We consider a production planning problem known as the discrete lot-sizing and scheduling problem (DLSP) and study a variant of the DLSP involving several identical parallel resources. We show how to solve the resulti...
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We consider a production planning problem known as the discrete lot-sizing and scheduling problem (DLSP) and study a variant of the DLSP involving several identical parallel resources. We show how to solve the resulting discrete optimisation problem as a mixed-integerlinear program using a commercial MIP solver. To achieve this, we exhibit a family of strong valid inequalities for which the associated separation problem is efficiently solvable. Our computational results show that the proposed solution algorithm is capable of providing optimal solutions for medium-sized instances.
Missions with high combinatorial complexity involving several logical and temporal constraints often arise in cooperative control of multiple Uninhabited Aerial Vehicles. In this paper, we propose a new class of probl...
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Missions with high combinatorial complexity involving several logical and temporal constraints often arise in cooperative control of multiple Uninhabited Aerial Vehicles. In this paper, we propose a new class of problems that generalizes the standard Vehicle Routing Problem (VRP) by addressing complex tasks and constraints on the mission, called the 'mission specifications', expressed in a high-level specification language. In the generalized problem setup, these mission specifications are naturally specified using the linear Temporal Logic language LTL-X. Using a novel systematic procedure, the LTL-X specification is converted to a set of constraints suitable to a mixed-integer linear programming (MILP) formulation, which in turn can be incorporated into two widely-used MILP formulations of the standard VRP. Solving the resulting MILP provides an optimal plan that satisfies the given mission specification. The paper also presents two mission planning applications. Copyright (C) 2011 John Wiley & Sons, Ltd.
This paper provides a technique to build hourly offering curves for a price-taker producer participating in a pool. The technique relies on solving a sequence of robust mixed-integer linear programming problems. Inste...
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This paper provides a technique to build hourly offering curves for a price-taker producer participating in a pool. The technique relies on solving a sequence of robust mixed-integer linear programming problems. Instead of using price predictions as input data, price confidence intervals are considered. These intervals are successively divided into a sequence of nested subintervals, which allow formulating a collection of meaningful and easy-to-solve robust mixed-integer linear programming problems. The solutions of these problems provide adequate information to build hourly offering curves.
This work addresses the scheduling of continuous single stage multiproduct plants with parallel units and shared storage tanks. Processing tasks are energy intensive and we consider time-dependent electricity pricing ...
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This work addresses the scheduling of continuous single stage multiproduct plants with parallel units and shared storage tanks. Processing tasks are energy intensive and we consider time-dependent electricity pricing and availability together with multiple intermediate due dates, handled as hard constraints. A new discrete-time aggregate formulation is proposed to rapidly plan the production levels. It is combined with a continuous-time model for detailed scheduling as the essential part of a rolling-horizon algorithm. Their computational performance is compared to traditional discrete and continuous-time full-space formulations with all models relying on the Resource-Task Network (RTN) process representation. The results show that the new models and algorithm can generate global optimal schedules much more efficiently than their counterparts in problems involving unlimited power availability. Under restricted power, the aggregate model underestimates the electricity cost, which may cause the rolling-horizon approach to converge to a suboptimal solution, becoming the discrete-time model a better approach. (c) 2010 Elsevier Ltd. All rights reserved.
In this work, a series of novel formulations for a commercial territory design problem motivated by a real-world case are proposed. The problem consists on determining a partition of a set of units located in a territ...
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In this work, a series of novel formulations for a commercial territory design problem motivated by a real-world case are proposed. The problem consists on determining a partition of a set of units located in a territory that meets multiple criteria such as compactness, connectivity, and balance in terms of customers and product demand. Thus far, different versions of this problem have been approached with heuristics due to its NP-completeness. The proposed formulations are integer quadratic programming models that involve a smaller number of variables than heretofore required. These models have also enabled the development of an exact solution framework, the first ever derived for this problem, that is based on branch and bound and a cut generation strategy. The proposed method is empirically evaluated using several instances of the new quadratic models as well as of the existing linear models. The results show that the quadratic models allow solving larger instances than the linear counterparts. The former were also observed to require fewer iterations of the exact method to converge. Based on these results the combination of the quadratic formulation and the exact method are recommended to approach problem instances associated with medium-sized cities.
This paper proposes a new unit commitment (UC) formulation for a power system with significant levels of wind generation. The proposed scheme departs from existing unit commitments in that it explicitly models the day...
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This paper proposes a new unit commitment (UC) formulation for a power system with significant levels of wind generation. The proposed scheme departs from existing unit commitments in that it explicitly models the day-ahead predicted residual demand probability density function (PDF) including the effect of wind power curtailment. This PDF is then used to define a constraint on the probability of the residual demand exceeding the scheduled reserve, which is imposed in addition to the standard N-1 deterministic security criterion. This hybrid probabilistic/deterministic form maintains the mixed-integerlinear structure that makes the proposed UC compatible with highly efficient commercially available solvers. Numerical examples illustrate the economical and technical benefits obtained by systematically including wind curtailment as decisions variables in the UC. In addition, the paper computes the hourly day-ahead UC schedule over the course of one year for a typical power system to illustrate the impact of wind power penetration on measures such as operation costs, incremental costs, emission levels, on/off unit switching operations, and reserve levels.
A standard approach to estimate intracellular fluxes on a genome-wide scale is flux-balance analysis (FBA), which optimizes an objective function subject to constraints on (relations between) fluxes. The performance o...
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A standard approach to estimate intracellular fluxes on a genome-wide scale is flux-balance analysis (FBA), which optimizes an objective function subject to constraints on (relations between) fluxes. The performance of FBA models heavily depends on the relevance of the formulated objective function and the completeness of the defined constraints. Previous studies indicated that FBA predictions can be improved by adding regulatory on/off constraints. These constraints were imposed based on either absolute [21], [3] or relative [20] gene expression values. We provide a new algorithm that directly uses regulatory up/down constraints based on gene expression data in FBA optimization (tFBA). Our assumption is that if the activity of a gene drastically changes from one condition to the other, the flux through the reaction controlled by that gene will change accordingly. We allow these constraints to be violated, to account for posttranscriptional control and noise in the data. These up/down constraints are less stringent than the on/off constraints as previously proposed. Nevertheless, we obtain promising predictions, since many up/down constraints can be enforced. The potential of the proposed method, tFBA, is demonstrated through the analysis of fluxes in yeast under nine different cultivation conditions, between which approximately 5,000 regulatory up/down constraints can be defined. We show that changes in gene expression are predictive for changes in fluxes. Additionally, we illustrate that flux distributions obtained with tFBA better fit transcriptomics data than previous methods. Finally, we compare tFBA and FBA predictions to show that our approach yields more biologically relevant results.
The feasibility pump (FP) has proved to be a successful heuristic for finding feasible solutions of mixedintegerlinear problems. Briefly. FP alternates between two sequences of points: one of feasible solutions for ...
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The feasibility pump (FP) has proved to be a successful heuristic for finding feasible solutions of mixedintegerlinear problems. Briefly. FP alternates between two sequences of points: one of feasible solutions for the relaxed problem, and another of integer points. This short paper extends FP, such that the integer point is obtained by rounding a point on the (feasible) segment between the computed feasible point and the analytic center for the relaxed linear problem. (C) 2011 Elsevier B.V. All rights reserved.
During the last 15 years, many mathematical models have been developed in order to solve process operation scheduling problems, using discrete or continuous-time representations. In this paper, we present a unified re...
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During the last 15 years, many mathematical models have been developed in order to solve process operation scheduling problems, using discrete or continuous-time representations. In this paper, we present a unified representation and modeling approach for process scheduling problems. Four different time representations are presented with corresponding strengthened formulations that rely on exploiting the non-overlapping graph structure of these problems through maximum cliques and bicliques. These formulations are compared, and applied to single-stage and multi-stage batch scheduling problems, as well as crude-oil operations scheduling problems. We introduce three solution methods that can be used to achieve global optimality or obtain near-optimal solutions depending on the stopping criterion used. Computational results show that the multi-operation sequencing time representation is superior to the others as it allows efficient symmetry-breaking and requires fewer priority-slots, thus leading to smaller model sizes. (C) 2010 Elsevier Ltd. All rights reserved.
The long-term economic outcome of energy-related industrial investment projects is difficult to evaluate because of uncertain energy market conditions. In this article, a general, multistage, stochastic programming mo...
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The long-term economic outcome of energy-related industrial investment projects is difficult to evaluate because of uncertain energy market conditions. In this article, a general, multistage, stochastic programming model for the optimization of investments in process integration and industrial energy technologies is proposed. The problem is formulated as a mixed-binary linearprogramming model where uncertainties are modelled using a scenario-based approach. The objective is to maximize the expected net present value of the investments which enables heat savings and decreased energy imports or increased energy exports at an industrial plant. The proposed modelling approach enables a long-term planning of industrial, energy-related investments through the simultaneous optimization of immediate and later decisions. The stochastic programming approach is also suitable for modelling what is possibly complex process integration constraints. The general model formulation presented here is a suitable basis for more specialized case studies dealing with optimization of investments in energy efficiency. (C) 2011 Elsevier Ltd. All rights reserved.
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