Railroad planning involves solving two optimization problems: (i) the blocking problem, which determines what blocks to make and how to route traffic over these blocks;and (ii) the train schedule design problem, which...
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Railroad planning involves solving two optimization problems: (i) the blocking problem, which determines what blocks to make and how to route traffic over these blocks;and (ii) the train schedule design problem, which determines train origins, destinations, and routes. Once the blocking plan and train schedule have been obtained, the next step is to determine which trains should carry which blocks. This problem, known as the block-to-train assignment problem, is considered in this paper. We provide two formulations for this problem: an arc-based formulation and a path-based formulation. The latter is generally smaller than the former, and it can better handle practical constraints. We also propose exact and heuristic algorithms based on the path-based formulation. Our exact algorithm solves an integerprogramming formulation with CPLEX using both a priori generation and dynamic generation of paths. Our heuristic algorithms include a Lagrangian relaxation-based method as well as a greedy construction method. We present computational results of our algorithms using the data provided by a major US railroad. We show that we can obtain an optimal solution of the block-to-train assignment problem within a few minutes of computational time, and can obtain heuristic solutions with 1-2% deviations from the optimal solutions within a few seconds. (C) 2007 Wiley Periodicals, Inc.
This paper focuses on guillotine cuts which often arise in real-life cutting stock problems. In order to construct a solution verifying guillotine constraints, the first step is to know how to determine whether a give...
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This paper focuses on guillotine cuts which often arise in real-life cutting stock problems. In order to construct a solution verifying guillotine constraints, the first step is to know how to determine whether a given cutting pattern is a guillotine pattern. For this purpose, we first characterize guillotine patterns by proving a necessary and sufficient condition. Then, we propose a polynomial algorithm to check this condition. Based on this mathematical characterization of guillotine patterns, we then show that guillotine constraints can be formulated into linear inequalities. The performance of the algorithm to check guillotine cutting patterns is evaluated by means of computational results. (c) 2007 Elsevier B.V. All rights reserved.
We study an optimal design problem for serial machining lines. Such lines consist of a sequence of stations. At every station, the operations to manufacture a product are grouped into blocks. The operations within eac...
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We study an optimal design problem for serial machining lines. Such lines consist of a sequence of stations. At every station, the operations to manufacture a product are grouped into blocks. The operations within each block are performed simultaneously by the same spindle head and the blocks of the same station are executed sequentially. The inclusion and exclusion constraints for combining operations into blocks and stations as well as the precedence constraints on the set of operations are given. The problem is to group the operations into blocks and stations minimizing the total line cost. A feasible solution must respect the given cycle time and all given constraints. In this paper, a heuristic multi-start decomposition approach is proposed. It utilizes a decomposition of the initial problem into several sub-problems on the basis of a heuristic solution. Then each obtained sub-problem is solved by an exact algorithm. This procedure is repeated many times, each time it starts with a new heuristic solution. Computational tests show that the proposed approach outperforms simple heuristic algorithms for large-scale problems. (C) 2007 Elsevier B.V. All rights reserved.
We consider the maximization of a multicommodity flow throughput in presence of constraints on the maximum number of paths to be used. Such an optimization problem is strongly NP-hard, and is known in the literature a...
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We consider the maximization of a multicommodity flow throughput in presence of constraints on the maximum number of paths to be used. Such an optimization problem is strongly NP-hard, and is known in the literature as the maximum routable demand fraction variant of the k-splittable flow problem. Here we propose an exact approach based on branch and bound rules and on an arc-flow mixed integer programming formulation of the problem. Computational results are provided, and a comparison with a standard commercial solver is proposed.
This paper presents a stochastic midterm risk-constrained hydrothermal scheduling algorithm in a generation company (GENCO). The objective of a GENCO is to maximize payoffs and minimize financial risks when scheduling...
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This paper presents a stochastic midterm risk-constrained hydrothermal scheduling algorithm in a generation company (GENCO). The objective of a GENCO is to maximize payoffs and minimize financial risks when scheduling its midterm generation of thermal, cascaded hydro, and pumped-storage units. The proposed schedule will be used by the GENCO for bidding purposes to the ISO. The optimization model is based on stochastic price-based unit commitment. The proposed GENCO solution may be used to schedule midterm fuel and natural water inflow resources for a few months to a year. The proposed stochastic mixed-integerprogramming solution considers random market prices for energy and ancillary services, as well as the availability of natural water inflows and generators in Monte Carlo scenarios. Financial risks associated with uncertainties are considered by applying expected downside risks which are incorporated explicitly as constraints. Variable time-steps are adopted to avoid the exponential growth in solution time and memory requirements when considering midterm constraints. A single water-to-power conversion function is used instead of several curves for representing water head and discharge parameters. Piecewise linearized head-dependant water-to-power conversion functions are used for computational efficiency. Illustrative examples examine GENCOs' midterm generation schedules, risk levels, fuel and water usage, and hourly generation dispatches for bidding in energy and ancillary services markets. The paper shows that GENCOs could decrease their financial risks by adjusting expected payoffs.
A lot sizing and scheduling problem prevalent in small market-driven foundries is studied. There are two related decision levels: (I the furnace scheduling of metal alloy production, and (2) moulding machine planning ...
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A lot sizing and scheduling problem prevalent in small market-driven foundries is studied. There are two related decision levels: (I the furnace scheduling of metal alloy production, and (2) moulding machine planning which specifies the type and size of production lots. A mixed integer programming (MIP) formulation of the problem is proposed, but is impractical to solve in reasonable computing time for non-small instances. As a result, a faster relax-and-fix (RF) approach is developed that can also be used on a rolling horizon basis where only immediate-term schedules are implemented. As well as a MIP method to solve the basic RF approach, three variants of a local search method are also developed and tested using instances based on the literature. Finally, foundry-based tests with a real-order book resulted in a very substantial reduction of delivery delays and finished inventory, better use of capacity, and much faster schedule definition compared to the foundry's own practice. (c) 2006 Elsevier Ltd. All rights reserved.
We address a multi-item capacitated lot-sizing problem with setup times and shortage costs that arises in real-world production planning problems. Demand cannot be backlogged, but can be totally or partially lost. The...
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We address a multi-item capacitated lot-sizing problem with setup times and shortage costs that arises in real-world production planning problems. Demand cannot be backlogged, but can be totally or partially lost. The problem is NP-hard. A mixedinteger mathematical formulation is presented. Our approach in this paper is to propose some classes of valid inequalities based on a generalization of Miller et al. [A.J. Miller, G.L. Nemhauser, M.W.P. Savelsbergh, On the polyhedral structure of a multi-item production planning model with setup times, Mathematical programming 94 (2003) 375-405] and Marchand and Wolsey [H. Marchand, L.A. Wolsey, The 0-1 knapsack problem with a single continuous variable, Mathematical programming 85 (1999) 15-33] results. We also describe fast combinatorial separation algorithms for these new inequalities. We use them in a branch-and-cut framework to solve the problem. Some experimental results showing the effectiveness of the approach are reported. (C) 2006 Elsevier B.V. All rights reserved.
We show that exact computation of a family of 'max weighted score' estimators, including Manski's max score estimator, can be achieved efficiently by reformulating them as mixedinteger programs (MIP) with...
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We show that exact computation of a family of 'max weighted score' estimators, including Manski's max score estimator, can be achieved efficiently by reformulating them as mixedinteger programs (MIP) with disjunctive constraints. The advantage of our MIP formulation is that estimates are exact and can be computed using widely available solvers in reasonable time. In a classic work-trip mode choice application, our method delivers exact estimates that lead to a different economic interpretation of the data than previous heuristic estimates. In a small Monte Carlo study we find that our approach is computationally efficient for usual estimation problem sizes. (C) 2008 Elsevier B.V. All rights reserved.
This study presents a decision-making framework for modelling containerisation of air cargo forwarding problems. The objective is to help logistics managers make decisions about how to rent air containers from air car...
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This study presents a decision-making framework for modelling containerisation of air cargo forwarding problems. The objective is to help logistics managers make decisions about how to rent air containers from air carriers and how to load air cargos into these containers optimally. The air carriers can provide different types of air containers with differing weight and volume limits. The problem is further complicated by the cost charged by the air carriers: this is based on a fixed cost for using the container and a variable cost that depends on the weight that the container will hold. A mathematic programming model is formulated to minimise the total rental cost while satisfying the customer's shipping requirements. The objective function in the model, however, is a non-decreasing piece-wise linear one. The model is changed into a mixedinteger linear programming model by introducing two new sets of variables, and the new model can be solved by employing many mathematical programming software packages available today. The model is illustrated with a practical problem faced by a logistics company and sensitivity analysis of three different scenarios.
The work presents a model which solves the heat exchanger network (HEN) synthesis problem using geometric mean temperature difference (GMTD) in place of the logarithmic mean temperature difference (LMTD). With the aid...
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The work presents a model which solves the heat exchanger network (HEN) synthesis problem using geometric mean temperature difference (GMTD) in place of the logarithmic mean temperature difference (LMTD). With the aid of logarithmic transformation and piecewise linearization, the problem is stated in a linear form and thus global optimality can be assured for the model. The accuracy of the approximation is discussed and the results obtained for three known case problems show that the usage of GMTD instead of LMTD can be justified. The GMTD-based model produces designs that are sufficiently accurate and comparable with the ones obtained using the LMTD. (C) 2007 Elsevier Ltd. All rights reserved.
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