Annals of Operations Research最新文献

This survey investigates the field of moderate exponential-time algorithms for ({mathcal{N}mathcal{P}})-hard scheduling problems, i.e., exact algorithms whose worst-case time complexity is moderately exponential with respect to brute force algorithms. Scheduling problems are very challenging problems for which interesting results have emerged in the literature since 2010. We will provide a comprehensive overview of the known results of these problems before detailing three general techniques to derive moderate exponential-time algorithms. These techniques are Sort & Search, Inclusion–Exclusion and Branching. In the last part of this survey, we will focus on side topics such as approximation in moderate exponential time, the design of lower bounds on worst-case time complexities or fixed-parameter tractability. We will also discuss the potential benefits of moderate exponential-time algorithms for efficiently solving in practice scheduling problems.

The spread of renewable energy has been accelerated by investment in power generation and transmission systems under environmental policy support such as a feed-in premium (FIP) scheme. This study examines the decision-making of the transmission system operator (TSO) and the power generation company (GENCO), where the TSO maximizes social surplus by investing in transmission lines, and the GENCO maximizes its profit by investing in power generation facilities. Specifically, the TSO decides the investment timing, while the GENCO decides the capacity. We develop a real options model to analyze the equilibrium investment timing and capacity under uncertainties in a framework of game between TSO and GENCO. We consider several scenarios in which the GENCO invests in non-renewable energy (NRE); invests in renewable energy (RE) with FIP; and invests in RE with its installation cost reduction. Our results indicate that FIP and the installation cost reduction of RE affect the equilibrium decision in a different manner. We find that FIP tends to be more welfare-enhancing than the reduction of RE installation cost when the degree of uncertainty is larger. We also demonstrate that social surplus can be increased without FIP if the installation cost of RE is reduced sufficiently in the future.

In this paper, we deal with a renewable-powered mini-grid, connected to an unreliable main grid, in a Joint Chance Constrained (JCC) programming setting. In several rural areas in Africa with low energy access rates, grid-connected mini-grid system operators contend with four different types of uncertainties: forecasting errors of solar power and load; frequency and outages duration from the main-grid. These uncertainties pose new challenges to the classical power system’s operation tasks. Three alternatives to the JCC problem are presented. In particular, we present an Individual Chance Constraint (ICC), Expected-Value Model (EVM) and a so called regular model that ignores outages and forecasting uncertainties. The JCC model has the capability to guarantee a high probability of meeting the local demand throughout an outage event by keeping appropriate reserves for Diesel generation and battery discharge. In contrast, the easier to handle ICC model guarantees such probability only individually for different time steps, resulting in a much less robust dispatch. The even simpler EVM focuses solely on average values of random variables. We illustrate the four models through a comparison of outcomes attained from a real mini-grid in Lake Victoria, Tanzania. The results show the dispatch modifications for battery and Diesel reserve planning, with the JCC model providing the most robust results, albeit with a small increase in costs.

Interval games are an extension of cooperative coalitional games in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval instead of a real number. In this paper, we focus on interval game versions of Shapley values. First, we modify Young’s strong monotonicity axiom for coalitional games into two versions so that they can be applied to the Shapley mapping and show that this can be axiomatized within the entire class of interval games using either version. Second, we derive the Shapley mapping for specific examples by employing two approaches used in the proof of the axiomatization and argue that our approach effectively works for a wide range of interval games.

A generalized n-site Asymmetric Simple Inclusion Process (ASIP) network is studied, where gate-opening instants are determined by a renewal process and arrivals occur to all sites. Various types of batch particle movements between sites are analyzed: (i) unidirectional probabilistic forward movements; (ii) probabilistic forward movements combined with feedback to the first site; and (iii) general probabilistic multidirectional movements. In contrast to the tedious successive substitution method used in previous ASIP studies, an efficient matrix approach is applied to derive the multidimensional probability generating function (PGF) of site occupancies right after gate opening instants. The complexity of the ASIP processes allows us to obtain explicit PGF results for small-size networks only, while for larger networks, a formula to calculate the mean site occupancies is derived for all types of movements. In movement case (i) the means are directly and explicitly calculated. For movement case (ii), where the network is homogeneous with equal probabilities of forward movements from site i to downstream sites (j ge i), we show that the ratio between the mean occupancies of consecutive sites approaches a constant when the network becomes large, and calculate this ratio. Finally, we investigate an n-site network where at gate opening instants all gates open simultaneously, and particles move in all directions. Numerical examples are presented.

Standard solutions for cooperative transferable utility (TU-) games assign to every player in a TU-game a real number representing the player’s payoff. In this paper, we introduce interval solutions for TU-games which assign to every player in a game a payoff interval. Even when the worths of coalitions are known, it might be that the individual payoff of a player is not known. According to an interval solution, every player knows at least a lower- and upper bound for its individual payoff. Therefore, interval solutions are useful when there is uncertainty about the payoff allocation even when the worths that can be earned by coalitions are known. Specifically, we consider two interval generalizations of the famous Shapley value that are based on marginal contributions in terms of intervals. To determine these marginal interval contributions, we apply the subtraction operator of Moore. We provide axiomatizations for the class of totally positive TU-games. We also show how these axiomatizations can be used to extend any linear TU-game solution to an interval solution. Finally, we illustrate these interval solutions by applying them to sequencing games.

We consider a shortest-path network interdiction problem under endogenous uncertainty on successful detection. Endogenous uncertainty arises from the fact that the interdictor may decide to enforce surveillance on some critical arcs, which would affect the prior probability of success on those arcs. The evader decision is formulated as a two-stage stochastic programming problem. In a “here and now situation”, he has to choose the shortest path in the network before realizing detection scenarios. Then, in the second stage, the evader tries to minimize the expected cost of being detected over all possible scenarios. We consider binary scenarios to represent whether or not the evader is detected on each path and apply a linearization method to deal with the non-linearity in the decision-dependent probability measure. A decomposition method is used to solve the proposed model for a case study of a worldwide drug trafficking network. The case study is concerned with finding the most critical arcs for interdicting drug trafficking. Numerical results show that a tiny increase in the probability of opium seizures leads to a significant change in the expected cost when the critical arcs are interdicted. Due to the exponential number of scenarios, the model could not be solved in a reasonable time. Common scenario reduction methods are designed for exogenous uncertainty. We apply an improved bundling method to reduce the number of scenarios in case of endogenous uncertainty. Computational results show that our method reduces the model size and solution time tremendously without significantly affecting the objective value.

Outsourcing operations have become an essential factor in enhancing the competitive advantage of software development enterprises. In this work, we examine the application of combinatorial auction in technician assignment and outsourcing service procurement, which is conducted by software enterprises to minimize the total cost of developing all the software. It gives rise to an unrelated parallel machine scheduling problem incorporating combinatorial auction (UPMSCA). Here, the jobs represent the software to be developed, and they consume the perishable time resources of the development technicians, which can be translated into monetary costs. The objective is to schedule the jobs on parallel machines or select the bid with the lowest cost. To solve the problem, we propose an arc-flow model and a set-partitioning formulation with column-based constraints. A branch-and-price algorithm with four branching rules is proposed and utilizes an effective dynamic programming algorithm to solve the pricing subproblem in the pattern-based formulation. To speed up computation, a bidirectional search method and a dominance rule are applied. Results from extensive computational tests on 100 sets of randomly generated instances demonstrate the performance of our algorithm.

The systematic prediction of real estate prices is a foundational block in the operations of many firms and has individual, societal and policy implications. In the past, a vast amount of works have used common statistical models such as ordinary least squares or machine learning approaches. While these approaches yield good predictive accuracy, most models work very differently from the human intuition in understanding real estate prices. Usually, humans apply a criterion known as “direct comparison”, whereby the property to be valued is explicitly compared with similar properties. This trait is frequently ignored when applying machine learning to real estate valuation. In this article, we propose a model based on a methodology called prototype-based learning, that to our knowledge has never been applied to real estate valuation. The model has four crucial characteristics: (a) it is able to capture non-linear relations between price and the input variables, (b) it is a parametric model able to optimize any loss function of interest, (c) it has some degree of explainability, and, more importantly, (d) it encodes the notion of direct comparison. None of the past approaches for real estate prediction comply with these four characteristics simultaneously. The experimental validation indicates that, in terms of predictive accuracy, the proposed model is better or on par to other machine learning based approaches. An interesting advantage of this method is the ability to summarize a dataset of real estate prices into a few “prototypes”, a set of the most representative properties.

Sports timetabling is a complex and challenging problem. The latest open benchmark dataset for the sport timetabling problem is from the International Timetabling Competition (ITC) 2021. Due to its complexity, only a few approaches have successfully generated feasible solutions for the problems in this dataset, as reported in scientific literature. To the best of our knowledge, there is only one study in the literature that has successfully generated feasible solutions for all 45 problems in the dataset. In this paper, we propose our novel efficient algorithm based on the Iterated Local Search algorithm to solve the ITC 2021 benchmark dataset. Unlike prior successful approaches that combined metaheuristics with an exact approach, our proposed approach is solely metaheuristic. Our contribution includes the design of strategies for both perturbation and local search phases, coupled with the integration of shuffling strategies. The experimental results show that our proposed algorithm is remarkably successful in generating feasible solutions for all 45 problems present in the ITC 2021 dataset.