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Purpose: A Nash bargaining game data envelopment analysis (NBG-DEA) model is proposed to measure the efficiency of dynamic multi-period network structures. This paper aims to propose NBG-DEA model to measure the performance of decision-making units with complicated network structures. Design/methodology/approach: As the proposed NBG-DEA model is a non-linear mathematical programming, finding its global optimum solution is hard. Therefore, meta-heuristic algorithms are used to solve non-linear optimization problems. Fortunately, the NBG-DEA model optimizes the well-formed problem, so that it can be solved by different non-linear methods including meta-heuristic algorithms. Hence, a meta-heuristic algorithm, called particle swarm optimization (PSO) is proposed to solve the NBG-DEA model in this paper. The case study is Industrial Management Institute (IMI), which is a leading organization in providing consulting management, publication and educational services in Iran. The sub-processes of IMI are considered as players where their pay-off is defined as the efficiency of sub-processes. The network structure of IMI is studied during multiple periods. Findings: The proposed NBG-DEA model is applied to measure the efficiency scores in the IMI case study. The solution found by the PSO algorithm, which is implemented in MATLAB software, is compared with that generated by a classic non-linear method called gradient descent implemented in LINGO software. Originality/value: The experiments proved that suitable and feasible solutions could be found by solving the NBG-DEA model and shows that PSO algorithm solves this model in reasonable central process unit time. [ABSTRACT FROM AUTHOR]

A cellular manufacturing system (CMS) allocates machines and parts to the cells in order to increase the system performance. Many valuable studies have been conducted in this area to examine various aspects of a CMS and introduce mathematical models for simulating real aspects of manufacturing with this system. The models assume that a factory is monopolistic without any competitor and their behaviour in the real market. Competition has influence on both demand and price, and these have bilateral relations with the production cost. Therefore, the behaviour of competitors to maximise their profits in the market influences the CMS parameters. This paper presents a mathematical programming model incorporated with cell formation and cell layout with the alternative process routing under duopoly Bertrand competition as a game. It is solved by a well-known meta-heuristic algorithm, namely particle swarm optimisation. Additionally, Monte Carlo simulation is used to estimate the production cost of a competitor. Finally, a number of numerical examples are used to demonstrate the presented model. [ABSTRACT FROM PUBLISHER]

We develop price-energy-saving competition and cooperation models for two green supply chains (GSCs) under government financial intervention. First, we study the best response strategies of the chains for the given tariffs of a government. Second, we formulate 16 mathematical programming models regarding governments’ energy-saving, social welfare, and revenue-seeking policies. We find that the government can orchestrate GSCs to fulfil the financial, social, and environmental objectives by an appropriate tariff mechanism. Moreover, cooperation in a GSC and between GSCs may facilitate the government’s sustainable development policies. A comprehensive analysis on case study of brick production GSCs reveals some important managerial insights. [ABSTRACT FROM AUTHOR]

This study investigates a multiowner maximum-flow network problem, which suffers from risky events. Uncertain conditions effect on proper estimation and ignoring them may mislead decision makers by overestimation. A key question is how self-governing owners in the network can cooperate with each other to maintain a reliable flow. Hence, the question is answered by providing a mathematical programming model based on applying the triangular reliability function in the decentralized networks. The proposed method concentrates on multiowner networks which suffer from risky time, cost, and capacity parameters for each network’s arcs. Some cooperative game methods such as τ-value, Shapley, and core center are presented to fairly distribute extra profit of cooperation. A numerical example including sensitivity analysis and the results of comparisons are presented. Indeed, the proposed method provides more reality in decision-making for risky systems, hence leading to significant profits in terms of real cost estimation when compared with unforeseen effects. [ABSTRACT FROM AUTHOR]

Many decision-making problems in the context of transhipment and logistics, distribution networks, airline planning and so on, can best be analyzed by the means of maximum-flow models in networks. In a multiple-owner network, several players possess arcs and nodes of a network. Since parameters of the network in many real problems are highly uncertain, maintaining a stable flow is as much important as maximizing the flow passing through the network. Thus, a key question is how the independent owners of a network should collaborate to maintain a reliable maximum flow. We address this question by presenting a stochastic mathematical programming model for the multiple-owner graph problem under uncertainty. Afterwards, a number of collaboration methods are studied based on the game theory. These methods are illustrated with an example to gain an insight into properties of the corresponding game results and behavior of the different solution concepts. [ABSTRACT FROM AUTHOR]

Highlights • An uncertain multi-objective multi-commodity multi-period multi-vehicle location-allocation model is proposed. • Two meta-heuristic method and one exact method are provided to solve the model. • Several types of injured people are considered in earthquake evacuation planning. • Failure rate of the centers are modeled using reliability and probability concepts. • The proposed model has been applied in a real case study in Tehran, Iran. Abstract In this paper, an uncertain multi-objective multi-commodity multi-period multi-vehicle location-allocation mixed-integer mathematical programing model is proposed for the response phase of the earthquake. The proposed model includes five echelons as affected areas, distribution centers, hospitals, temporary accommodation centers and temporary care centers. Two objective functions as minimizing the total cost of the location-allocation of facilities and minimizing the amount of the shortage of relief supplies, are considered. The uncertainty is modeled using a scenario-based probability approach. The main decisions made by the proposed model are locating of the temporary care and accommodation centers, allocation of the affected areas to the located centers and hospitals, as well as the allocation of the distribution centers to temporary accommodation centers. Several decisions associated with flow of injured people and commodities between facilities, and decisions associated with number of vehicles between facilities and shortage and inventory level at centers are also made by the proposed model. Several sets of constraints including demand and flow of relief commodities, capacity of centers, transportation of injured people, capacity of transportation vehicles for commodities and injured people, and back up centers are considered in multiple periods of planning in the proposed model. The proposed model is applied in a real case study in Tehran. The model is solved using modified multiple-objective particle swarm optimization (MMOPSO), Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) and epsilon constraint method. The performance of the solution procedures is analyzed using multi-objective performance evaluation metrics. The results reveal the superiority of the MMOPSO over the other solution approaches. A preferred solution, from the set of non-dominated solutions generated by MMOPSO, has been selected, analyzed and described. Sensitivity analysis on main parameters of proposed model and the probabilities of the earthquake and failures of the facilities has also been accomplished. [ABSTRACT FROM AUTHOR]

In this study, a stochastic multi-objective mixed-integer mathematical programming is proposed for logistic distribution and evacuation planning during an earthquake. Decisions about the pre- and post-phases of the disaster are considered seamless. The decisions of the pre-disaster phase relate to the location of permanent relief distribution centers and the number of the commodities to be stored. The decisions of the second phase are to determine the optimal location for the establishment of temporary care centers to increase the speed of treating the injured people and the distribution of the commodities at the affected areas. Humanitarian and cost issues are considered in the proposed models through three objective functions. Several sets of constraints are also considered in the proposed model to make it flexible to handle real issues. Demands for food, blood, water, blanket, and tent are assumed to be probabilistic which are related to several complicated factors and modeled using a complicated network in this study. A simulation is setup to generate the probabilistic distribution of demands through several scenarios. The stochastic demands are assumed as inputs for the proposed stochastic multi-objective mixed integer mathematical programming model. The model is transformed to its deterministic equivalent using chance constraint programming approach. The equivalent deterministic model is solved using an efficient epsilon-constraint approach and an evolutionary algorithm, called non-dominated sorting genetic algorithm (NSGA-II). First several illustrative numerical examples are solved using both solution procedures. The performance of solution procedures is compared and the most efficient solution procedure, i.e., NSGA-II, is used to handle the case study of Tehran earthquake. The results are promising and show that the proposed model and the solution approach can handle the real case study in an efficient way. • Stochastic multi-objective optimization model is proposed for logistic distribution and evacuation planning. • Demands are assumed to be probabilistic and estimated using a simulation approach through several scenarios. • The stochastic optimization model is transformed to its deterministic equivalent using chance constraint programming. • The model is solved using an efficient epsilon-constraint approach and non-dominated sorting genetic algorithm (NSGA-II). • The proposed optimization model and solution approach are used to handle the case study of Tehran earthquake. [ABSTRACT FROM AUTHOR]