Nalysis and Optimization of Multistage Hybrid Service system With Stochastic Input

A. Background (General Description)
we study a multistage Hybrid service systems ,Customers must all receive service at a series of (4) different service stages in a fixed sequence, where each stage consists of parallel servers.
Each stage performs certain operations and is dedicated to a specific task.
Units of adjacent stages are connected flexibly to form the system network. After completing all the stages, the customer leaves the system.
In manufacturing, typical applications exist in Food Processing and Cosmetics Industries ( stages are mixing, filling, inspection, packaging), Home appliances (stages are Cut to size, Injection, Assembly, Inspection,..), and Ready made clothes Industries ( patronizing, cutting, sewing, assembly, … ).

B. Research Objectives
1- Construct a mathematical model , and it will be complicated so,
2- Device an approximation for measure of System performance (heuristics)
3- Meanwhile, Simulate the model to validate the approximation
4- Apply design of experiments to assess and validate the results of the approximation to know that it is working in different cases
5- Generalized measure of performance (multi criteria) , because Such systems possess a diversity of performance measures such as, total throughput time, total cost of processors, total delay, and response. I suggest here a bi criteria which contains two conflicting objectives:
1-(minimizing (the time the message spend in the system)
2 the optimum number of processors in each stage (So you may use a weight for every objective in the objective function in the mathematical model i.e. zw1E1+w2E2) or you can use another suggested way

C. Required Computer Packages

1) (LINGO) for Optimization
2) (ARENA Professional”) For Simulation

D. all work must be in detailed
E. 2 files will be uploaded to the writer one includes more information and the other includes data collected and some analysis which should be used in the dissertation because they were under the supervision of my supervisor