Many real projects complete through the realization of one and only one path of various possible network paths.Here, these networks are called alternative stochastic networks (ASNs). It is supposed that the nodes of considered network are probabilistic with exclusive-or receiver and exclusive-or emitter. First, an analytical approach is proposed to simplify the structure of the network. This approach transforms the network into a simpler equivalent one. This paper discusses the constrained consumable resource allocation problem in an ASN. Many recent researchers apply heuristic and simulation methods to solve the constrained resource allocation in these problems. In this paper, we propose an analytical approach based on Multi-objective modeling. The objective functions of this model are the cumulative distribution function of the completion time of ASN paths. These functions must be maximized within the desired network completion time. Lexicographic method is used to solve the proposed Multi-objective model.The proposed method is illustrated by an example.

This study presents a Multi-objective nurse scheduling model by considering andintegrating teamwork and decision making styles in order to maximize jobsatisfaction. To achieve high job satisfaction, teamwork that minimizesincompatibility among team members is considered. Teamwork has a sustainable impact on job satisfaction in healthcare. In this study, a new mathematical model isproposed for scheduling nurses based on teamwork. First, nursing teams are generated by considering decision making styles. Then, each team is assigned towork shifts in the planning horizon. The unique Multi-objective mathematical model considers the inconsistency of nurses’,decision making styles, reliability ofteams, allocation costs and penalty of violating soft constraints as the objective functions. A real case study is considered to show the applicability of the proposedmodel. Finally, the proposed Multi-objective model is solved using the goal programming method. Sensitivity analysis shows the robustness of the proposedmathematical programming model and solution methodology.

A workflow consists of a set of independent tasks, while workflow scheduling in a cloud environment is a proper permutation of these tasks involving virtual machines. Selecting the permutation with minimum completion time from among all of the arrangements, in which the requests and diversity of virtual machines increase, is an NP-hard problem. Given that, in addition to the makespan, other objectives should be considered in the scheduling problem in a real environment, which, in most cases, are conflicting objectives, the scheduling problem becomes more complicated. Therefore, Multi-objective heuristic algorithms represent the perfect solution to these problems.To this end, we extended a recent heuristic algorithm known as black hole optimization (BHO) and presented a Multi-objective scheduling method for a workflow application based on the Pareto optimizer algorithm. Since Multi-objective algorithms select a set of permutations with an optimal trade-off from among conflicting objectives, we use a decision-making method- the weighted aggregated sum product assessment (WASPAS)-in the following and select a solution that offers suitable permutation from among all solutions of the Pareto optimal set. Our proposed method is able to consider user requirements, as well as the interests of service providers. Using a balanced and unbalanced workflow, we compare our proposed method with the SPEA2 and NSGA2 algorithms based on conflicting objectives: (1) makespan, (2) cost and (3) resource efficiency.

A Multi-objective optimization problem (MOP) is a simultaneous optimization of more than one real-valued conflicting objective function subject to some constraints. Most MOP algorithms try to provide a set of Pareto optimal solutions which are equally good in terms of the objective functions. The set can be infinite, and hence, analysis and choice task of one or several solutions among the equally good solutions is hard for a decision maker (DM). In this paper, a new scalarization approach is proposed to select a Pareto optimal solution for convex MOPs such that the relative importance assigned to its objective functions is very close together. In addition, two decision-making methods are developed to analyze convex and non-convex MOPs based on evaluating a set of Pareto optimal solutions and the relative importance of the objective functions. These methods support the DM to rank the solutions and obtain one or several of them for real implementation without having any familiarity about MOPs.

In this paper, a new hybrid method is developed for optimal design of truss structures.This method is based on a modified Multi-objective particle swarm optimization, tournament decision making process, and a local search algorithm. In structural design practice, different objectives are usually considered in the selection of the final design in which most of these objectives contradict each other. The use of a Multi-objective optimization method guides the decision makers to find the most suitable design. Incorporating a decision making process with this optimization, it becomes possible to find a solution which covers most of the requirements. The developed hybrid algorithm is applied to three truss structures to illustrate its ability in finding the optimal solution.

Bi-level programming, a tool for modeling decentralized decisions, consists of the objective (s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define Multi-level programs with any number of levels. Supply chain planning problems are concerned with synchronizing and optimizing Multiple activities involved in the enterprise, from the start of the process, such as procurement of the raw materials, through a series of process operations, to the end, such as distribution of the final product to customers.Enterprise-wide supply chain planning problems naturally exhibit a Multi-level decision network structure, where for example, one level may correspond to a local plant control/scheduling/planning problem and another level to a corresponding plant-wide planning/network problem. Such a Multi-level decision network structure can be mathematically represented by using "Multi-level programming" principles. This paper studies a "bi-level linear Multi-objective decision making" model in with "interval" parameters and presents a solution method for solving it; this method uses the concepts of tolerance membership function and Multi objective Multi-level optimization when all parameters are imprecise and interval.