A fixed-charge transportation problem in two-stage supply chain network in Gaussian type-2 fuzzy environments

The new approaches for solving hierarchical Chinese postman problem with stochastic travel times

The hierarchical Chinese postman problem (HCPP) aims to find the shortest tour or tours by passing through the arcs classified according to precedence relationship. HCPP, which has a wide application area in real-life problems such as shovel snow and routing patrol vehicles where precedence relations are important, belongs to the NP-hard problem class. In real-life problems, travel time between the two locations in city traffic varies due to reasons such as traffic jam, weather conditions, etc. Therefore, travel times are uncertain. In this study, HCPP was handled with the chance-constrained stochastic programming approach, and a new type of problem, the hierarchical Chinese postman problem with stochastic travel times, was introduced. Due to the NP-hard nature of the problem, the developed mathematical model with stochastic parameter values cannot find proper solutions in large-size problems within the appropriate time interval. Therefore, two new solution approaches, a heuristic method based on the Greedy Search algorithm and a meta-heuristic method based on ant colony optimization were proposed in this study. These new algorithms were tested on modified benchmark instances and randomly generated problem instances with 817 edges. The performance of algorithms was compared in terms of solution quality and computational time.

Intuitionistic Type-2 Fuzzy Set and Its Properties

Decision making under uncertainty describes situations that consider a profound lack of knowledge, where the functional form is completely unknown, and often, the relevant input and output variables are unknown as well. Data, being the vital input of decision making, contain a dissimilar level of imprecision that necessitates different approaches for making a proper and legitimate decision. In this article, we propose the concept of the intuitionistic type-2 fuzzy set (IT2FS). Several arithmetic operations on IT2FS such as union, intersection, complement, containment, etc., are defined, and the related algebraic properties of IT2FS are also studied. Subsequently, we define two new operators, namely the necessity operator and the possibility operator, to convert an IT2FS into an ordinary T2FS, and then discuss some of their basic properties. Moreover, in this study, two distance measures, the Hamming distance and Euclidian distance of IT2FS, are proposed, and their applications are illustrated with an example.

Hierarchical network modeling with multidimensional information for aquatic safety management in the cold chain

The cold-chain information has characterized by the loss and dispersion according to the different collecting methods. The description for the quality decay factors of aquatic products can be defined as the multidimensional information. A series of nodes with multidimensional information are assembled to be hierarchies aiming at describing the environment conditions and locations in the supply chain. Each of the single hierarchy levels constitutes a sequence of node information in a network, which is applied as internal information analysis. The cross-layer information structure is defined as "bridge" information which is able to record the information transmissions among every hierarchy from the point of view of the whole chain. The study has established a novel structured modeling to describe the cold chain of aquatic products based on a network-hierarchy framework. An organized and sustainable transmission process can be built and recorded by the multidimensional attributes for the whole course of cold chain of aquatic products. In addition, seamless connections among every hierarchy are attainable by the environmental information records continuously to monitor the quality of aquatic products. The quality assessments and shelf life predictions are estimated properly as the risk control in order to monitor and trace the safety of aquatic products under the supply chain perspective.

A Parametric Programming Method on Gaussian Type-2 Fuzzy Set and Its Application to a Multilevel Supply Chain

The transportation problem is an important and relevant supply chain optimization problem in the traffic engineering. This paper minimizes shipping costs of a three channel distribution system comprised of plants, distribution centers, and customers. Plants manufacture several products that are delivered to distribution centers. If a distribution center is used then fixed cost is charged. Customers are replenished by an only one distribution center. To characterize the uncertainty that typically occurs in many practical decision environments, this paper considers the supply capacities, demands as Gaussian type-2 fuzzy variables. To provide a modelling framework for optimization problems with multi-fold uncertainty, different reduction methods are proposed to transform a Gaussian type-2 fuzzy variable into a type-1 fuzzy variable by mean reduction method. Then the transportation problem is reformulated as a chance-constrained expected value model enlightened by the credibility optimization method. The deterministic models are then solved using two different soft computing techniques (i) Generalized Reduced Gradient (Lingo-14.0), and (ii) modified Particle Swarm Optimization(PSO), where the position of each particle is adjusted according to its own experience and that of its neighbors. The numerical experiments illustrate the application and effectiveness of the proposed solution approaches.