to travel from home to a terminal location and back again must consider whether their AFVs can be recharged on the way. One of the approaches to solve this problem is to install alternative fuel charging stations on suitable locations to provide recharging services. However, when the budget is limited, the selection of locations and the types of alternative fuel charging stations becomes a decision problem, since it will directly affect the number of potential AFV users that can be served. This paper develops a mixed-integer programming model to address this problem and to maximize the number of people who can complete round-trip itineraries. A hybrid heuristic approach is proposed to solve this model. Numerical results show that the proposed heuristic approach only requires a small amount of CPU time to attain confident solutions. (C) 2014 Elsevier Ltd. All rights reserved.
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