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  • Computational comparisons of different formulations for the Stackelberg minimum spanning tree game

    Let G=(V,E) be a given graph whose edge set is partitioned into a set R of red edges and a set B of blue edges, and assume that red edges are weighted and contain a spanning tree of G. Then, the Stackelberg minimum spanning tree game (StackMST) is that of pricing (i.e., weighting) the blue edges in such a way that the total weight of the blue edges selected in a minimum spanning tree of the resulting graph is maximized. In this paper, we present different new mathematical programming formulations for the StackMST based on the properties of the minimum spanning tree problem and the bilevel optimization. We establish a theoretical and empirical comparison between these new formulations that are able to solve random instances of 20–70 nodes. We also test our models on instances in the literature, outperforming previous results.

  • A revised sales rebate contract with effort‐dependent demand: a channel coordination approach

    In this paper, simultaneous coordination of order quantity and sales effort (SE) decisions in a supplier/retailer system with stochastic effort‐dependent demand is investigated. The main aim of the proposed model is to attain an optimal balance that results in a Pareto‐efficient solution for both channel members. A revised sales rebate (RSR) contract is developed to achieve channel coordination. In addition to the usual incentive approach of sales rebate schemes, a punitive approach is designed for the new proposed contract as a stockout penalty. Furthermore, some numerical experiments are examined to analyze the performance of the presented model under three decision‐making scenarios (i.e., decentralized, centralized, and RSR). Additionally, some in‐depth sensitivity analyses are conducted to examine the behavior of the supply chain performance under alteration of different parameters. The results show that the proposed RSR contract leads to channel coordination, while both channel members experience a Pareto improving situation. Moreover, it is proved that the RSR contract has significant potential on neutralizing adverse impacts of demand fluctuations on channel performance indicators.

  • Human migration networks and policy interventions: bringing population distributions in line with system optimization

    In this paper, we demonstrate that, through policy interventions, in the form of subsidies, a system‐optimum for a multiclass human migration network can be achieved, despite the migrants, who can be refugees, behaving in a user‐optimized manner. The formulation and analysis are conducted using variational inequality theory. The policy intervention allows governmental decision‐makers to moderate the flow of migrants while enhancing societal welfare. An algorithm is proposed and applied to compute the solutions to a series of numerical examples, with changes in initial populations and utility functions, inspired by a pandemic, followed by a natural disaster.

  • Using kernel density estimation to model surgical procedure duration

    Estimating the length of surgical cases is an important research topic due to its significant effect on the accuracy of the surgical schedule and operating room (OR) efficiency. Several factors can be considered in the estimation, for example, surgeon, surgeon experience, case type, case start time, etc. Some of these factors are correlated, and this correlation needs to be considered in the prediction model in order to have an accurate estimation. Extensive research exists that identifies the preferred estimation methods for cases that occur frequently. However, in practice, there are many procedure types with limited historical data, which makes it hard to use common statistical methods (such as regression) that rely on a large number of data points. Moreover, only point estimates are typically provided. In this research, kernel density estimation (KDE) is implemented as an estimator for the probability distribution of surgery duration, and a comparison against lognormal and Gaussian mixture models is reported, showing the efficiency of the KDE. In addition, an improvement procedure for the KDE that further enables the algorithm to outperform other methods is proposed. Based on the analysis, KDE can be recommended as an alternative estimator of surgical duration for cases with low volume (or limited historical data).

  • Controlling lead times and minor ordering costs in the joint replenishment problem with stochastic demands under the class of cyclic policies

    In this paper, we consider the periodic review joint replenishment problem under the class of cyclic policies. For each item, the demand in the protection interval is assumed stochastic. Moreover, a fraction of shortage is lost, while the other quota is backordered. We suppose that lead times and minor ordering costs are controllable. The problem concerns determining the cyclic replenishment policy, the lead times, and the minor ordering costs in order to minimize the long‐run expected total cost per time unit. We established several properties of the cost function, which permit us to derive a heuristic algorithm. A lower bound on the minimum cost is obtained, which helps us to evaluate the effectiveness of the proposed heuristic. The heuristic is also compared with a hybrid genetic algorithm that is specifically developed for benchmarking purposes. Numerical experiments have been carried out to investigate the performance of the heuristic.

  • Interactive approaches for biobjective problems with progressively changing solution sets

    In this study, we develop interactive approaches to find a satisfactory alternative of a decision maker (DM) having a quasiconvex preference function where the alternative set changes progressively. In this environment, we keep searching the available set of alternatives and estimating the preference function of the DM. As new alternatives emerge, we make better use of the available preference information and eventually converge to a preferred alternative of the DM. We test our approaches on biobjective, multi‐item, multi‐round auction problems. The results show that our approaches work well in terms of both the preference function value of the obtained solution and the amount of preference information required.

  • Agile optimization of a two‐echelon vehicle routing problem with pickup and delivery

    In this paper, we consider a vehicle routing problem in which a fleet of homogeneous vehicles, initially located at a depot, has to satisfy customers' demands in a two‐echelon network: first, the vehicles have to visit intermediate nodes (e.g., a retail center or a consolidation center), where they deliver raw materials or bulk products and collect a number of processed items requested by the customers in their route; then, the vehicles proceed to complete their assigned routes, thus delivering the processed items to the final customers before returning to the depot. During this stage, vehicles might visit other intermediate nodes for reloading new items. In some real‐life scenarios, this problem needs to be solved in just a few seconds or even milliseconds, which leads to the concept of “agile optimization.” This might be the case in some rescue operations using drones in humanitarian logistics, where every second can be decisive to save lives. In order to deal with this real‐time two‐echelon vehicle routing problem with pickup and delivery, an original constructive heuristic is proposed. This heuristic is able to provide a feasible and reasonably good solution in just a few milliseconds. The constructive heuristic is extended into a biased‐randomized algorithm using a skewed probability distribution to modify its greedy behavior. This way, parallel runs of the algorithm are able to generate even better results without violating the real‐time constraint. Results show that the proposed methodology generates competitive results in milliseconds, being able to outperform other heuristics from the literature.

  • A generalized parametric divisor method for political apportionment

    The political apportionment problem has been studied for more than 200 years. In this paper, we introduce a generalized parametric divisor method (GPDM), which generalizes most of the classical and widely used apportionment methods from the literature as special cases. Moreover, it allows for very flexible interpolation between previous methods by appropriately setting two parameters in the GPDM. We identify an inequity measure that the GPDM globally optimizes. We also identify two natural inequity measures for which an apportionment given by the GPDM is locally optimal. These results generalize similar results for classical apportionment methods, and justify the use of a large class of new apportionment methods given by the GPDM. From this class, we identify and recommend specific new methods. Our numerical experiments compare the apportionments given by the new methods with those given by existing methods using real data for the United States, Germany, Canada, Australia, England, and Japan. Explicit definition of the GPDM has enabled us to perform computational experiments for evaluating the unbiasedness of the GPDM using two standard measures while comparing with other traditional methods. Based upon our generalization technique and numerical experiments, we show that the GPDM outperforms all the traditional apportionment methods by selecting appropriate parameter values. Thus, we can conclude that the GPDM is the most “unbiased” and fairer if parameters can be agreed ex ante, and the GPDM is applicable to actual electoral voting systems.

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  • Mixed coordination mechanisms for scheduling games on hierarchical machines

    In this paper, we study scheduling games under mixed coordination mechanisms on hierarchical machines. The two scheduling policies involved are LG‐LPT and LG‐SPT, where LG‐LPT (resp., LG‐SPT) policy sequences jobs in nondecreasing order of their hierarchies, and jobs of the same hierarchy in nonincreasing (resp., nondecreasing) order of their processing times. We first show the existence of a Nash equilibrium. Then we present the price of anarchy and the price of stability for the games with social costs of minimizing the makespan and maximizing the minimum machine load. All the bounds given in this paper are tight.

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