the construction industry is notorious of overrunning budget and delays. there are several real life examples of the aforesaid failures. It is argued that planning is the key for success or failure. Eisenhower the former U.S president in his famous quote said "In preparing for battle I have always found that plans are useless, but planning is indispensable". The planning is divided to three levels starting from the strategic planning, tactical planning and operational planning. Organisations' success is dependent of the formulation of good planning and aligning the planning levels from the top all the way down.
Strategic, Tactical Operation Pyramid 
In construction the company strategy is formulating the policy of the organisation that is subsequently transformed into procedures that are aligned with the policy created in the strategic planning stage. The procedures are then used to govern the execution planning. The focus of this research will be on the execution planning and more precisely Construction Planning Optimization Problem.
The aim of this research to answer the following questions
How do construction planners schedule projects?
What is the extent of involving Optimization techniques in the scheduling process?
How the construction professionals map various scheduling tools to different projects?
Moreover, the goal of the research is to solve the problem of solving linear schedules under uncertainty.
The Construction Schedule Optimization (CSO) problem it's main objective is to achieve the optimal sequence of tasks and allocating resources to the tasks subsequently. The problem and complexity of the problem that it try to optimize conflicting objectives. For example by reducing the project duration [aka crashing] will consequently increase direct cost as debated by Wang (1997). In a typical construction project the Owner of the project will usually target to minimize the project duration for several reasons such as reducing their finance cost, avoiding tenants compensations and several other reasons. While the contractor will always strive to reduce their costs in order to maximize their profit. This time-cost trade-off problems is suitable to be solved by optimization techniques.
The aforementioned time-cost trade-off was subject to extensive research efforts and satisfactory results of these researches were achieved. The research efforts then were expanded after identifying a problem of decrease of quality with the duration are crashed. El Rayes and Kandil (2005) included quality in the model to extend the trade-off to time-cost-quality trade-off optimization problem. They quantified the quality by using measurable KPIs and using weights to measure the overall quality performance.
The optimization techniques can be classified to four main categories (Singiresu, 2009) which are listed as follow:
• Mathematical Optimization such as, Linear, Quadratic and Dynamic programming;...