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Commonly shared logistics services help manufacturing companies to cut down redundant logistics investments while enhance the overall service quality. Such service-sharing mode has been naturally adopted by group companies to form the so-called headquarter-managed centralized distribution center (HQ-CDC). The HQ-CDC manages the common inventories for the group’s subsidiaries and provides shared storage services to the subsidiaries through appropriate sizing, pricing and common replenishment. Apart from seeking a global optimal solution for the whole group, the purpose of this paper is to investigate balanced solutions between the HQ-CDC and the subsidiaries.

Two decision models are formulated. Integrated model where the group company makes all-in-one decision to determine the space allocation, price setting and the material replenishment on behalf of HQ-CDC and subsidiaries. Bilevel programming model where HQ-CDC and subsidiaries make decisions sequentially to draw a balance between their local objectives. From the perspective of result analysis, the integrated model will develop a managerial benchmark which minimizes the group company’s total cost, while the bilevel programming model could be used to measure the interactive effects between local objectives as well as their final effect on the total objective.

Through comparing the numerical results of the two models, two major findings are obtained. First, the HQ-CDC’s profit is noticeably improved in the bilevel programming model as compared to the integrated model. However, the improvement of HQ-CDC’s profit triggers the cost increasing of subsidiaries. Second, the analyses of different sizing and pricing policies reveal that the implementation of the leased space leads to a more flexible space utilization in the HQ-CDC and the reduced group company’s total cost especially in face of large demand and high demand fluctuation.

Several classical game-based decision models are to be introduced to examine the more complex relationships between the HQ-CDC and the subsidiaries, such as Nash Game model or Stackelberg Game model, and more complete and meaningful managerial implications may be found through result comparison with the integrated model. The analytical solutions may be developed to achieve more accurate results, but the mathematical models may have to be with easier structure or tighter assumptions.

The group company should take a comprehensive consideration on both cost and profit before choosing the decision framework and the coordination strategy. HQ-CDC prefers a more flexible space usage strategy to avoid idle space and to increase the space utilization. The subsidiaries with high demand uncertainties should burden a part of cost to induce the subsidiaries with steady demands to coordinate. Tanshipments should be encouraged in HQ-CDC to reduce the aggregate inventory level as well as to maintain the customer service level.

The proposed decision frameworks and warehousing policies provide guidance for the managers in group companies to choose the proper policy and for the subsidiaries to better coordinate.

This research studies the services sharing on the warehouse sizing, pricing and common replenishment in a HQ-CDC. The interactive decisions between the HQ-CDC and the subsidiaries are formulated in a bilevel programming model and then analyzed under various practical scenarios.

This article addresses the problem of air traffic service (ATS) pricing over a domestic air transportation system with either private or public ATS providers. In both cases, to take into account feedback effects on the air transportation market, it is considered that the adopted pricing approaches can be formulated through optimization problems where an imbedded optimization problem is concerned with the supply of air transportation (offered seat capacity and tariffs for each connection). Under mild assumptions in both situations the whole problem can be reformulated as a mathematical program with linear objective function and quadratic constraints. A numerical application is performed to compare both pricing schemes when different levels of taxes are applied to air carriers and passengers.

This paper considers an option contract in a two-stage supplier-retailer supply chain (SC) when market demand is stochastic. The problem is a Stackelberg game with the supplier as a leader. This research assumes demand information sharing. The purpose of this study is to determine the optimal pricing strategy of the supplier along with the optimal order strategy of the retailer in three option contract cases.

The paper model the option contract pricing problem as a bilevel problem. The problem is then solved using bilevel programing methods. After computing, the generated outcomes are compared to a benchmark (wholesale price contract) to evaluate the contract.

The results reveal that only one of the contract cases can arbitrarily allocate the SC profit. In both other cases, the Stackelberg supplier manages to earn the total SC profit. Further analysis of the first contract, show that from the supplier’s perspective, the first stage forecast inaccuracy is beneficial, whereas the demand uncertainty in the second stage is detrimental. This contracting strategy guarantees both players better outcomes compared to the wholesale price contract.

To the best of the authors’ knowledge, this research is the first that links the option contract literature to the bilevel programing literature. It also the first to solve the pricing problem of the commitment option contract with demand update where the retailer exercises the option before knowing the exact demand.

The purpose of this paper is to seek an efficient method to tackle the energy provision problem for smart grid with sparse constraints and distributed energy and storage devices.

A complex smart grid is first studied, in which sparse constraints and the complex make-up of different energy consumption due to the integration of distributed energy and storage devices and the emergence of multisellers are discussed. Then, a real-time pricing scheme is formulated to tackle the demand response based on sparse bilevel programming. And then, a bilevel genetic algorithm (BGA) is further designed. Finally, simulations are conducted to evaluate the performance of the proposed approach.

The considered situation is widespread in practice, and meanwhile, the other cases including traditional model without the sparse constraints can be seen as its extensions. The BGA based on sparse bilevel programming has advantages of “no need of convexity of the model.” Moreover, it is feasible without the need to disclose the private information to others; therefore, privacies are protected and system scalability is kept. Simulation results validate the proposed approach has good performance in maximizing social welfare and balancing system energy distribution.

In this paper, the authors consider the sparse constraints due to the fact that each user can only choose limited utility companies per time slot. In reality, there exist some other sparse cases, which deserve further study in the future.

To the best of the authors’ knowledge, this is one of the very first studies to address pricing problems for the smart grid with consideration of sparse constraints and integration of distributed energy and storage devices.

One of the most important problems concerning the toll roads is the setting of an appropriate cost for traveling through private arcs of a transportation network. The purpose of this paper is to consider this problem by stating it as a bilevel programming (BLP) model. At the upper level, one has a public regulator or a private company that manages the toll roads seeking to increase its profits. At the lower level, several companies-users try to satisfy the existing demand for transportation of goods and/or passengers, and simultaneously, to select the routes so as to minimize their travel costs. In other words, what is sought is kind of a balance of costs that bring the highest profit to the regulating company (the upper level) and are still attractive enough to the users (the lower level).

With the aim of providing a solution to the BLP problem in question, a direct algorithm based on sensitivity analysis (SA) is proposed. In order to make it easier to move (if necessary) from a local maximum of the upper level objective function to another, the well-known “filled function (FF)” method is used.

The paper proposes and tests two versions of the heuristic algorithm to solve the toll optimization problem (TOP) based upon SA for linear programming (LP) problems. The algorithm makes use of an SA procedure for the LP problem at the lower level, as well as of the “filled” function technicalities in order to reach the global optimum when “jammed” at some local optimum. Numerical experiments with a series of small and medium dimension test problems show the proposed algorithm’s robustness and decent convergence characteristics.

Numerical experiments with a series of small- and medium dimension test problems show the proposed algorithm’s robustness and reasonable convergence characteristics. In particular, while ceding in efficiency to other algorithms when solving small problems, the proposed method wins in the case of medium (higher dimensional) test models. Because of that, one can expect a serious real-life impact on the TOP when the proposed methods and/or their improved versions are developed further to be applicable in practice in the near future.

The proposed algorithms are original and perform well when solving small and medium test numerical problems. The proposed heuristics aim at filling in a gap in a series of numerical approaches to the solution of TOP problem listed in the Introduction. To the authors knowledge, no systematic attempts to apply the SA tools to the toll assigned problem have been recently made. Moreover, the combination of these powerful tools with the “FFs” techniques brings forward some new global optimization ideas. Exactly these features build up the knowledge this specific paper offers in relation to previous relevant works.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

This study proposes and demonstrates a novel approach to analyzing customer channel preferences and willingness-to-pay (WTP) in the dual sales channel (DSC) system involving direct online channels and conventional offline retailers, and to how the pricing decisions are made under specific game competition.

Questionnaire survey based on central composite experiment design was utilized to obtain primary data. The model for customer channel preferences and WTP was then built by using multinomial logistic regression. The propensity of a customer to make purchases in either channel estimated by using the logit model was inserted in the bilevel programming model to formulate and solve for the Stackelberg competition where the conventional retailer acted as a leader.

The study found that channel prices have nonlinear impacts on WTP and channel preference. The empirical results complement the mathematical formulation well where high-order own-price and cross-price effects on channel selection are generally not analytical tractable. Under the Stackelberg competition, the traditional retailer (as the leader) still achieves higher profits than the online facility.

The proposed framework provides an empirical approach that can easily address the competition model in the sales channel when complicated own-price or cross-price effects are present.

The present work provides a novel approach to analyze customer preference and WTP of the DSC systems. This alternative method simplifies the procedure for investigating and estimating price sensitivity, especially when the online and offline prices affect customer WTP and channel preferences nonlinearly. This model is also utilized in the game competition to facilitate data-driven price decision making to better formulate and understand real-world DSC problems.

The paper aims to introduce a novel concept to solve the bi-level multi-criteria nonlinear fractional programming (BL-MCNFP) problems. Bi-level programming problem (BLPP) is rigorously flourished and studied by several researchers, which deals with decentralized decisions by comprising a sequence of two optimization problems, namely upper and lower-level problems. However, on the other hand, many real-world decision-making problems involve multiple objectives with fraction aspects, called fractional programming problems that reflect technical and economic performance.

This paper introduces a VIKOR (“VlseKriterijumska Optimizacija I Kompromisno Resenje”) approach to solve the BL-MCNFP problem. In this approach, an aggregating function based on L_P metrics is formulated on the basis of the “closeness” scheme from the “ideal” solution. The three steps perform the solution process: First, a new concept is attempted to minimize and maximize of the numerators and denominators from their respective ideal solutions and anti-ideal values simultaneously. Second, for each level, the K-dimensional objective space of each level is converted to a one-dimensional space by an aggregating function. Third, to obtain the final solution, all levels are combined into single-level model where the decision variables of upper levels are interrelated with other levels through fuzzy strategy-based linear and nonlinear membership functions.

The effectiveness of the proposed VIKOR is demonstrated by numerical examples, where the reported results affirm that the extended VIKOR method provides superior results in comparison with the same methods in the literature, and it is a good alternative to BL-MCNFP problems.

In terms of the assistance-based right decision, a parametric analysis for the weight of the majority is provided to exhibit a wide range of compromise solutions for the decision-maker.

This research attempts to present a solid transportation problem (STP) mechanism in uncertain and indeterminate contexts, allowing decision makers to select their acceptance, indeterminacy and untruth levels.

Due to the lack of reliable information, changeable economic circumstances, uncontrolled factors and especially variable conditions of available resources to adapt to the real situations, the authors are faced with a kind of uncertainty and indeterminacy in constraints and the nature of the parameters of STP. Therefore, an approach based on neutrosophic logic is offered to make it more applicable to real-world circumstances. In this study, the triangular neutrosophic numbers (TNNs) have been utilized to represent demand, transportation capacity, accessibility and cost. Then, the neutrosophic STP was converted into an interval programming problem with the help of the variation degree concept. Then, two simple linear programming models were extracted to obtain the lower and upper bounds of the optimal solution.

The results reveal that the new model is not complicated but more flexible and more relevant to real-world issues. In addition, it is evident that the suggested algorithm is effective and allows decision makers to specify their acceptance, indeterminacy and falsehood thresholds.

Under the transportation literature, there are several solutions for TP and STP in crisp, fuzzy set (FS) and intuitionistic fuzzy set (IFS) conditions. However, the STP has never been explored in connection with neutrosophic sets to the best of the authors’ knowledge. So, this work tries to fill this gap by coming up with a new way to solve this model using NSs.