3 research outputs found
A multi-objective multi-item solid transportation problem with vehicle cost, volume and weight capacity under fuzzy environment
Generally, in transportation problem, full vehicles (e.g., light commercial
vehicles, medium duty and heavy duty trucks, etc.) are to be booked, and
transportation cost of a vehicle has to be paid irrespective of the fulfilment
of the capacity of the vehicle. Besides the transportation cost, total time
that includes travel time of a vehicle, loading and unloading times of products
is also an important issue. Also, instead of a single item, different types of
items may need to be transported from some sources to destinations through
different types of conveyances. The optimal transportation policy may be
affected by many other issues like volume and weight of per unit of product,
unavailability of sufficient number of certain types of vehicles, etc. In this
paper, we formulate a multi-objective multi-item solid transportation problem
by addressing all these issues. The problem is formulated with the
transportation cost and time parameters as fuzzy variables. Using credibility
theory of fuzzy variables, a chance-constraint programming model is formulated,
and is then transformed into the corresponding deterministic form. Finally
numerical example is provided to illustrate the problem
A multi-objective reliability-redundancy allocation problem with active redundancy and interval type-2 fuzzy parameters
This paper considers a multi-objective reliability-redundancy allocation
problem (MORRAP) of a series-parallel system, where system reliability and
system cost are to be optimized simultaneously subject to limits on weight,
volume, and redundancy level. Precise computation of component reliability is
very difficult as the estimation of a single number for the probabilities and
performance levels are not always possible, because it is affected by many
factors such as inaccuracy and insufficiency of data, manufacturing process,
environment in which the system is running, evaluation done by multiple
experts, etc. To cope with impreciseness, we model component reliabilities as
interval type-2 fuzzy numbers (IT2 FNs), which is more suitable to represent
uncertainties than usual or type-1 fuzzy numbers. To solve the problem with
interval type-2 fuzzy parameters, we first apply various type-reduction and
defuzzification techniques, and obtain corresponding defuzzified values. As
maximization of system reliability and minimization of system cost are
conflicting to each other, so to obtain compromise solution of the MORRAP with
defuzzified parameters, we apply five different multi-objective optimization
methods, and then corresponding solutions are analyzed. The problem is
illustrated numerically for a real-world MORRAP on pharmaceutical plant, and
solutions are obtained by standard optimization solver LINGO, which is based on
gradient-based optimization - Generalized Reduced Gradient (GRG) technique
Some Network Optimization Models under Diverse Uncertain Environments
Network models provide an efficient way to represent many real life problems
mathematically. In the last few decades, the field of network optimization has
witnessed an upsurge of interest among researchers and practitioners. The
network models considered in this thesis are broadly classified into four types
including transportation problem, shortest path problem, minimum spanning tree
problem and maximum flow problem. Quite often, we come across situations, when
the decision parameters of network optimization problems are not precise and
characterized by various forms of uncertainties arising from the factors, like
insufficient or incomplete data, lack of evidence, inappropriate judgements and
randomness. Considering the deterministic environment, there exist several
studies on network optimization problems. However, in the literature, not many
investigations on single and multi objective network optimization problems are
observed under diverse uncertain frameworks. This thesis proposes seven
different network models under different uncertain paradigms. Here, the
uncertain programming techniques used to formulate the uncertain network models
are (i) expected value model, (ii) chance constrained model and (iii) dependent
chance constrained model. Subsequently, the corresponding crisp equivalents of
the uncertain network models are solved using different solution methodologies.
The solution methodologies used in this thesis can be broadly categorized as
classical methods and evolutionary algorithms. The classical methods, used in
this thesis, are Dijkstra and Kruskal algorithms, modified rough Dijkstra
algorithm, global criterion method, epsilon constraint method and fuzzy
programming method. Whereas, among the evolutionary algorithms, we have
proposed the varying population genetic algorithm with indeterminate crossover
and considered two multi objective evolutionary algorithms.Comment: Thesis documen