Single floor facility layout problem (FLP) is related to finding the arrangement of a given number of departments within a facility;while in multi-floor FLP, the departments should be imbedded in some floors inside th...
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Single floor facility layout problem (FLP) is related to finding the arrangement of a given number of departments within a facility;while in multi-floor FLP, the departments should be imbedded in some floors inside the facility. The significant influence of layout design on the effectiveness of any organization has turned FLP into an important issue. This paper presents a three- (two-) stage mathematical programming method to find competitive solutions for multi-(single-) floor problems. At the first stage, the departments are assigned to the floors through a mixedintegerprogramming model (the single floor version does not require this stage). At the second stage, a nonlinear programming model is used to specify the relative position of the departments on each floor;and at the third stage, the final layouts within the floors are determined, through another nonlinear programming model. The multi-floor version is studied in the states in which the locations of the elevators are either formerly specified or not. Computational results show that this framework can find a wide variety of high quality layouts at competitive cost (up to 43% reduction) within a short amount of time for small and especially large size problems, compared to the existing methods in the literature. Also, the proposed method is flexible enough to accommodate the complicated and real-world problems, because of using mathematical programming model and solving it directly. (C) 2016 Elsevier Inc. All rights reserved.
In this paper, mixed-integer programming for the railway network design problem with a new objective function is proposed. The model considers development projects (new line construction and existing line improvement)...
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In this paper, mixed-integer programming for the railway network design problem with a new objective function is proposed. The model considers development projects (new line construction and existing line improvement), available budget, block capacity, and origin-destination matrix demand. A standard code is used to calculate the capacity of the blocks. The objective function is to minimize the Loud cost of direct and indirect (external) costs. We add the effect of railway network development on the road network to the model. The proposed model is implemented for the railway network of Iran and solved by an exact method. (C) 2018 American Society of Civil Engineers.
In Wireless Sensor Networks (WSNs), energy-efficiency and reliability are two critical requirements for attaining a long-term stable communication performance. Using error control (EC) methods is a promising technique...
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In Wireless Sensor Networks (WSNs), energy-efficiency and reliability are two critical requirements for attaining a long-term stable communication performance. Using error control (EC) methods is a promising technique to improve the reliability of WSNs. EC methods are typically utilized at the network-level, where all sensor nodes use the same EC method. However, improper selection of EC methods on some nodes in the network-level strategy can reduce the energy-efficiency, thus the lifetime of WSNs. In this study, a node-level EC strategy is proposed via mixed-integer programming (MIP) formulations. The MIP model determines the optimum EC method (i.e., automatic repeat request (ARQ), forward error correction (FEC), or hybrid ARQ (HARQ)) for each sensor node to maximize the network lifetime while guaranteeing a pre-determined reliability requirement. Five meta-heuristic approaches are developed to overcome the computational complexity of the MIP model. The performances of the MIP model and meta-heuristic approaches are evaluated for a wide range of parameters such as the number of nodes, network area, packet size, minimum desired reliability criterion, transmission power, and data rate. The results show that the node-level EC strategy provides at least 4.4% prolonged lifetimes and 4.0% better energy-efficiency than the network-level EC strategies. Furthermore, one of the developed meta-heuristic approaches (i.e., extended golden section search) provides lifetimes within a 3.9% neighborhood of the optimal solutions, reducing the solution time of the MIP model by 89.6%.
Food waste contributes significantly to greenhouse emissions and represents a substantial portion of overall waste within hospital facilities. Furthermore, uneaten food leads to a diminished nutritional intake for pat...
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Food waste contributes significantly to greenhouse emissions and represents a substantial portion of overall waste within hospital facilities. Furthermore, uneaten food leads to a diminished nutritional intake for patients, that typically are vulnerable and ill. Therefore, this study developed mathematical models for constructing patient meals in a 1000-bed hospital located in Florida. The objective is to minimize food waste and mealbuilding costs while ensuring that the prepared meals meet the required nutrients and caloric content for patients. To accomplish these objectives, four mixed-integer programming models were employed, incorporating binary and continuous variables. The first model establishes a baseline for how the system currently works. This model generates the meals without minimizing waste or cost. The second model minimizes food waste, reducing waste up to 22.53 % compared to the baseline. The third model focuses on minimizing meal-building costs and achieves a substantial reduction of 37 %. Finally, a multi-objective optimization model was employed to simultaneously reduce both food waste and cost, resulting in reductions of 19.70 % in food waste and 32.66 % in meal-building costs. The results demonstrate the effectiveness of multi-objective optimization in reducing waste and costs within large-scale food service operations.
We present a mathematical formulation and a heuristic solution approach for the optimal planning of delivery routes in a multi-modal system combining truck and Unmanned Aerial Vehicle (UAV) operations. In this system,...
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We present a mathematical formulation and a heuristic solution approach for the optimal planning of delivery routes in a multi-modal system combining truck and Unmanned Aerial Vehicle (UAV) operations. In this system, truck and UAV operations are synchronized, i.e., one or more UAVs travel on a truck, which serves as a mobile depot. Deliveries can be made by both UAVs and the truck. While the truck follows a multi-stop route, each UAV delivers a single shipment per dispatch. The presented optimization model minimizes the waiting time of customers in the system. The model determines the optimal allocation of customers to truck and UAVs, the optimal route sequence of the truck, and the optimal launch and reconvene locations of the UAVs along the truck route. We formulate the problem as a mixed-integer Linear programming (MILP) model and conduct a bound analysis to gauge the maximum potential of the proposed system to reduce customer waiting time compared to a traditional truck-only delivery system. To be able to solve real-world problem size instances, we propose an efficient Truck and Drone Routing Algorithm (TDRA). The solution quality and computational performance of the mathematical model and the TDRA are compared together and with the truck-only model based on a variety of problem instances. Further, we apply the TDRA to a real-world case study for e-commerce delivery in Sao Paulo, Brazil. Our numerical results suggest significant reductions in customer waiting time to be gained from the proposed multi-modal delivery model. (C) 2019 Elsevier Inc. All rights reserved.
It iswell known that selecting a good mixed-integer programming (MIP) formulation is crucial for effectively obtaining a solution with state-of-the art solvers. Although best practices and guidelines for constructing ...
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It iswell known that selecting a good mixed-integer programming (MIP) formulation is crucial for effectively obtaining a solution with state-of-the art solvers. Although best practices and guidelines for constructing good formulations abound, there is rarely a single systematic construction approach that leads to the best possible formulation. Here, we introduce embedding formulations and complexity as a new MIP formulation paradigm for systematically constructing formulations for disjunctive constraints that are optimal with respect to size. More specifically, they yield the smallest possible ideal formulation (i.e., one whose LP relaxation has integral extreme points) among all formulations that only use 0-1 auxiliary variables. We use the paradigm to characterize optimal formulations for special ordered sets of type 2 and certain piecewise linear functions of two variables. We also show that the resultant formulations can provide a significant computational advantage over all known formulations for piecewise linear functions.
We derive polyhedral results for discrete-time mixed-integer programming (MIP) formulations for the production planning of multi-stage continuous chemical processes. We express the feasible region of the LP-relaxation...
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We derive polyhedral results for discrete-time mixed-integer programming (MIP) formulations for the production planning of multi-stage continuous chemical processes. We express the feasible region of the LP-relaxation as the intersection of two sets. The constraints describing the first set yield the convex hull of its integer points. For the second set, we show that for integral data the constraint matrix is kappa-regular, and that the corresponding polyhedron is integral if the length of the planning period is selected appropriately. We use this result to show that for rational data, integer variables can also assume integral values at the vertices of the polyhedron. We also discuss how these results provide insight and can be used to effectively address large-scale problems. Finally, we present computational results for a series of example problems. (C) 2009 Elsevier Ltd. All rights reserved.
Hepatocellular carcinoma (HCC) is the most common type of liver cancer and the fastest-growing cause of cancer-related deaths in the United States. Most HCC cases are attributed to chronic hepatitis C virus infection,...
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Hepatocellular carcinoma (HCC) is the most common type of liver cancer and the fastest-growing cause of cancer-related deaths in the United States. Most HCC cases are attributed to chronic hepatitis C virus infection, which affects nearly 3 million Americans and 100 million people globally. Although surveillance for HCC m hepatitis C patients can improve survival, the optimal surveillance policies remain unknown. In this study, we develop a mixed-integer programming (MlP)-based framework to systematically analyze a rich set of policies and determine the optimal HCC surveillance policies that maximize societal net benefit. Our MIP-based framework addresses two problem features that make dynamic programming-based formulation computationally intractable. In particular, our proposed framework allows the formulation of (1) M-switch policies that are practical for implementation and (2) tailored surveillance policies with screening intervals stratified by the precursor disease states. We theoretically analyze the HCC surveillance problem, characterize when the surveillance policies should be adapted to populations with different disease progression rates, and quantify the trade-off between decreasing HCC incidence and increasing treatment outcomes. We parameterize our model using clinical trial data, a previously validated simulation model, and published clinical studies. Our numerical analyses lead to three main results with important policy implications. First, we find that, in addition to cirrhotic patients, expanding surveillance to patients in the earlier stages of hepatitis C infection improves the cost-effectiveness of HCC surveillance. Second, compared with the "one size fits all" routine policies, we fmd that it is cost-effective to stratify surveillance strategies based on the stage of hepatitis C infection with less frequent cancer surveillance in the earlier stages of infection. Finally, we find that a little flexibility in the policy structure as captured by
Recently, mixed-integer programming (MIP) techniques have been applied to learn optimal decision trees. Empirical research has shown that optimal trees typically have better out-of-sample performance than heuristic ap...
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Recently, mixed-integer programming (MIP) techniques have been applied to learn optimal decision trees. Empirical research has shown that optimal trees typically have better out-of-sample performance than heuristic approaches such as CART. However, the underlying MIP formulations often suffer from weak linear programming (LP) relaxations. Many existing MIP approaches employ big-M constraints to ensure observations are routed throughout the tree in a feasible manner. This paper introduces new MIP formulations for learning optimal decision trees with multivariate branching rules and no assumptions on the feature types. We first propose a strong baseline MIP formulation that still uses big-M constraints, but yields a stronger LP relaxation than its counterparts in the literature. We then introduce a problem-specific class of valid inequalities called shattering inequalities. Each inequality encodes an inclusion-minimal set of points that cannot be shattered by a multivariate split, and in the context of a MIP formulation, the inequalities are sparse, involving at most the number of features plus two variables. We propose a separation procedure that attempts to find a violated inequality given a (possibly fractional) solution to the LP relaxation;in the case where the solution is integer, the separation is exact. Numerical experiments show that our MIP approach outperforms two other MIP formulations in terms of solution time and relative gap, and is able to improve solution time while remaining competitive with regards to out-of-sample accuracy in comparison to a wider range of approaches from the literature.
Big events lead to temporary very high traffic volumes which usually exceed traffic capabilities of the existing infrastructure. Hence, it is necessary to control traffic in a way that helps to keep traffic congestion...
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Big events lead to temporary very high traffic volumes which usually exceed traffic capabilities of the existing infrastructure. Hence, it is necessary to control traffic in a way that helps to keep traffic congestion as low as possible. In this paper we introduce a traffic planning model for big events which optimizes traffic routing, allocates parking space, and defines locations for spot checks on traffic. We extend and modify a traffic flow model that has successfully been used in previous work on evacuation planning. A computational study demonstrates the model's applicability to a real world situation.
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