In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.

Flows in Networks

Lecture Notes in Economics and Mathematical Systems

The banking industry has been the object of DEA analyses by a significant number of researchers and probably is the most heavily studied of all business sectors. Various DEA models have been applied in performance assessing problems, and the banks' complex production processes have further motivated the extension and improvement of DEA techniques. This paper surveys 80 published DEA applications in 24 countries/areas that specifically focus on bank branches. Key issues related to the design of DEA models in these studies are discussed. Much advice is included on how to design future experiments and studies in this domain. A number of areas where further research could be fruitful are suggested.

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A survey on bank branch efficiency and performance research with data envelopment analysis

A new method for solving fully fuzzy linear programming problems

The healthcare sector in general and hospitals in particular represent a main application area for Data Envelopment Analysis (DEA). This paper reviews 262 papers of DEA applications in healthcare with special focus on hospitals and therefore closes a gap of over ten years that were not covered by existing review articles. Apart from providing descriptive statistics of the papers, we are the first to examine the research purposes of the publications. These research goals can be grouped into four distinct clusters according to our proposed framework. The four clusters are (1) "Pure DEA efficiency analysis", i.e. performing a DEA on hospital data, (2) "Developments or applications of new methodologies", i.e. applying new DEAy approaches on hospital data, (3) "Specific management question", i.e. analyzing the effects of managerial specification, such as ownership, on hospital efficiency, and (4) "Surveys on the effects of reforms", i.e. researching the impact of policy making, such as reforms of health systems, on hospital efficiency. Furthermore, we analyze the methodological settings of the studies and describe the applied models. We analyze the chosen inputs and outputs as well as all relevant downstream techniques. A further contribution of this paper is its function as a roadmap to important methodological literature and publications, which provide crucial information on the setup of DEA studies. Thus, this paper should be of assistance to researchers planning to apply DEA in a hospital setting by providing information on a) what has been published between 2005 and 2016, b) possible pitfalls when setting up a DEA analysis, and c) possible ways to apply the DEA analysis in practice. Finally, we discuss what could be done to advance DEA from a scientific tool to an instrument that is actually utilized by managers and policymakers.

The use of Data Envelopment Analysis (DEA) in healthcare with a focus on hospitals.

Linear programming problems with fuzzy variables have been investigated by many researchers in the recent literature. Some methods to solve these problems, such as the primal simplex method and the dual simplex method, are based on the concept of comparison of fuzzy numbers by using ranking functions. In this paper, we give a new primal-dual algorithm for solving linear programming problems with fuzzy variables by using duality results, which was proposed by Mahdavi-Amiri and Nasseri (2007). This algorithm will be useful for sensitivity analysis when the activity vectors change for basic columns.

A primal-dual method for linear programming problems with fuzzy variables

http://tavana.us/publications/DEA-3STAGE.pdf

A three-stage Data Envelopment Analysis model with application to banking industry

A simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers

In this paper, a well-known network-structured problem called the transportation problem (TP) is considered in an uncertain environment. The transportation costs, supply and demand are represented by trapezoidal intuitionistic fuzzy numbers (TrIFNs) which are the more generalized form of trapezoidal fuzzy numbers involving a degree of acceptance and a degree of rejection. We formulate the intuitionistic fuzzy TP (IFTP) and propose a solution approach to solve the problem. The IFTP is converted into a deterministic linear programming (LP) problem, which is solved using standard LP algorithms. The main contributions of this paper are fivefold: (1) we convert the formulated IFTP into a deterministic classical LP problem based on ordering of TrIFNs using accuracy function; (2) in contrast to most existing approaches, which provide a crisp solution, we propose a new approach that provides an intuitionistic fuzzy optimal solution; (3) in contrast to existing methods that include negative parts in the obtained intuitionistic fuzzy optimal solution and intuitionistic fuzzy optimal cost, we propose a new method that provides non-negative intuitionistic fuzzy optimal solution and optimal cost; (4) we discuss about the advantages of the proposed method over the existing methods for solving IFTPs; (5) we demonstrate the feasibility and richness of the obtained solutions in the context of two application examples.

Ali Ebrahimnejad

Papers

A primal-dual method for linear programming problems with fuzzy variables

A three-stage Data Envelopment Analysis model with application to banking industry

A simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers

A new approach for solving fully intuitionistic fuzzy transportation problems

Using complementary slackness property to solve linear programming with fuzzy parameters