Modeling and Problem Solving

Transcription

1 Modeling and Problem Solving Gonca Yıldırım Department of Industrial Engineering Çankaya University November 4, 2014

2 Objectives of Today s Lecture another definition of Industrial Engineering and a part of what we do basic steps in problem solving some types of models used in Industrial Engineering Gonca Yıldırım, 4 November / 21

3 Industrial Engineering According to Institute of Industrial Engineers (IIE) Industrial Engineering (IE) is concerned with the design, improvement, and installation of integrated systems of people, material, equipment, and energy... Another definition Industrial engineers are scientific problem solvers. Gonca Yıldırım, 4 November / 21

4 What types of problems do Industrial Engineers solve? Industrial and Systems Engineers Make a Difference Everywhere Gonca Yıldırım, 4 November / 21

5 Problems... typically do not go away unless we do something to resolve them. This intervention is called Problem Solving. Gonca Yıldırım, 4 November / 21

6 How do Industrial Engineers solve problems? 1 Define the problem 2 Observe the system 3 Build a model of the system Build a model of the system 4 Verify the model and solve the model 5 Select a suitable alternative 6 Present the results to the organization 7 Implement and evaluate the recommendations Gonca Yıldırım, 4 November / 21

7 What is a Model? Gonca Yıldırım, 4 November / 21

8 Introduction Problem Solving Modeling Conclusion What is a Model? Figure: Mersin International Port Building. Gonca Yıldırım, 4 November / 21

9 What is a Model?!!!!! Actual'System' ASSUMED ' System! Model' A model is a representation of the reality that captures the essence of reality. Most models we build are mathematical models. Gonca Yıldırım, 4 November / 21

10 Modeling Examples: 1. Simulation A simulation model mathematical model imitates the behavior of a system over a period of time helps observing the system behavior and performance of the system as statistical observations used to model complex systems containing randomness A MOSIMTEC Emergency Department Simulation Model Gonca Yıldırım, 4 November / 21

11 Modeling Examples: 2. Queueing Queue: Waiting line A queueing model mathematical model deals with waiting lines (or queues) deals with randomness in arrival and service branch of Operations Research Gonca Yıldırım, 4 November / 21

12 Modeling Examples: 2. Queueing T: Time period Arrival Wait A: Number of arrivals =A=T C: Number of departures 1 W: Waiting time 2 S: Service time m R: Response time (waiting plus service) : Mean interarrival time : Arrival rate ¹: Service rate Previous arrival Arrival Service ¹=1=S Begin service W S R Finish service Completion X=C=T time Gonca Yıldırım, 4 November / 21

13 Introduction Problem Solving Modeling Conclusion Modeling Examples: 3. Network Gonca Yıldırım, 4 November / 21

14 Modeling Examples: 3. Network What if we have hundreds of nodes and arcs? Gonca Yıldırım, 4 November / 21

15 Modeling Examples: 3. Network A network optimization model Conceptual model Mathematical model Minimize total travel duration under the following conditions Start from source node (origin) Each node visited must be departed End at the sink node (destination) Minimize subject to j x ij k x ij 0, i c ij x ij j 1, i = s x ki = 0, otherwise -1, i = t (i,j) A Gonca Yıldırım, 4 November / 21

16 Modeling Examples: 3. Network Use an optimization package and code the model to solve it Gonca Yıldırım, 4 November / 21

17 Modeling Examples: 4. Inventory Inventory: Stock Companies keep inventories in order to meet demand of customers on time (in general) Keeping inventories is costly Ordering, purchasing and inventory holding costs Gonca Yıldırım, 4 November / 21

18 Modeling Examples: 4. Inventory Economic Order Quantity (EOQ) Model Inventory level Q {D 0 T 2T 3T time Place an order of size Q at these points in time Gonca Yıldırım, 4 November / 21

19 Modeling Examples: 4. Inventory Annual cost Annual total cost TC(Q) Annual holding cost (hq/2) Annual ordering cost (KD/Q) EOQ Quantity Economic Order Quantity (EOQ) Model ( ) ( ) ( ) Total cost per time = Ordering cost }{{} per time + Purchasing cost per time + Holding cost per time }{{}}{{}}{{} TC(Q) KD/Q cd hq/2 Find Q that minimizes TC(Q) Gonca Yıldırım, 4 November / 21

20 Modeling The scientific approach to decision making involves the use of models There are many different types of models Modeling is an art and it takes practice. Gonca Yıldırım, 4 November / 21

21 Concluding Remarks As future Industrial Engineers, you will be problem solvers model systems Study hard to get ready for an exciting and rewarding career! Gonca Yıldırım, 4 November / 21