Abstract: Typical models of the production inventory systems assume that lot sizes of raw materials and final products are treated separately which leads to sub- optimization production process. In this paper, a unified inventory model of an integrated production inventory system, where each of production, demand and deterioration rates are general functions of time, is considered. Shortage for the final product is allowed but it is partially backordered. The objective is to find an optimal production schedule that yields a minimum total cost of this integrated system. We develop an exact formula for the total inventory cost per unit of time. Then, we use rigorous mathematical methods to find the optimal solution of the underlying integrated system and to show that this solution is unique and global optimal.

Brief Biography of the Speaker:
Degrees: .B.Sc. in mathematics (Probability and Mathematical Statistics Section) Damascus University 1971-High Diploma in pure mathematics ,Damascus University 1979 - Studying several post graduate courses in Optimization, Probability and Statistics Brussels University 1980 - Dr. of Science in applied mathematics (Belgian Ph.D in applied mathematics- OR oriented) with honors, University of Brussels 1983.
Positions: Professor in King Saud University, College of Science, Department of Statistics and Operations Research since May 2005.,Associate Professor King Suad University, College of Science, Department of Statistics and Operations Research, 1998 -Assistant Professor, King Saud University, College of Science, Department of Statistics and Operations Research, From 1983 to 1998- Demonstrator in Mathematic Department in Damascus University 1979.
Professional Experience: He has about 27 years academic teaching experience in Operations Research, Statistics, and Mathematics, supervising several M.Sc. and PhD thesis., Main contributor in the design and development of the B.Sc. and M.Sc. and PhD Programs in Operations Research And Statistics in the Department of Statistics and Operations Research in King Saud University.(Riyadh - Saudi Arabia), Member in the editorial board of "Journal of Scientific Inquiry" , Acting as a referee for more than 15 specialized and leading international journals (more than 20 papers per year) . He contributed in many Local and International Scientific Conferences and Symposiums ,Plenary Speaker in the 3rd International Conference on COMPUTATIONAL INTELEGENCE(CI09)- Iv.Javakhishvili Tbilisi State University - Georgia .
He contributed in giving consultations in solving local real problems in Saudi Arabia using the OR techniques.
His Research Interests: are in Applied Mathematic (Operations Research Oriented). In particular, Optimal Search problems where he has more than 10 research papers. Recently his research turns to Inventory Control problems with more than 35 publications in scientific and leading journals. He also authored 4 books in Fundamentals of Operations Research, Inventory Control, Game Theory, and Integer Programming.
He is Syrian, and he is establishing a private University in Syria, but he in now working is Saudi Arabia.