Abstract
Stratified random sampling is an effective sampling technique for estimating the population characteristics. The determination of strata boundaries and the allocation of sample size to the strata are two of the most critical factors in maximizing the precision of the estimates. Most surveys are conducted in an environment of severe budget constraints and a specific time is required to finish the survey. So cost and time are two important objectives that are taken under consideration in most surveys. The study suggested Mathematical goal programming model for determining optimum stratum boundaries for an exponential study variable under multiple objectives model when cost and time are under consideration. Compared to other techniques, Goal programming has many advantages in resources planning. Determining the required resources to satisfy the desired goals and the effectiveness of the available resources as well as providing best solutions under different amounts of resources are examples of the advantages of Goal programming. In addition the paper used data on Covid-19 to evaluate the performance of the suggested model for the exponential distribution. The study divided the number of new cases diseases into small, medium and high numbers. It also compared the results with the findings in the reports of the World Health Organization. The suggested mathematical goal programming revealed that Egypt was exposed to three waves of infection during the interval (5/3/2020 to 12/8/2021). These results are identical to the actual reality of covid-19 waves in Egypt.