We tackle home healthcare planning scenarios in the UK using decomposition methods that incorporatemixed integer programming solvers and heuristics. Homehealthcare planning is a difficult problem that integrates aspec...
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We tackle home healthcare planning scenarios in the UK using decomposition methods that incorporatemixed integer programming solvers and heuristics. Homehealthcare planning is a difficult problem that integrates aspects from scheduling and routing. Solving real-world size instances of these problems still presents a significant challenge to modern exact optimization solvers. Nevertheless, we propose decomposition techniques to harness the power of such solvers while still offering a practical approach to produce high-quality solutions to real-world problem instances. We first decompose the problem into several smaller sub-problems. Next, mixed integer programming and/or heuristics are used to tackle the sub-problems. Finally, the sub-problem solutions are combined into a single valid solution for the whole problem. The different decomposition methods differ in the way in which sub-problems are generated and the way in which conflicting assignments are tackled (i.e. avoided or repaired). We present the results obtained by the proposed decomposition methods and compare them to solutions obtained with other methods. In addition, we conduct a study that reveals how the different steps in the proposed method contribute to those results. The main contribution of this paper is a better understanding of effective ways to combine mixed integer programming within effective decomposition methods to solve real-world instances of home healthcare planning problems in practical computation time.
This paper addresses the single-item single-stocking location non-stationary stochastic lot sizing problem under the (s, S) control policy. We first present a mixedinteger non-linear programming (MINLP) formulation f...
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This paper addresses the single-item single-stocking location non-stationary stochastic lot sizing problem under the (s, S) control policy. We first present a mixedinteger non-linear programming (MINLP) formulation for determining near-optimal (s, S) policy parameters. To tackle larger instances, we then combine the previously introduced MINLP model and a binary search approach. These models can be reformulated as mixedinteger linear programming (MILP) models which can be easily implemented and solved by using off-the-shelf optimization software. Computational experiments demonstrate that optimality gaps of these models are less than 0.3% of the optimal policy cost and computational times are reasonable. (C) 2018 Elsevier B.V. All rights reserved.
With an increasing proportion of the world's population living in urban areas, probably the greatest potential for saving energy lies in designing more efficient cities. This has been known for many years and has ...
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With an increasing proportion of the world's population living in urban areas, probably the greatest potential for saving energy lies in designing more efficient cities. This has been known for many years and has led to the development of a large number of mathematical models designed to optimise urban energy systems. Despite the wide variety of models available, many are specific to particular energy pathways or contain specific equations for each type of technology, making them difficult to apply to a very broad spectrum of problems. Further, many models only consider a network of conversion technologies and there are very few that can include storage and transport technologies in a flexible and general manner. This paper presents a general mixed-integer linear programming (MILP) model for the simultaneous design and operation of urban energy systems. It is based on a flexible value web framework for representing integrated networks of resources and technologies. The resources represent any energy or material involved in the provision of services such as heat and electricity;whereas the technologies represent any type of technology for conversion, transport or storage of resources. It can be applied to urban energy systems problems at different temporal and spatial scales. The model is illustrated using an eco-town in central England as a case study. Demands for heat and electricity must be met by importing grid electricity, natural gas and/or two types of biomass and using a variety technologies, including domestic gas-fired boilers, domestic wood-chip boilers and various biomass-fired combined heat and power plants. The model optimises the design and operation of the integrated heat and electricity networks. The cost optimal solution indicates that all of the heat can be met using a single biomass CHP plant along with a backup boiler;electricity needs to be imported from the grid during periods of low heat demand. (C) 2018 The Authors. Published by Elsevier Ltd.
This rejoinder responds to the commentary by van der Linden and Li entiled "Comment on Three-Element Item Selection Procedures for Multiple Forms Assembly: An Item Matching Approach" on the article "Thr...
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This rejoinder responds to the commentary by van der Linden and Li entiled "Comment on Three-Element Item Selection Procedures for Multiple Forms Assembly: An Item Matching Approach" on the article "Three-Element Item Selection Procedures for Multiple Forms Assembly: An Item Matching Approach" by Chen. Van der Linden and Li made a strong statement calling for the cessation of test assembly heuristics development, and instead encouraged embracing mixed integer programming (MIP). This article points out the nondeterministic polynomial (NP)-hard nature of MIP problems and how solutions found using heuristics could be useful in an MIP context. Although van der Linden and Li provided several practical examples of test assembly supporting their view, the examples ignore the cases in which a slight change of constraints or item pool data might mean it would not be possible to obtain solutions as quickly as before. The article illustrates the use of heuristic solutions to improve both the performance of MIP solvers and the quality of solutions. Additional responses to the commentary by van der Linden and Li are included.
mixed fruit-vegetable cropping systems are a promising way of ensuring environmentally sustainable agricultural production systems in response to the challenge of being able to fulfill local market requirements. Indee...
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ISBN:
(纸本)9783319600451;9783319600444
mixed fruit-vegetable cropping systems are a promising way of ensuring environmentally sustainable agricultural production systems in response to the challenge of being able to fulfill local market requirements. Indeed, they combine productions and they make a better use of biodiversity. These agroforestry systems are based on a complex set of interactions modifying the utilization of light, water and nutrients. Thus, designing such a system must optimize the use of these resources: by maximizing positive interactions (facilitation) and minimizing negative ones (competition). To attain these objectives, the system's design has to include the spatial and temporal dimensions, taking into account the evolution of above-and belowground interactions over a time horizon. For that, we define the mixed Fruit-Vegetable Crop Allocation Problem (MFVCAP) using a discrete representation of the land and the interactions between vegetable crops and fruit trees. First, we give a direct formulation as a binary quadratic program (BQP). Then we reformulate the problem using a Benders decomposition approach. The master problem has 0/1 binary variables and deals with tree positioning. The subproblem deals with crop quantities. The BQP objective function becomes linear in the continuous subproblem by exploiting the fact that it depends only on the quantity of crops assigned to land units having shade, root, or nothing. This problem decomposition allows us to reformulate the MFVCAP into a mixedinteger linear Program (MIP). The detailed spatial-temporal crop allocation plan is easy to obtain after solving the MIP. Experimental results show the efficiency of our approach compared to a direct solving of the original BQP formulation.
As distributed energy resources (DERs) proliferate power systems, power grids face new challenges stemming from the variability and uncertainty of DERs. To address these problems, virtual power plants (VPPs) are estab...
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As distributed energy resources (DERs) proliferate power systems, power grids face new challenges stemming from the variability and uncertainty of DERs. To address these problems, virtual power plants (VPPs) are established to aggregate DERs and manage them as single dispatchable and reliable resources. VPPs can participate in the day-ahead (DA) market and therefore require a bidding method that maximizes profits. It is also important to minimize the variability of VPP output during intra-day (ID) operations. This paper presents mixedinteger quadratic programming-based scheduling methods for both DA market bidding and ID operation of VPPs, thus serving as a complete scheme for bidding-operation scheduling. Hourly bids are determined based on VPP revenue in the DA market bidding step, and the schedule of DERs is revised in the ID operation to minimize the impact of forecasting errors and maximize the incentives, thus reducing the variability and uncertainty of VPP output. The simulation results verify the effectiveness of the proposed methods through a comparison of daily revenue.
In this paper we describe the automatic instantiation of a Variable Neighborhood Descent procedure from a mixed integer programming model. We extend a recent approach in which a single neighborhood structure is automa...
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In this paper we describe the automatic instantiation of a Variable Neighborhood Descent procedure from a mixed integer programming model. We extend a recent approach in which a single neighborhood structure is automatically designed from a mixed integer programming model using a combination of automatic extraction of semantic features and automatic algorithm configuration. Computational results on four well-known combinatorial optimization problems show improvements over both a previous model-derived Variable Neighborhood Descent procedure and the approach with a single automatically-designed neighborhood structure. (C) 2017 The Authors. Published by Elsevier Ltd.
In both industry and the research literature, mixed integer programming (MIP) is often the default approach for solving scheduling problems. In this paper we present and evaluate four MIP formulations for the classica...
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In both industry and the research literature, mixed integer programming (MIP) is often the default approach for solving scheduling problems. In this paper we present and evaluate four MIP formulations for the classical job shop scheduling problem (JSP). While MIP formulations for the JSP have existed since the 1960s, it appears that comprehensive computational studies have not been performed since then. Due to substantial improvements in MIP technology in recent years, it is of interest to compare the standard JSP models using modern optimization software. We perform a fully crossed empirical study of four MIP models using CPLEX, GUROBI and SCIP, focusing on both the number of instances that can be proved optimal and the solution quality over time. Our results demonstrate that modern MIP solvers are able to prove optimality for moderate-sized problems very quickly. Comparing the four MIP models, the disjunctive formulation proposed by Manne performs best on both performance measures. We also investigate the performance of MIP with multi-threading and parameter tuning using CPLEX. Noticeable performance gain is observed when compared to the results using only single thread and default parameter settings. Our results serve as a snapshot of the performance of modern MIP solvers for an important, well-studied scheduling problem. Finally, the results of MW is compared to constraint programming (CP), another common approach for scheduling, and the best known complete algorithm to provide a broad view among different approaches. (C) 2016 Elsevier Ltd. All rights reserved.
integerprogramming models for clustering have applications in diverse fields addressing many problems such as market segmentation and location of facilities. integerprogramming models are flexible in expressing obje...
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integerprogramming models for clustering have applications in diverse fields addressing many problems such as market segmentation and location of facilities. integerprogramming models are flexible in expressing objectives subject to some special constraints of the clustering problem. They are also important for guiding clustering algorithms that are capable of handling high-dimensional data. Here, we present a novel mixedinteger linear programming model especially for clustering relational networks, which have important applications in social sciences and bioinformatics. Our model is applied to several social network data sets to demonstrate its ability to detect natural network structures.
In this paper, a rescheduling problem to insert new jobs into original schedule is studied. First, this rescheduling problem is reduced to the NP-hard problem. Then the rescheduling problem is formulated as two mixed ...
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ISBN:
(纸本)9781538635247
In this paper, a rescheduling problem to insert new jobs into original schedule is studied. First, this rescheduling problem is reduced to the NP-hard problem. Then the rescheduling problem is formulated as two mixed integer programming (MIP) formulations, and solved by using CPLEX. Further, the computational performance is showed and analysised for two proposed different MIP.
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