The unit commitment model with concave emissions costs: a hybrid Benders’ Decomposition with nonconvex master problems

We present a unit commitment model which determines generator schedules, associated production and storage quantities, and spinning reserve requirements. Our model minimizes fixed costs, fuel costs, shortage costs, and emissions costs. A constraint set balances the load, imposes requirements on the way in which generators and storage devices operate, and tracks reserve requirements. We capture cost functions with piecewise-linear and (concave) nonlinear constructs. We strengthen the formulation via cut addition. We then describe an underestimation approach to obtain an initial feasible solution to our model. Finally, we constitute a Benders’ master problem from the scheduling variables and a subset of those variables associated with the nonlinear constructs; the subproblem contains the storage and reserve requirement quantities, and power from generators with convex (linear) emissions curves. We demonstrate that our strengthening techniques and Benders’ Decomposition approach solve our mixed integer, nonlinear version of the unit commitment model more quickly than standard global optimization algorithms. We present numerical results based on a subset of the Colorado power system that provide insights regarding storage, renewable generators, and emissions.     

Managing inventories with one-way substitution: A newsvendor analysis

This paper presents an insightful approach to analyze two-item periodic inventory systems with one-way substitution. The objective is to minimize the expected total cost per period, which consists of expected purchasing costs, expected inventory holding costs, expected shortage costs, and expected adjustment costs. This approach helps derive the optimality conditions in both single-period and infinite horizon settings and yields useful insights into the impact of substitution on the service level, the optimality of a borderline case in which the order-up-to level of the inflexible item is reduced to zero, and the pivotal role of the purchasing cost.     

Reliable design of a logistics network under uncertainty: A fuzzy possibilistic-queuing model

This paper proposes a bi-objective model for designing a reliable network of bi-directional facilities in logistics network under uncertainties. For this purpose, the model utilizes an effective reliability approach to find a robust logistics network design. The objectives of the model are to minimize the total costs and the expected transportation costs after failures of bi-directional facilities of the logistics network. To solve the model, a new solution approach is proposed by combining queuing theory, fuzzy possibilistic programming and fuzzy multi-objective programming. Finally, the computational experiments are provided to illustrate the effectiveness of the proposed model and solution approach.     

A boundary integral equation method for the transmission eigenvalue problem

We propose a new integral equation formulation to characterize and compute transmission eigenvalues for constant refractive index that play an important role in inverse scattering problems for penetrable media. As opposed to the recently developed approach by Cossonnière and Haddar [1,2] which relies on a two by two system of boundary integral equations our analysis is based on only one integral equation in terms of Dirichlet-to-Neumann or Robin-to-Dirichlet operators which results in a noticeable reduction of computational costs. We establish Fredholm properties of the integral operators and their analytic dependence on the wave number. Further we employ the numerical algorithm for analytic non-linear eigenvalue problems that was recently proposed by Beyn [3] for the numerical computation of transmission eigenvalues via this new integral equation.     

Solving nonconvex economic load dispatch problem using particle swarm optimization with time varying acceleration coefficients

This article presents the design and application of an efficient hybrid heuristic search method to solve the practical economic dispatch problem considering many nonlinear characteristics of power generators, and their operational constraints, such as transmission losses, valve‐point effects, multi‐fuel options, prohibited operating zones, ramp rate limits and spinning reserve. These practical operation constraints which can usually be found at the same time in realistic power system operations make the economic load dispatch (ELD) problem a nonsmooth optimization problem having complex and nonconvex features with heavy equality and inequality constraints. A particle swarm optimization with time varying acceleration coefficients is proposed to determine optimal ELD problem in this paper. The proposed methodology easily takes care of solving nonconvex ELD problems along with different constraints like transmission losses, dynamic operation constraints, and prohibited operating zones. The proposed approach has been implemented on the 3‐machines 6‐bus, IEEE 5‐machines 14‐bus, IEEE 6‐machines 30‐bus systems and 13 thermal units power system. The proposed technique is compared with solve the ELD problem with hybrid approach by using the valve‐point effect. The comparison results prove the capability of the proposed method give significant improvements in the generation cost for the ELD problem. © 2015 Wiley Periodicals, Inc. Complexity 21: 299–308, 2016     

An approach based on level set method for void identification of continuum structure with time-domain dynamic response

An approach based on the level set method has been developed to identify the position and geometry of voids in continuum structure using time-domain dynamic response. The level set method is employed in the proposed approach to represent the boundary of the voids implicitly. The voids are identified by solving an optimization problem which minimizes an objective function about the displacement error. The boundary of the voids is evolved by updating the level set function. The shape derivative of the objective function for the time-domain dynamic response is derived and used to construct the velocity field. Then, the level set function is updated through the velocity field. The proposed approach has been applied to several numerical examples of void identification in continuum structure. The results indicate that the proposed approach based on the level set method can identify voids effectively and accurately with time-domain dynamic response. Moreover, the effects of measure points, excitation force, noise, void distribution, numerical error, element size and boundary conditions on the approach are studied. Meanwhile, the computational costs of some examples are provided.     

Minimizing fleet operating costs for a container transportation company

This paper focuses on a fleet management problem that arises in container trucking industry. From the container transportation company perspective, the present and future operating costs to minimize can be divided in three components: the routing costs, the resource (i.e., driver and truck) assignment costs and the container repositioning costs (i.e., the costs of restoring a given container fleet distribution over the serviced territory, as requested by the shippers that own the containers).This real-world problem has been modeled as an integer programming problem. The proposed solution approach is based on the decomposition of this problem in three simpler sub-problems associated to each of the costs considered above.Numerical experiments on randomly generated instances, as well as on a real-world data set of an Italian container trucking company, are presented.     

Unit commitment in electricity pool markets

We consider an electricity generator making offers of energy into an electricity pool market over a horizon of several trading periods (typically a single trading day). The generator runs a set of generating units with given start-up costs, shut-down costs and operating ranges. At the start of each trading period the generator must submit to the pool system operator a new supply curve defining quantities of offered energy and the prices at which it wants these dispatched. The amount of dispatch depends on the supply curve offered along with the offers of the other generators and market demand, both of which are random, but do not change in response to the actions of the generator we consider. After dispatch the generator determines which units to run in the current trading period to meet the dispatch. The generator seeks a supply function that maximizes its expected profit. We describe an optimization procedure based on dynamic programming that can be used to construct optimal offers in successive time periods over a fixed planning horizon.     

A boundary integral equation for the transmission eigenvalue problem for Maxwell equation

We propose a new integral equation formulation to characterize and compute transmission eigenvalues in electromagnetic scattering. As opposed to the approach that was recently developed by Cakoni, Haddar and Meng (2015) which relies on a two‐by‐two system of boundary integral equations, our analysis is based on only one integral equation in terms of the electric‐to‐magnetic boundary trace operator that results in a simplification of the theory and in a considerable reduction of computational costs. We establish Fredholm properties of the integral operators and their analytic dependence on the wave number. Further, we use the numerical algorithm for analytic nonlinear eigenvalue problems that was recently proposed by Beyn (2012) for the numerical computation of the transmission eigenvalues via this new integral equation.     

Optimum service capacity and demand management with price incentives

Service firms periodically face fluctuating demand levels. They incur high costs to handle peak demand and pay for under-utilized capacity during low demand periods. In this paper, we develop a mixed integer programming (MIP) model based on the real life experience of a Brazilian telecommunications firm. The model determines the optimum staffing requirements with different seniority levels for employees, as well as the distribution and balancing of workload utilizing flexibility of some customers in their service completion day. The proposed MIP uses monetary incentives to smooth the workload by redistributing some of the peak demand, thereby increasing capacity utilization. Due to the intractable nature of optimizing the proposed MIP model, we present a heuristic solution approach. The MIP model is applied to the case of the examined Brazilian Telecommunications firm. The computational work on this base case and its extensions shows that the proposed MIP model is of merit, leading to approximately seventeen percent reduction in the base case operating costs. Extensive computational work demonstrates that our heuristic provides quality solutions in very short computational times. The model can also be used to select new customers based on the workload, the revenue potential of these new customers and their flexibility in accepting alternate service completion dates. The generic structure of the proposed approach allows for its application to a wide variety of service organizations facing similar capacity and demand management challenges. Such wide applicability enhances the value of our work and its expected benefits.     

Product and process yield estimation with Gaussian quadrature (GQ) reduction: Improvements over the GQ full factorial approach

Manufacturing or multivariate yield, the fraction of unscreened products which conforms to all product specification limits, is an important and commonly used metric for assessing and improving the quality of a production process. Current procedures for multivariate yield evaluation, such as Monte Carlo simulation, require substantial computing effort, making the iterative adjustment of design parameters often impractical. This paper introduces a new approach to multivariate yield evaluation based on a numerical integration procedure called Gaussian quadrature reduction (GQR). The advantage of this approach is a large reduction in the computational burden associated with multivariate yield evaluation with virtually no loss in accuracy of the estimates. The proposed procedure can be generalized to evaluate many other multivariate criteria such as expected costs and the desirability index. The method is demonstrated for three yield evaluation test problems, and comparisons to Monte Carlo-based evaluations are presented.     

Design models for unit load storage and retrieval systems using autonomous vehicle technology and resource conserving storage and dwell point policies

Computationally efficient design conceptualization models are proposed for automated unit load storage and retrieval systems based on autonomous vehicle technology. Vehicle and lift travel times and the probability distribution for 12 service scenarios occurring under realistic operating assumptions are formulated and used to generate expected transaction service times. Additional measures of system performance including transaction waiting time and vehicle utilization are formulated for systems using random storage and point-of-service-completion dwell point rules. The models provide a practical means of predicting key aspects of system performance based on five design variables that drive the majority of system costs. They are illustrated in the context of a conceptualization study adapted from an actual system installation.     

Global analysis of an environmental disease transmission model linking within-host and between-host dynamics

In this paper, a multi-scale mathematical model for environmentally transmitted diseases is proposed which couples the pathogen-immune interaction inside the human body with the disease transmission at the population level. The model is based on the nested approach that incorporates the infection-age-structured immunological dynamics into an epidemiological system structured by the chronological time, the infection age and the vaccination age. We conduct detailed analysis for both the within-host and between-host disease dynamics. Particularly, we derive the basic reproduction number R₀ for the between-host model and prove the uniform persistence of the system. Furthermore, using carefully constructed Lyapunov functions, we establish threshold-type results regarding the global dynamics of the between-host system: the disease-free equilibrium is globally asymptotically stable when R₀ < 1, and the endemic equilibrium is globally asymptotically stable when R₀ > 1. We explore the connection between the within-host and between-host dynamics through both mathematical analysis and numerical simulation. We show that the pathogen load and immune strength at the individual level contribute to the disease transmission and spread at the population level. We also find that, although the between-host transmission risk correlates positively with the within-host pathogen load, there is no simple monotonic relationship between the disease prevalence and the individual pathogen load.     

Improved load balancing and resource utilization for the Skill Vehicle Routing Problem

The Skill Vehicle Routing Problem (Skill VRP) considers vehicle routing under the assumption of skill requirements given on demand nodes. These requirements have to be met by the serving vehicles. No further constraints, like capacity or cost restrictions, are imposed. Skill VRP solutions may show a tendency to have a bad load balancing and resource utilization. In a majority of solutions only a subset of vehicles is active. Moreover, a considerable share of demand nodes is served by vehicles that have a skill higher than necessary. A reason for that solution behavior lies in the model itself. As no resource restrictions are imposed, the Skill VRP tends to produce TSP-like solutions. To obtain better balanced solutions, we introduce two new approaches. First we propose a minmax model that aims at minimizing the maximal vehicle tour length. Second we suggest a two-step method combining the minmax approach with a distance constrained model. Our experiments illustrate that these approaches lead to improvements in load balancing and resource utilization, but, with different impact on routing costs.     

Improved utilization for joint HCCA–EDCA access in IEEE 802.11e WLANs

This paper presents a model for improving utilization in IEEE 802.11e wireless LAN via a Markov decision process (MDP) approach. A Markov chain tracking the utilized transmission window for two separate access mechanisms is devised. Subsequently, the action space and the rewards of the MDP are judiciously selected with the aim of improving overall utilization without explicit blocking. The proposed MDP model for 802.11e reveals that proportional allocation of access opportunities improve overall utilization compared to completely randomized access. Simulation results go on to show that a policy that limits HCCA access as a function of channel load improves utilization by an average 8 %. The optimization framework proposed in this paper is promising as a practical decision support tool for resource planning in 802.11e.     

A production–recycling–inventory system with imprecise holding costs

This paper presents an optimal control recycling production inventory system in fuzzy environment. The used items are bought back and then either put on recycling or disposal. Recycled products can be used for the new products which are sold again. Here, the rate of production, recycling and disposal are assumed to be function of time and considered as control variables. The demand inversely depends on the selling price. Again selling price is serviceable stock dependent. The holding costs (for serviceable and non-serviceable items) are fuzzy variables. At first we define the expected values of fuzzy variable, then the system is transferred to the fuzzy expected value model. In this paper, an optimal control approach is proposed to optimize the production, recycling and disposal strategy with respect so that expected value of total profit is maximum. The optimum results are presented both in tabular form and graphically.     

Using GRASP to Solve the Unit Commitment Problem

In this paper, the Unit Commitment (UC) problem is presented and solved, following an innovative approach based on a metaheuristic procedure. The problem consists on deciding which electric generators must be committed, over a given planning horizon, and on defining the production levels that are required for each generator, so that load and spinning reserve requirements are verified, at minimum production costs. Due to its complexity, exact methods proved to be inefficient when real size problems were considered. Therefore, heuristic methods have for long been developed and, in recent years, metaheuristics have also been applied with some success to the problem. Methods like Simulated Annealing, Tabu Search and Evolutionary Programming can be found in several papers, presenting results that are sufficiently interesting to justify further research in the area. In this paper, a resolution framework based on GRASP – Greedy Randomized Adaptive Search Procedure – is presented. To obtain a general optimisation tool, capable of solving different problem variants and of including several objectives, the operations involved in the optimisation process do not consider any particular characteristics of the classical UC problem. Even so, when applied to instances with very particular structures, the computational results show the potential of this approach.     

A linear Bayesian stochastic approximation to update project duration estimates

By relaxing the unrealistic assumption of probabilistic independence on activity durations in a project, this paper develops a hierarchical linear Bayesian estimation model. Statistical dependence is established between activity duration and the amount of resource, as well as between the amount of resource and the risk factor. Upon observation or assessment of the amount of resource required for an activity in near completion, the posterior expectation and variance of the risk factor can be directly obtained in the Bayesian scheme. Then, the expected amount of resources required for and the expected duration of upcoming activities can be predicted. We simulate an application project in which the proposed model tracks the varying critical path activities on a real time basis, and updates the expected project duration throughout the entire project. In the analysis, the proposed model improves the prediction accuracy by 38.36% compared to the basic PERT approach.     

不确定环境下服务资源配置优化

在服务资源配置过程中,按维修状态将服务对象分成三类:完全维修、部分维修及最小维修.由于维修服务的特性,服务成本与服务时间均是一个模糊数,并且维修对象在服务时所处的维修状态也具有一定的不确定性.针对这类情况下的服务资源配置问题,提出了同时考虑模糊服务成本和模糊服务时间及不确定维修状态的最小化服务成本为优化指标的服务资源配置模型.在模型的求解过程中采用多粒子群算法,通过仿真计算表明了该方法的可行性和有效性.