Representation of Maximal Monotone Operators in Hadamard Spaces

This paper is devoted to study some topics of monotone operator theory in the context of Hadamard spaces. For a fixed element $p$ in an Hadamard space $X$, the notion of $p$-Fenchel conjugate is introduced and a generalization of Fenchel-Young inequality is proved. Moreover, $p$-Fitzpatrick transform of a monotone set-valued operator from an Hadamard space $X$ to its linear dual space $X^\lozenge$ and its main properties are investigated. Finally, a characterization result for maximality of monotone operator $T:X\multimap X^\lozenge$, based on certain classes of proper, convex, l.s.c. extended real-valued function $h$ on $X\times X^\lozenge$, is given

Monotonicity of sets in Hadamard spaces from polarity point of view

This paper is devoted to introduce and investigate the notion of monotone sets in Hadamard spaces. First, flat Hadamard spaces are introduced and investigated. It is shown that an Hadamard space $X$ is flat if and only if X\times X^\medlozenge has $\mathcal{F}_l$-property, where X^\medlozenge is the linear dual of $X$. Moreover, monotone and maximal monotone sets are introduced and also monotonicity from polarity point of view is considered. Some characterizations of (maximal) monotone sets, specially based on polarity, is given. Finally, it is proved that any maximal monotone set is sequentially $bw\times${\|\cdot\|_\loz}-closed in X\times X^\medlozenge

Formulating and Solving Sustainable Stochastic Dynamic Facility Layout Problem: A Key to Sustainable Operations

Facility layout design, a NP Hard problem, is associated with the arrangement of facilities in a manufacturing shop floor, which impacts the performance, and cost of system. Efficient design of facility layout is a key to the sustainable operations in a manufacturing shop floor. An efficient layout design not only optimizes the cost and energy due to proficient handling but also increase flexibility and easy accessibility. Traditionally, it is solved using meta-heuristic techniques. But these algorithmic or procedural methodologies do not generate effective and efficient layout design from sustainable point of view, where design should consider multiple criteria such as demand fluctuations, material handling cost, accessibility, maintenance, waste and more. In this paper, to capture the sustainability in the layout design these parameters are considered, and a new Sustainable Stochastic Dynamic Facility Layout Problem (SDFLP) is formulated and solved. SDFLP is optimized for material handling cost and rearrangement cost using various meta-heuristic techniques. The pool of layouts thus generated is then analyzed by Data Envelopment Analysis (DEA) to identify efficient layouts. A novel hierarchical methodology of consensus ranking of layouts is proposed which combines the multiple attributes/criteria. Multi Attribute decision-making (MADM) Techniques such as Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Interpretive Ranking Process (IRP) and Analytic hierarchy process (AHP), Borda-Kendall and Integer Linear Programming based rank aggregation techniques are applied. To validate the proposed methodology data sets for facility size N=12 for time period T=5 having Gaussian demand are considered

Intelligent Systems; Investigators at Multimedia University Detail Research in Intelligent Systems

According to news reporting originating from Melaka, Malaysia, by VerticalNews correspondents, research stated, "Since Facility Layout Problem (FLP) affects the total manufacturing cost significantly, it can be considered as a critical issue in the early stages of designing Flexible Manufacturing Systems (FMSs), particularly in volatile environments where uncertainty in product demands is inevitable

Intelligent Systems; Investigators at Multimedia University Detail Research in Intelligent Systems

According to news reporting originating from Melaka, Malaysia, by VerticalNews correspondents, research stated, "Since Facility Layout Problem (FLP) affects the total manufacturing cost significantly, it can be considered as a critical issue in the early stages of designing Flexible Manufacturing Systems (FMSs), particularly in volatile environments where uncertainty in product demands is inevitable

Intelligent design of dynamic and robust layouts in uncertain environment of flexible manufacturing systems

Designing dynamic, robust, and static facility layouts are well-known approaches to cope with the stochastic dynamic facility layout problem (SDFLP). A dynamic layout includes an optimal layout in each period of the planning horizon, whereas a robust layout is a good layout over the entire time planning horizon, but not necessarily an optimal layout for a particular time period. Using the static approach each period is solved separately, regardless of other periods data. This dissertation deals with the SDFLP, where the product demands are assumed to be dependent normally distributed random variables with known expected value, variance, and covariance that change from period to period at random. Development of a new quadratic assignment-based mathematical model to design each of the dynamic, robust, static, the most robust, the most stable, and the robust stable machine layouts are the first main objectives of the thesis. Then, each of the dynamic and robust machine layout design models is generalised to a model for concurrent design of dynamic and robust inter and intra-cell layouts. Another major objective of this dissertation is development of a novel hybrid algorithm named AC-CS-SA by using ant colony (AC), clonal selection (CS), simulated annealing (SA), and robust layout design approaches to solve the SDFLP formulated by each of the aforementioned models

Manufacturing; Findings from Multimedia University Broaden Understanding of Manufacturing

Dynamic and robust layouts are flexible enough to cope with fluctuations and uncertainties in product demands in volatile environment of flexible manufacturing systems. Since the facility layout is a hard combinatorial optimization problem, intelligent approaches are the most appropriate methods for solving the large size of this problem in reasonable computational time

Intelligent design of a dynamic machine layout in uncertain environment of flexible manufacturing systems

Since Facility Layout Problem (FLP) affects the total manufacturing cost significantly, it can be considered as a critical issue in the early stages of designing Flexible Manufacturing Systems (FMSs), particularly in volatile environments where uncertainty in product demands is inevitable. This paper proposes a new mathematical model by using the Quadratic Assignment Problem formulation for designing an optimal machine layout for each period of a dynamic machine layout problem in FMSs. The product demands are considered as independent normally distributed random variables with known Probability Density Function (PDF), which changes from period to period at random. In this model, the decision maker's defined confidence level is also considered. The confidence level represents the decision maker's attitude about uncertainty in product demands in such a way that it affects the results of the problem significantly. To validate the proposed model, two different size test problems are generated at random. Since the FLP, especially in multi-period case is a hard Combinatorial Optimization Problem (COP), Simulated Annealing (SA) meta-heuristic resolution approach programmed in Matlab is used to solve the mathematical model in a reasonable computational time. Finally, the computational results are evaluated statistically

Routing flexibility for unequal–area stochastic dynamic facility layout problem in flexible manufacturing systems

It is indispensable that any manufacturing system is consistent with potential changes such as fluctuations in demand. The uncertainty also makes it more essential. Routing Flexibility (RF) is one of the necessities to any modern manufacturing system such as Flexible Manufacturing System (FMS). This paper suggests three mixed integer nonlinear programming models for the Unequal–Area Stochastic Dynamic Facility Layout Problems (UA–SDFLPs) by considering the Routing Flexibility. The models are proposed when the independent demands follow the random variable with the Poisson, Exponential, and Normal distributions. To validation of the proposed models, many small-sized test problems has solved that derived from a real case in literature. The large-sized test problems are solved by the Genetic Algorithm (GA) at a reasonable computational time. The obtained results indicate that the discussed models for the UA–SDFLPs are valid and the managers can take these models to the manufacturing floor to adapt to the potential changes in today's competitive market