In this paper, we study probabilistically constrained problems involving individual chance constraints, random univariate right-hand sides, and risk tolerances defined as decision variables which affect part of the ob...
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In this paper, we study probabilistically constrained problems involving individual chance constraints, random univariate right-hand sides, and risk tolerances defined as decision variables which affect part of the objective function. Built on the concept of efficient points, we formulate the problems as mixed-integer programs by using binary variables to determine an optimal risk tolerance for each chance constraint. We develop two benchmark approaches, both of which solve chance-constrained programs with fixed risk values in a bisection algorithm or by enumeration. We specify our approaches for a minimum cost flow problem and a network capacity design problem, both of which involve chance constraints for bounding the risk of demand shortages. We test instances with diverse size and complexity of the two network problems, and demonstrate the computational efficacy as well as give managerial insights. (C) 2014 Elsevier Ltd. All rights reserved.
We develop a finite-horizon discrete-time constrained Markov decision process (MDP) to model diagnostic decisions after mammography where we maximize the total expected quality-adjusted life years (QALYs) of a patient...
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We develop a finite-horizon discrete-time constrained Markov decision process (MDP) to model diagnostic decisions after mammography where we maximize the total expected quality-adjusted life years (QALYs) of a patient under resource constraints. We use clinical data to estimate the parameters of the MDP model and solve it as a mixed-integer program. By repeating optimization for a sequence of budget levels, we calculate incremental cost-effectiveness ratios attributable to consecutive levels of funding and compare actual clinical practice with optimal decisions. We prove that the optimal value function is concave in the allocated budget. Comparing to actual clinical practice, using optimal thresholds for decision making may result in approximately 22% cost savings without sacrificing QALYs. Our analysis indicates short-term follow-ups are the immediate target for elimination when budget becomes a concern. Policy change is more drastic in the older age group with the increasing budget, yet the gains in total expected QALYs related to larger budgets are predominantly seen in younger women along with modest gains for older women.
The new energy dispatch problem has aroused more and more attention. In this paper, we investigate the problem of determining the optimal usage of generating power during a scheduling period. A set of MIP formulations...
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The new energy dispatch problem has aroused more and more attention. In this paper, we investigate the problem of determining the optimal usage of generating power during a scheduling period. A set of MIP formulations are adopted for precise modeling of the variety of power systems (different power generation units) and the actual situation in china. Based on these formulations, we construct a new energy dispatch model which includes many MIP sub-problems. An auto-tuning MIP solver CMIP is given to effectively improve the performance of solving the proposed model. The CMIP focuses on optimizations for presolver, the LP solver for corresponding relaxation problem, and the primal heuristics. Actual predict data is used in performance experiments. Computational results conform to the viability of optimization. Our optimizations further reduce 27.6% of the average execution time compared to CPLEX. (C) 2015 Elsevier B.V. All rights reserved.
Shorter product life cycles in the chemical industry have led to uncertain demand in terms of volume, location and type. Modular production concepts can be used to serve such volatile customer demand more efficiently....
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Shorter product life cycles in the chemical industry have led to uncertain demand in terms of volume, location and type. Modular production concepts can be used to serve such volatile customer demand more efficiently. Modular plants increase the tactical flexibility of the supply chain substantially compared to centralized production with large-scale plants. Furthermore, production facilities can be flexibly opened, deactivated and reactivated. Modular plants can be relocated in the medium term, and their production capabilities can be reconfigured via process module changes. This work proposes new mixed-integer programming formulations for the tactical planning of production networks in the chemical industry;these formulations prescribe the volume, location, and process of modular plants in the production network over a multi-period planning horizon. The economic value of modular flexibility is investigated in a case study from the chemical industry under the consideration of diverse demand structures. The results have several managerial implications for the technical implementation and development of modular production technology in the chemical industry. (C) 2019 Elsevier B.V. All rights reserved.
This paper addresses a routing and scheduling problem from two different perspectives: economic and environmental. From economic perspective, we aim to optimize the vehicle routing plan to reduce the operating cost, b...
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This paper addresses a routing and scheduling problem from two different perspectives: economic and environmental. From economic perspective, we aim to optimize the vehicle routing plan to reduce the operating cost, but from environmental perspective, we aim to optimize the vehicle routing and speed decisions to reduce the carbon emissions. This research can provide two different decision plans under these two different perspectives, and the comparison of the results from the two different perspectives will be very meaningful and helpful to the logistics decision-makers. We formulate the problem using two mixed-integer programming (MIP) models with different objectives. However, this problem is very challenging, with medium-sized instances already difficult for the MIP solver. In order to solve it with larger scale instances, we propose an exact branch-and-price (BAP) algorithm. The BAP algorithm relies on efficiently solving the pricing sub-problem with different objectives. We design two different tailored labeling algorithms to solve it. Extensive computational experiments demonstrate the effectiveness of the proposed BAP algorithm, comparing with the MIP formulation solved by CPLEX with a time limit of 2 h.
Nowadays, energy-efficient scheduling has assumed a key role in ensuring the sustainability of manufacturing processes. In this context, we focus on the bi-objective problem of scheduling a set of jobs on identical pa...
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Nowadays, energy-efficient scheduling has assumed a key role in ensuring the sustainability of manufacturing processes. In this context, we focus on the bi-objective problem of scheduling a set of jobs on identical parallel machines to simultaneously minimize the maximum completion time and the total energy consumption over a time horizon partitioned into a set of discrete slots. The energy costs are determined by a time-of-use pricing scheme, which plays a crucial role in regulating energy demand and flattening its peaks. First, we uncover a symmetry-breaking property that characterizes the structure of the solution space of the problem. As a consequence, we provide a novel, compact mixed-integer linear programming formulation at the core of an efficient exact solution algorithm. A thorough experimental campaign shows that the use of the novel mathematical programming formulation enables the solution of larger-scale instances and entails a reduction in the computational times as compared to the formulation already available in the literature. Furthermore, we propose a new heuristic that improves the state-of-the-art in terms of required computational effort and quality of solutions. Such a heuristic outperforms the existing heuristics for the problem and is also capable of speeding up the exact solution algorithm when used for its initialization. Finally, we introduce a novel dynamic programming algorithm that is able to compute the optimal timing of the jobs scheduled on each machine to further improve the performance of the new heuristic.& COPY;2023 Elsevier B.V. All rights reserved.
We consider a region suffering from irrigation water scarcity. Candidate crops differ widely in their growth cycles, economic values and water consumption. We develop an integrated dynamic programming-mixedinteger pr...
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We consider a region suffering from irrigation water scarcity. Candidate crops differ widely in their growth cycles, economic values and water consumption. We develop an integrated dynamic programming-mixedintegerprogramming model to solve for optimal land exploitation over a one year horizon for multiple crops. The model applies deficit irrigation in order to increase the irrigated area at the expense of reducing crop yield per unit area. The dynamic program (DP) guarantees that deficit irrigation is only considered when it is economically efficient. Moreover, it provides optimal combinations of irrigation levels for each growth stage of candidate crops, accounting for the varying impact of water stress over time and the seasonal supply of irrigation water. The output of the DP serves as input to the mixedinteger program (MIP). The MIP selects the most pro. table crops in the right sequence to benefit the most from the crop-yield dependence on crop predecessor and allocates water and land optimally to maximize total profit. The objective function accounts for the attitude of the decision-maker toward risk by incorporating in its expression a risk-aversion coefficient.
In the fixed-charge transportation problem, the goal is to optimally transport goods from depots to clients when there is a fixed cost associated to transportation or, equivalently, to opening an arc in the underlying...
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In the fixed-charge transportation problem, the goal is to optimally transport goods from depots to clients when there is a fixed cost associated to transportation or, equivalently, to opening an arc in the underlying bipartite graph. We further motivate its study by showing that it is both a special case and a strong relaxation of the big-bucket multi-item lot-sizing problem, and a generalization of a simple variant of the single-node flow set. This paper is essentially a polyhedral analysis of the polynomially solvable special case in which the associated bipartite graph is a path. We give a O(n(3))-time optimization algorithm and a O(n(2))-size linear programming extended formulation. We describe a new class of inequalities that we call "path-modular" inequalities. We give two distinct proofs of their validity. The first one is direct and crucially relies on sub-and super-modularity of an associated set function. The second proof is by showing that the projection of the extended linear programming formulations onto the original variable space yields exactly the polyhedron described by the path-modular inequalities. Thus we also show that these inequalities suffice to describe the convex hull of the set of feasible solutions.
This paper is concerned with the problem of assigning employees to a number of work centres taking into account employees' expressed preferences for specific shifts, off-days, and work centres. This particular pro...
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This paper is concerned with the problem of assigning employees to a number of work centres taking into account employees' expressed preferences for specific shifts, off-days, and work centres. This particular problem is faced by the Kuwait National Petroleum Corporation that hires a firm to prepare schedules for assigning employees to about 86 stations distributed all over Kuwait. The number of variables in a mixed-integer programming model formulated for this problem is overwhelming, and hence, a direct solution to even the continuous relaxation of this model for relatively large-scale instances is inconceivable. However, we demonstrate that a column generation method, which exploits the special structures of the model, can readily solve the continuous relaxation of the model. Based on this column generation construct, we develop an effective heuristic to solve the problem. Computational results indicate that the proposed approach can facilitate the generation of good-quality schedules for even large-scale problem instances in a reasonable time.
The steady-state economic optimum in chemical process plants generally lies at the intersection of constraints. However, in order to maintain feasible operation in the face of disturbances. the steady-state operating ...
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The steady-state economic optimum in chemical process plants generally lies at the intersection of constraints. However, in order to maintain feasible operation in the face of disturbances. the steady-state operating point needs to be moved some distance from the constraints into the feasible region. The optimal back-off is a function of the plant dynamics, the type and magnitude of the expected disturbances, and the plant control system. This paper considers calculation of the optimal back-off with regulation under constrained predictive control. The resulting optimization problem is multilevel in nature. and is formulated and solved as a mixed-integer quadratic or linear programming problem for which global optimality is guaranteed. Case studies comprising CSTRs in series and a fluid catalytic cracking unit illustrate the application of the strategy. (c) 2007 Elsevier Ltd. All rights reserved.
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