Interval-valued Environment Research Articles

The impact of R&D expenditures and screening in an economic production rate (EPR) inventory model for a flawed production system with imperfect screening under an interval-valued environment

In this paper, a single product of a single manufacturing unit for an imperfect production inventory system is modelled to minimize the total cost of a production cycle. A large fraction of defective items is passed to customers by manufacturers due to imperfect screening method so manufacturer replace them with new ones while incurring penalties. This fraction depends on the investment of research and development (R&D). This paper optimizes the R&D cost to minimize the defective items produced in a production line. The demand function depends on the selling price, advertisement cost, and product quality. The quality of the produce items is measured by screening time effort and investment in R&D. Further, we considered all the costs of the production cycle in interval-valued form and elaborately discuss the application of interval metric in the total cost interval objective function. A necessary and sufficient conditions are derived for the proposed model with the help of modified KKT conditions. Results show that applying screening and R&D costs significantly reduces the number of defective items and simultaneously reduces the total cost. A numerical example is presented along with sensitivity analyses on different parameters with the help of MATLAB software.

Multi-objective immune genetic algorithm solving nonlinear interval-valued programming

This work studies one multi-objective immune genetic algorithm with small population to solve a general kind of unconstrained multi-objective interval-valued programming. In this optimization approach, those competitive individuals are discriminated based on interval arithmetic rules and a possibility model; a crowding degree model in interval-valued environments is developed to eliminate redundant individuals; the current population promotes different individuals to evolve towards specific directions by population sorting and immune evolution, while those elitist individuals found accelerate to explore the desired regions through genetic evolution. The theoretical analysis has showed that the computational complexity of the proposed approach depends mainly on the elitist population size. Comparative experiments have illustrated that the approach can take a rational tradeoff between effect and efficiency. It can perform well over the compared approaches as a whole, and has the potential to solving multi-modal and hard multi-objective interval-valued programming problems.

New efficiency conditions for multiobjective interval-valued programming problems

In this paper, we focus on necessary and sufficient efficiency conditions for optimization problems with multiple objectives and a feasible set defined by interval-valued functions. A new concept of Fritz-John and Karush–Kuhn–Tucker-type points is introduced for this mathematical programming problem based on the gH-derivative concept. The innovation and importance of these concepts are presented from a practical and computational point of view. The problem is approached directly, without transforming it into a real-valued programming problem, thereby attaining theoretical results that are more powerful and computationally more efficient under weaker hypotheses. We also provide necessary conditions for efficiency, which have been inexistent in the relevant literature to date. The identification of necessary conditions is important for the development of future computational optimization techniques in an interval-valued environment. We introduce new generalized convexity notions for gH-differentiable interval-valued problems which are a generalization of previous concepts and we prove a sufficient efficiency condition based on these concepts. Finally, the efficiency conditions for deterministic programming problems are shown to be particular instances of the results proved in this paper. The theoretical developments are illustrated and justified through several numerical examples.