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This paper aims to develop a grey decentralized bi-level multi-objective programming (MOP) model. A solution approach is also proposed for the given model. A production and transportation plan for a closed loop supply chain network under an uncertain environment and different scenarios is also developed.

In this paper, we combined grey linear programming (GLP) and fuzzy set theory to present a solution approach for the problem. The proposed model first solves the given problem using GLP. Membership functions for the decision variables under the control of the leader and for the goals are created. These membership functions are then used to generate the final solutions.

This paper provides insight for fomenting the decision-making process while providing a more flexible approach in uncertain logistics problems. The deviations of the final solution from the individual best solutions of the two levels are very little. These deviations can further be reduced by adjusting the tolerances associated with the decision variables under the control of the leader.

The proposed approach uses the concept of membership functions of linear form, and thus, requires less computational efforts while providing effective results. Most of the organizations exhibit decentralized decision-making under the presence of uncertainties. Therefore, the present study is helpful in dealing with such scenarios.

This is the first time, formulation of a decentralized bi-level multi-objective model under a grey environment is carried out as per the best knowledge of the authors. A solution approach is developed for bi-level MOP under grey uncertainty.

The purpose of this paper is to study a transportation service procurement bid construction problem from a less than a full truckload perspective. It seeks to establish stochastic mixed integer programming to allow for the proper bundle of loads to be chosen based on price, which could improve the likelihood that carrier can earn its maximum utility.

The authors proposes a bi-level programming that integrates the bid selection and winner determination and a discrete particle swarm optimization (PSO) solution algorithm is then developed, and a numerical simulation is used to make model and algorithm analysis.

The algorithm comparison shows that although GA could find a little more Pareto solutions than PSO, it takes a longer time and the quality of these solutions is not dominant. The model analysis shows that compared with traditional approach, our model could promote the likelihood of winning bids and the decision effectiveness of the whole system because it considers the reaction of the shipper.

The highlights of this paper are considering the likelihood of winning the business and describing the conflicting and cooperative relationship between the carrier and the shipper by using a stochastic mixed integer programming, which has been rarely examined in previous research.

The purpose of this paper is to design petroleum products’ supply chain management, which includes efficient integration of suppliers, manufacturers, storehouses and retailers.

This paper proposes that a three-level supply chain will be turned into a bi-level supply chain of petroleum products by simultaneous integration of the middle level with the upstream and downstream levels. Also, it is integrally optimized by considering the multiple managerial flows' mutual results at various supply chain levels. Also, it is integrally optimized by considering the multiple managerial flows' mutual results at various supply chain levels.

The concepts of the design, structure and outputs are led by the model's solution. The model also responds to the variations in the market via coordination in the related decisions to the distribution, production and inventory issues, and also coordinating between the demands and production.

This paper has limited its analysis to definite values due to the over-expansion of calculations and analysis. Future works can study other aspects of the proposed model for a multi-level petroleum product supply chain in different states of certain parameters and time zones.

The designed model can directly and transparently help the oil managers and decision-makers lower the costs of manufacturing, distribution and sales with respect to the determined criteria.

This paper establishes that effectiveness of the dynamic petroleum materials supply chain design will increase by considering maintained and increased production costs and coordinate management flows at all levels by supply chain creation’s integration.

The facility in an emergency system could be immobilized because of the huge destructive power of an irregular emergency and the uncertainty of the time, place and scale of occurrence. So facility failure scenarios must be considered at the time of location. The purpose of this paper is to establish a location model based on the worst facility failure, the objective of which is to minimize the cost and cover the demand maximally. It is demonstrated that location choice, considering facility failure, has significant meaning when considering economic benefit and covering the demand.

A bi‐level programming model which studies the facility location is established by using the methods of scenario analysis and robust optimization. It is compared with a classic location model, without considering facility failure, from the points of view of economic benefit and maximal covering demand.

Compared to the classic location model, without considering facility failure, it is demonstrated that the location model which considers facility failure can save more costs from the economic benefit point of view and, from the maximal covering of the demand point of view, has a higher covering ratio. So facility failure scenario should be considered in the location of an emergency facility.

The paper studies facility location based on the worst scenario, from the two aspects of economic benefits and maximal covering demand.

This paper aims to optimize the configuration of assembly lines (ALs) considering the two long-term decision problems within the line balancing and part feeding (PF) contexts, when the supermarket concept is applied in PF.

To this purpose, a bi-level mathematical model is proposed to deal with the assembly line balancing problem (ALBP) and supermarket location problem (SLP) during the strategic decision-making phase of ALs’ configuration. The proposed model is applied on the known test problems taken from the ALBP literature to verify its performance.

The computational results verify that when the proposed structure is applied, the resulting AL configurations are optimized from both ALBP and SLP considerations in terms of the number of stations and line efficiency as well as supermarket transportation and installation costs.

No study has yet dealt with the long-term decision problem of configuring ALs considering both ALBP and SLP. Also, this study validates the effect of the ALBP on the SLP solutions as two long-term interrelated decision problems.

Fortification-interdiction models provide system designers with a broader perspective to identify and protect vital components. Based on this concept, the authors examine how disruptions impact critical supply systems and propose the most effective protection strategies based on three levels of decision-makers. This paper aims to investigate location and fortification decisions at the first level. Moreover, a redesign problem is presented in the third level to locate backup facilities and reallocate undisrupted facilities following the realization of the disruptive agent decisions at the second level.

To address this problem, the authors develop a tri-level planner-attacker-defender optimization model. The model minimizes investment and demand satisfaction costs and alleviates maximal post-disruption costs. While decisions are decentralized at different levels, the authors develop an integrated solution algorithm to solve the model using the column-and-constraint generation (CCG) method.

The model and the solution approach are tested on a real supply system consisting of several hospitals and demand areas in a region in Iran. Results indicate that incorporating redesign decisions at the third level reduces maximum disruption costs.

The paper makes the following contributions: presenting a novel tri-level optimization model to formulate facility location and interdiction problems simultaneously, considering corrective measures at the third level to reconfigure the system after interdiction, creating a resilient supply system that can fulfill all demands after disruptions, employing a nested CCG method to solve the model.

This chapter examines the airline performance effect arising from collaboration between airlines and high speed railway (HSR). The analysis presents scenario simulations using a bi-level model, which takes into account the effect of competition among airlines and HSR. Using real data, we examine the Japanese domestic market and the Japan-based international market: the markets consist of Tokyo Metropolitan Area, Osaka Metropolitan Area, Seoul/Korea, Frankfurt/Germany, Paris/France, London/United Kingdom, and Los Angeles/United States. Analysis of the domestic market assumes airlines and HSR compete against each other, and analysis of the international market assumes airlines only compete with each other. Initially, we conduct performance analysis using a simulation that mimics the current relationship between airlines and HSR. Then we present three scenarios for different combinations of collaboration between airline and HSR based on airline alliances. The results from this exercise are then used to examine the impact of the collaboration on the profits of airlines and HSR, passenger’s utility, and the network design of airlines. Last, we show the potential benefit to airlines – profitability, market share, and demand growth – from the airline-HSR collaboration. Our model shows that in Japan: (1) Airlines can improve their profitability in international operations by the collaboration with HSR when airlines set their hubs so they can connect to HSR; (2) The airline which has a lower unit operating cost than rivals and sets its hubs to connect to HSR can improve its joint profit with HSR through collaboration; (3) Airlines that don’t operate domestic flights and don’t set their hubs to connect to HSR encourage increased fare competition by coordinating with HSR, but their profit decreases. Whether these results are generalizable to other regions should be the subject of future study.

Critical links in traffic networks are those who should be better protected because their removal has a significant impact on the whole network. So, the purpose of this paper is to identify the critical links of traffic networks.

This paper proposes the definition of the critical link for an urban traffic network and establishes mathematical model for determining critical link considering the travellers’ heterogeneous risk-taking behavior. Moreover, in order to improve the computational efficiency, the impact area of a link is quantified, a partial network scan algorithm for identifying the critical link based on the impact area is put forward and the efficient paths-based assignment algorithm is adopted.

The proposed algorithm can significantly reduce the search space for determining the most critical links in traffic network. Numerical results also demonstrate that the structure of efficient paths has significant impact on identifying the critical links.

This paper identifies the critical links by using a bi-level programming approach and proposes a partial network scan algorithm for identifying critical links accounting for travellers’ heterogeneous risk-taking behavior.