TY  - BOOK
AU  - Maha Ismail Mahfouz Ismail, 
AU  - Zeinab Ali Abd El-Aziz Khadr
AU  - Mahmoud Mostafa Rashwan
AU  - Mohammed Abd El-Ghani Ramadan
TI  - Optimal Stochastic Allocation in Multivariate Stratified Sampling / 
U1  - 519.5 
PY  - 2023///
KW  - Statistics
KW  - qrmak
KW  - Multivariate Stratified Sampling
KW  - Multi-Objective Programming
KW  - Weighted Goal programming
N1  - Thesis (Ph.D)-Cairo University, 2023; Bibliography: pages 70-74; Issued also as CD
N2  - The allocation of stratified sampling is the problem of determining the number of 
observations to be selected from each stratum. Many authors introduced optimization-based 
allocation techniques that utilize the mathematical programming approach to obtain an optimal 
allocation that optimizes certain objective function under some constraints. The main challenge 
of the optimal allocation is the compromise between the two conflicting objectives of the cost of 
the survey and the precision of the estimates. In the literature, the optimal allocations obtained 
either minimize variation for the estimates under a given cost of the survey or minimize cost at a 
given precision level of the estimates. In multivariate surveys, the optimal allocation for one 
characteristic may result in a loss of the precision of the estimates of the other characteristics. 
This study proposes a multivariate optimal compromise allocation using a multi-objective 
mathematical programming model that simultaneously minimizes the total cost of the survey and 
the variation of the overall stratified mean of all of the characteristics of interest. The 
proportional increase in the estimator's variance due to minimizing the variance compared to the 
estimator's variance due to minimizing the cost is set as a constraint and is upper-bounded by a 
pre-determined quantity. Weighted Goal Programming is adopted as a solution technique, which 
has the flexibility of introducing different weights to the different goals according to the decision 
maker’s requirements. Integer programming is used to guarantee integer values for the optimal 
allocation. 
However, in practice, because the population data are usually unknown and are estimated 
under uncertainty, thus, their sample estimates should be better treated as random variables. 
Therefore, the proposed model introduces another form implementing a Stochastic Programming 
model that is solved using the Chance-Constrained Programming technique. A simulation-based 
comparative study is conducted to assess the performance of the proposed allocation models 
versus other allocation techniques. The results show that, according to the criteria used for 
comparison, the proposed models produced estimators with the highest precision in most of the 
cases.;  الهدف الرئيسى من هذه الدراسة هو تقديم أسلوب برمجة متعدد الأهداف يهدف للتعامل مع مشكلة التخصيص في المعاينة العشوائية الطبقية عن طريق تصغير كل من تباين مقدر متوسط المجتمع، بالإضافة إلى الميزانية المستخدمة فى آن واحد. وتم تقديم صورة أخرى من النموذج فى شكل برمجة إحتمالية مع افتراض أن التباين وبعض بنود الميزانية هى متغيرات عشوائية تتبع توزيع احتمالى معين. بالإضافة إلى ذلك، يتم مقارنة النماذج المُقترحة مع نماذج أخرى قُدمت فى الدراسات السابقة من خلال دراسة محاكاة. ويتم تقييم أداء النماذج باستخدام ثلاثة معايير لقياس كفاءة النماذج فى الحصول على مقدرات المجتمع. و بناءاً على هذه المعايير، أفادت النتائج التى تم التوصل اليها أن النماذج المقترحة كانت الأكثر كفاءة في الحصول على مقدرات المتوسطات داخل الطبقات و ذلك في معظم الحالات
ER  -