This nal project discusses the optimal solution of inventory model with power demand pattern index 0 < n < 1 with shortage. Power demand pattern index 0 < n < 1 is the one where the demand increases at the end of inventory cycle. The inventory model with power demand pattern index 0 < n < 1 assumes that only a fraction of demand is backlogged during the shortage periode and the remainder …
This final project discusses how to solve inventory problems considering the products with finite self-life which cause deterioration. The market demand is assumed in a linear form and production rate is constant in which the production starts with buffer stock. This research is completed using the EPQ inventory method. The objective of the model is to obtain optimum ordering cycle and the…
This nal project discusses the inventory model with demand pattern index n > 1 that allows shortages. It is assumed that there is a backlogged demand during the shortage period and the remainder is considered lost sales. This research is completed by using the deterministic inventory model method, namely the EOQ model. The result of using the EOQ method is to determine the lot size and th…
This nal project discusses some identities of generalization of Jacobsthal polynomial and Jacobsthal Lucas polynomials and their generating matrix. The identity of the Jacobsthal polynomial and Jacobsthal Lucas polynomial are proven by Binet's formula while generating matrix is proven by mathematical induction. This nal project is a review of some parts of Catarino and Morgado [Analele S…
This final project discusses two regression estimators for the average of population in random sampling by using quartiles, deciles and cofficient of variation from additional variables written by Subzar et al. [Journal of Reliability and Statistical Studies, 10 (2017), 65–82]. The estimator is bias estimator. Furthermore, the two estimators are compared with the ratio estimator through …
This final project discusses a method for solving a quadratic programming problems with interval coefficient. The method used is extenstion of Wolfe’s method. Wolfe modified the simplex method to solve quadratic programming problem by adding conditions of the Karush-Kuhn-Tucker and transform quadratic programming problems with interval coefficient into two linear programming problems mod…
This final project discusses incomplete tribonacci-Lucas numbers and polynomials. Furthermore, the recurrence relations of homogeneous and nonhomogeneous and the sum of incomplete tribonacci-Lucas number and polynomials are also discussed. This is a review of some parts of Yilmaz and Tascara’s paper [Advances in Applied Clifford Algebras, 25 (2015), 741-753]. Keywords: Tribonacci-Lucas n…
This final project discusses two ratio estimator for the population mean in simple random sampling using quartile information, deciles and coefficient of skewness of an auxiliary variable which are assumed to be able to provide information to the characters examined. The two estimators are biased estimators, then the mean square errors (MSE) of the two estimators are obtained by Taylor ser…
This nal project discusses the inventory model with power demand pattern index n = 1 and partial backlogging that allows shortages. This research is completed by using the EOQ method and the results of using the method is the stock level and replenishment cycle optimal which aims to maximize the prot. Ilustrative examples is given to show the use of this model. Keywords: Economic order q…
This final project discusses the generalization of fractional integral with order ∈ (0; 1), which depends on a kernel k. Furthermore, from the generalization of fractional integral definition, some basic properties are obtained, such as inverse property, partial fractional integral, mean value theorem for fractional integral and fractional integral rules. This final project is a review …
This nal project discusses some identities of the generalized Jacobsthal and Jacobsthal-Lucas sequences based on some properties such as D'ocagne's property, Catalan's property and Cassini's property or Simpson's property. Then it discusses the relationship between p(x)-Jacobsthal and p(x)-Jacobsthal-Lucas by the roots of and , also the proof of some identities of p(x)-Jacobsthal and p…
This final project discusses a new method to solve transportation called harmonic mean approach method, where the proposed method is easy and efficient since computation works. Northwest corner method, least cost method and Vogel’s approximation method is used to determine basic feasible solution and to compare with the new method. Then simplex transportation method is used to obtain the…
This nal project discusses the localization of the eigenvalue using Gershgorin disk method which is a review of the article of Pe~na [Applied Mathematics and Computation, 219 (2013), 7725-7729]. Applying the certain pivoting strategies through Gaussian elimination reduces the length of the radii of the Gershgorin disk. This indicates that the area where the eigenvalue is located becomes s…
The ratio estimators studied here are ratio estimators for population mean on simple random sampling by using the auxiliary information of second quartile, quartile deviation and decile mean. Each estimator is biased estimator. Furthermore, the mean square error (MSE) from each estimator is determined so that an efficient estimator can be obtained by comparing MSE from each estimator with …
ABSTRACT Congruent is a special type of an equivalent relation that plays an important role in algebraic structures. This final project discusses the concept of semigroup, (n,m)-semigroup, homomorphism on (n,m)-semigroup and congruence on (n,m)-semigroup. This final project is a review of part of the article of Xiao [Pure and Applied Mathematics Journal, 6 (2017), 120-123] Keywords: Semig…
ABSTRACT This nal project discuss a family of high order numerical methods for so- lving nonlinear equations with simple root. The proposed methods can achieve convergence of order p, where p is a positive integer . The Newton method (p = 2) and Chebyshev's method (p = 3) are special cases of this family of methods. The method requires one and two evaluations of the function per iteratio…
This final project discusses the properties of the generalized addition and multiplication coupled Fibonacci sequence of rth order using the development of the properties of the generalized addition and multiplication coupled Fibonacci sequence of the second and third order. Then these properties are proven by using induction method. This final project is a review of articles of Sharma et …
This nal project discusses the relationship of generalized Fibonacci matrix sequence and k-Pell matrix sequence. Some properties of generalized Fibonacci matrix sequence, k-Pell matrix sequence, and the multiplication properties of the matrix are proven using mathematical induction and algebra calculations. Using some of these properties, the relationship of generalized Fibonacci matrix s…
This nal project discusses some properties of tribonacci and tribonacci-Lucas quaternion polynomial that is dened recursively, and determine the relation between tribonacci and tribonacci-Lucas quaternion polynomial. Binet's formula is used to prove the properties. This is a review of articles of Cerda-Morales [International Journal of Mathematics, 1 (2017), 1-11]. Keywords: Tribonacci n…
In this final project three types of estimators are discussed, namely mean estimator in simple random sampling, linear regression estimator and regression ratio estimator using information on auxiliary variable. These estimators are biased for regression ratio estimators and unbiased for linear regression and average estimators, then the Mean Square Error (MSE) of each estimator is determi…