Beams are the constituent elements of several machine parts and sophisticated structures. In this paper, efforts are made to develop suitable methods that can serve as the basis to detect crack location and to crack size from measured axial vibration data. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of axial natural frequencies, which are global parameter and can be easily measured from any point on the structure. In theoretical analysis, the relationship between the natural frequencies, crack location, and crack size has been developed. For identification of crack location and crack size, it was shown that data on the variation of the first two natural frequencies is sufficient. The experimental analysis is done to verify the practical applicability of the theoretical method developed.

Leagile supply chain management has emerged as a proactive approach for improving business value of companies. The companies that face volatile and unpredictable market demand of their products must pioneer in leagile supply chain strategy for competition and various demands of customers. There are literally many approaches for performance metrics of supply chain in general, yet little investigation has identified the reliability and validity of such approaches particularly in leagile supply chains. This study examines the consistency approaches by confirmatory factor analysis that determines the adoption of performance dimensions. The prioritization of performance enablers under these dimensions of leagile supply chain in small and medium enterprises are determined through fuzzy logarithmic least square method (LLSM). The study developed a generic hierarchy model for decision-makers who can prioritize the supply chain metrics under performance dimensions of leagile supply chain.

Finite element method is used to study the free vibration analysis of functionally graded skew plates. The material properties of the skew plates are assumed to vary continuously through their thickness according to a power-law distribution of the volume fractions of the plate constituents. The first order shear deformation theory is used to incorporate the effects of transverse shear deformation and rotary inertia. Convergence study with respect to the number of nodes has been carried out and the results are compared with those from past investigations available in the literature. Two types of functionally graded skew plates - Al/ZrO2 and Al/Al2O3 are considered in this study and the effects of the volume fraction, different external boundary conditions and thickness ratio on the natural frequencies are studied in detail.

In this paper, wire electrical discharge machining of WC-Co composite is studied. Influence of taper angle, peak current, pulse-on time, pulse-off time, wire tension and dielectric flow rate are investigated for material removal rate (MRR) and surface roughness (SR) during intricate machining of a carbide block. In order to optimize MRR and SR simultaneously, grey relational analysis (GRA) is employed along with Taguchi method. Through GRA, grey relational grade is used as a performance index to determine the optimal setting of process parameters for multiple machining characteristics. Analysis of variance (ANOVA) shows that the taper angle and pulse-on time are the most significant parameters affecting the multiple machining characteristics. Confirmatory results, proves the potential of GRA to optimize process parameters successfully for multi-machining characteristics.

The terminal condition of inventory level to be zero at the end of the cycle time adopted by Soni and Shah (2008, 2009) is not viable when demand is stock-dependent. To rectify this assumption, we extend their model for (1) an ending – inventory to be non-zero; (2) limited floor space; (3) a profit maximization model; (4) selling price to be a decision variable, and (5) units in inventory deteriorate at a constant rate. The algorithm is developed to search for the optimal decision policy. The working of the proposed model is supported with a numerical example. Sensitivity analysis is carried out to investigate critical parameters.

This paper deals with an inventory model, which considers the impact of marketing strategies such as pricing and advertising as well as the displayed inventory level on the demand rate of the system. In addition, the demand rate during the stock-out period differs from that during the stock-in period by a function varied on the waiting time up to the beginning of the next cycle. Shortage are allowed and partially backlogged. Here, the deterioration rate is assumed to follow the Weibull distribution. Considering all these factors with others, different scenarios of the system are investigated. To obtain the solutions of these cases and to illustrate the model, an example is considered. Finally, to study the effects of changes of different parameters of the system, sensitivity analyses have been carried out with respect to the different parameters of the system.

The selection of appropriate alternative in the industrial environment is an important but, at the same time, a complex and difficult problem because of the availability of a wide range of alternatives and similarity among them. Therefore, there is a need for simple, systematic, and logical methods or mathematical tools to guide decision makers in considering a number of selection attributes and their interrelations. In this paper, a hybrid decision making method of graph theory and matrix approach (GTMA) and analytical hierarchy process (AHP) is proposed. Three examples are presented to illustrate the potential of the proposed GTMA-AHP method and the results are compared with the results obtained using other decision making methods.

In this research, the integrated inventory models are developed for price–sensitive stock– dependent demand and delay in payments are permissible. Two level trade credit police in the vendor–buyer and buyer–customer is considered. An easy–to–use solution algorithm is derived for the integrated models to determine the buyer’s optimal pricing and ordering strategy. A negotiation scenario is incorporated to distribute the extra profit between the vendor and buyer. A numerical example and sensitivity analysis are given to validate the proposed models. It is observed that the total joint profit of the integrated system can increase even if the price discount is offered to the buyer in proposed models.

This paper discusses the mathematical modeling and performance optimization of CO2 cooling system of a fertilizer plant using genetic algorithm. The fertilizer plant comprises of various systems viz. shell gasification and carbon recovery, desulphurization, co-shift conversion, decarbonation- CO2 cooling, CO2 removal, nitrogen wash and ammonia synthesis, etc. One of the most important functionaries of a fertilizer plant is CO2 cooling system. The CO2 cooling system of a fertilizer plant has five main subsystems, arranged in series. We propose a mathematical model, which considers exponential distribution for the probable failures and repairs. We also use probabilistic approach and derive differential equations based on Markov birth-death process. These equations are then solved using normalizing conditions to determine the steady state availability of the CO2 cooling system. The performance of each subsystem of CO2 cooling system of a fertilizer plant is also optimized using genetic algorithm. The results of the proposed model of this paper is useful to the plant management for the timely execution of proper maintenance decisions and hence to enhance the system performance.

This paper proposes a mathematical model for retailer’s optimal inventory policy for deteriorating items under the conditions of permissible delay in payment in supply chain coordination. In this paper, supplier offers full trade credit to his/her retailer and the retailer, in turn, provides the partial trade credit to his/her customer. This research article helps the retailer determine the optimal cost, more accurately. The primary objective is to minimize the retailer’s cost and to determine the optimal inventory policy for retailer. The results of this article generalize some already published results by incorporating deterioration on inventory items. We use some numerical examples to analyze the effects of various parameters on retailer’s inventory policy.