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Numerical Algebra, Control & Optimization

2017 , Volume 7 , Issue 4

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Performance evaluation of four-stage blood supply chain with feedback variables using NDEA cross-efficiency and entropy measures under IER uncertainty
Shiva Moslemi and  Abolfazl Mirzazadeh
2017, 7(4): 379-401 doi: 10.3934/naco.2017024 +[Abstract](88) +[HTML](62) +[PDF](381.9KB)

Blood supply chain management has been considered by many managers in recent years, as one of the major challenges in health systems. In order to ensure the optimal performance of the supply chain, enable continuous improvement and create competitive advantage, establishment of a performance evaluation system is essential. For this purpose, the current study proposes a Network Data Envelopment Analysis (NDEA) model for measuring efficiency of four-stage serial network of blood supply chain in presence of feedback variables by identifying comprehensive and balanced criteria as evaluation variables. Since criteria values are obtained from subjective judgment of individuals, are uncertain. Interval Evidential Reasoning (IER) approach that deals with a variety of uncertainties such as ignorance and vagueness, has been used to control the uncertainty and provide reliable evaluation. In order to rank the units a new cross-efficiency based model is presented as a remedy for the issue of non-uniqueness of optimal weights in cross efficiency. Then, Gibbs entropy is utilized to measure the uncertainty of obtained interval cross efficiency. Finally, a numerical example is provided to illustrate the proposed model.

A new Monte Carlo based procedure for complete ranking efficient units in DEA models
Mazyar Zahedi-Seresht , Gholam-Reza Jahanshahloo , Josef Jablonsky and  Sedighe Asghariniya
2017, 7(4): 403-416 doi: 10.3934/naco.2017025 +[Abstract](94) +[HTML](33) +[PDF](351.3KB)

Traditional data envelopment analysis (DEA) models split DMUs into two classes – namely efficient and inefficient. Due to the identical maximum efficiency scores of the efficient units, they cannot be ranked directly. That is why various models allowing the complete ranking of DMUs have been proposed in the past. Those models are based on different principles and have various advantages and disadvantages (infeasibility, alternative optimum, computational aspects, etc.). The method proposed in this paper uses the magnitude of the area under the efficient curve. In order to estimate this magnitude we suggest to use Monte Carlo simulation for the complete ranking originally efficient DMUs so as to overcome the problems arisen from other ranking methods and it is very simple, computationally. This method generates random weights for the inputs and outputs in the feasible region and finally derives probability the DMUs are efficient. The procedure proposed is illustrated by a numerical example and its results are compared with three of most important and popular methods for ranking efficient units (i.e. cross-efficiency evaluation, Andersen and Petersen super-efficiency model, and common set of weights method).

A robust multi-trip vehicle routing problem of perishable products with intermediate depots and time windows
Erfan Babaee Tirkolaee , Alireza Goli , Mani Bakhsi and  Iraj Mahdavi
2017, 7(4): 417-433 doi: 10.3934/naco.2017026 +[Abstract](157) +[HTML](112) +[PDF](571.0KB)

Distribution of products within the supply chain with the highest quality is one of the most important competitive activities in industries with perishable products. Companies should pay much attention to the distribution during the design of their optimal supply chain. In this paper, a robust multi-trip vehicle routing problem with intermediate depots and time windows is formulated to deals with the uncertainty nature of demand parameter. A mixed integer linear programming model is presented to minimize total traveled distance, vehicles usage costs, earliness and tardiness penalty costs of services, and determine optimal routes for vehicles so that all customers' demands are covered. A number of random instances in different sizes (small, medium, and large) are generated and solved by CPLEX solver of GAMS to evaluate the robustness of the model and prove the model validation. Finally, a sensitivity analysis is applied to study the impact of the maximum available time for vehicles on the objective function value.

An investigation of the most important factors for sustainable product development using evidential reasoning
Farzaneh Ahmadzadeh , Kathrina Jederström , Maria Plahn , Anna Olsson and  Isabell Foyer
2017, 7(4): 435-455 doi: 10.3934/naco.2017027 +[Abstract](75) +[HTML](108) +[PDF](542.2KB)

Those working in product development need to consider sustainability, being careful not to compromise the future generation's ability to satisfy its needs. Several strategies guide companies towards sustainability. This paper studies six of these strategies: eco-design, green design, cradle-to-cradle, design for environment, zero waste, and life cycle approaches. Based on a literature review and semi-structured interviews, it identifies 22 factors of sustainability from the perspective of manufacturers. The purpose is to determine which are the most important and to use them as a foundation for a new design strategy. A survey based on the 22 factors was given to people working with product development; they graded each factor by importance. The resulting qualitative data were analyzed using evidential reasoning. The analysis found the factors "minimize use of toxic substances, " "increase competitiveness, " "economic benefits, " "reduce material usage, " "material selection, " "reduce emissions, " and "increase product functionality" are more important and should serve as the foundation for a new approach to sustainable product development.

A study of numerical integration based on Legendre polynomial and RLS algorithm
Hongguang Xiao , Wen Tan , Dehua Xiang , Lifu Chen and  Ning Li
2017, 7(4): 457-464 doi: 10.3934/naco.2017028 +[Abstract](73) +[HTML](30) +[PDF](291.3KB)

A quadrature rule based on Legendre polynomial functions is proposed to find approximate values of definite integrals in this paper. This method uses recursive least squares (RLS) algorithm to compute coefficients of Legendre polynomial fitting functions, and then approximately computes values of definite integrals by using obtained the coefficients. The main advantage of this approach is its efficiency and simple applicability. Finally some examples are given to test the convergence and accuracy of the method.

A hybrid meta-heuristic algorithm to minimize the number of tardy jobs in a dynamic two-machine flow shop problem
Mostafa Abouei Ardakan , A. Kourank Beheshti , S. Hamid Mirmohammadi and  Hamed Davari Ardakani
2017, 7(4): 465-480 doi: 10.3934/naco.2017029 +[Abstract](61) +[HTML](76) +[PDF](437.8KB)

In this paper, first, the problem of dynamic two-machine flow shop scheduling with the objective of minimizing the number of tardy jobs is investigated. Second, a hybrid algorithm based on genetic algorithm and parallel simulated annealing algorithm is presented. In order to solve large scale instances of the problem and to generate the initial population for the hybrid approach, a heuristic algorithm is also presented. To evaluate the efficiency of the proposed algorithms, they are compared with an optimal branch-and-bound algorithm which has been already developed in the literature. Computational experiments demonstrate that the proposed hybrid algorithm can solve the entire small-sized problems and more than 95% of medium-sized problems optimally.

Numerical method for solving optimal control problems with phase constraints
Alexander Tyatyushkin and  Tatiana Zarodnyuk
2017, 7(4): 481-492 doi: 10.3934/naco.2017030 +[Abstract](269) +[HTML](31) +[PDF](541.6KB)

The main idea of the method consists in successive solving auxiliary problems, which minimizes a special constructed Lagrange function, subject to linearized phase constraints. The linearly constrained auxiliary problems are more simple than the original ones because linear constraints can be easily processed. We shall discuss different aspects connected with approximating control problems and using the program system for solving them. We shall then pay attention to optimal control problems with constraints on inertia of control functions. For illustrations, four control problems will be solved using the proposed software.




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