Integrated Production Scheduling and Vehicle Routing Problem to Minimum Total Cost

1. Integrated Production Scheduling and Vehicle Routing Problem to Minimum Total Cost Student: Bing-Yu Gao Student ID: M10021024 Advisor: Chin-Yao Low, Ph.D.

2. Outline • Introduction • Background • Motivation • Literature review • HVRP • Integration problem (Type I & Type II) • Research method • MILP/ and verification • Conclusions

3. Background • Pull based • How to response customer at once • In the Past year: • Production scheduling . • Vehicle routing planning. • But most of literatures of above are discussed individually. ‧Push based supply chain Forecast accurately

4. Background • Comparison as following table:

5. Motivation • Based on above description, 2 motivations are presented as follows: • The plant needs more effect that pick goods and delivering plan. • Most of problems are discussed individually by literatures.

6. Literature review Research method comparison results Research process Theme direction decided Similar literatures review Theme decided Single machine scheduling HVRP literature review Formula MILP model • Integrated Scheduling and Delivering • Include type I and type II Meta-algorithm conclusions

7. Literature review – VRP with heterogeneous fleet

8. Literature review – VRP with heterogeneous fleet

9. Literature review – Integrated Scheduling and Delivering • Type I: Single machine or parallel machine and deliver to single customer with multiple orders. Customer Plant How many times of delivering? How to schedule? When to deliver? AND Fixed distance.

10. Literature review – Integrated Scheduling and Delivering M: number of Parallel Machines.(1 denotes no parallel machine) D: number of Demands.

11. Literature review – Integrated Scheduling and Delivering • Type II: Single machine and deliver to multiple customers with multiple orders but release one time. Customer Customer Customer Plant Customer How to do the production schedule?

12. Literature review – Integrated Scheduling and Delivering • Type II: Single machine and deliver to multiple customers with multiple orders but release one time. Customer Customer Customer Plant Customer When to deliver? How to solve the VRP problem?

13. Literature review – Integrated Scheduling and Delivering M: number of Parallel Machines.(1 denotes no parallel machine) V: Variety of the vehicle capacity.(1 denotes only one type)

14. Research method– Question description Customer 2 Ct23 d2 Customer 3 Plant 0 Ct01 Customer 1 Ct10 Customer 4

15. Research method– Another Question restrict • All of out of control aren’t considered whether conveyer or vehicle. • The state of road aren’t considered. • All orders are released on time zero. • All customer site can be visited only once, and all vehicles back to plant are needed.

16. Research method– Question description • Example: Production scheduling stage 2 4 1 3 2 0 0 VRP stage 4 0 0 e4 l4 e2 l2 Time

17. Research method– Question description • If the routing costs are considered, then it may give an integration solution as follow picture. Production scheduling stage 2 4 1 3 4 2 0 0 VRP stage e4 e2 l4 l2 Time

18. Research method– Question description • How to scheduling involve HVRP problem is this research want to present mainly. Production scheduling stage ? … ? ? ? 0 0 VRP stage ? … … 0 0 Time

19. Research method– Formula the MILP model

20. Research method– Formula the MILP model

21. Research method– Formula the MILP model

22. Research method– Formula the MILP model Min Total cost = fixed cost + travel cost + delay penalty + early penalty Flow constraints Vehicle capacity constraints Connection and subtour-breaking constraints

23. Research method– Formula the MILP model • Production stage Scheduling constraints, and the sequence only has one combination. Production constraints When customer i is processed before j then do the above constraint.

24. Research method– Formula the MILP model • Transportation stage Arrival time calculation constraints. Soft time windows constraints.

25. Research method– Formula the MILP model • Nonnegative constraints: All decision variables are nonnegative. But this model has some problems need to modified. In the next chapter will describe in detail.

26. Research method– MILP model verification

27. Research method– MILP model verification • The scheduling result as follows: • 4-3-1-2 • The VRP result as follows: • 0-2-0 use type 2 • 0-3-4-1-0 use type 3

28. Research method– MILP model verification • All completion of the production time as follows: • Hand calculations: • Demands of customer 4: d4*t4 = 60 • And as follow is 3, 20*2 + 60 = 100 • 1 is 20*2 + 100 = 140 • And the customer 2 is 380.

29. Research method– MILP model verification • All Arrival time as follows: • Hand calculations: • Customer 3:140+13=153→176 (it can be accepted) • At the same route, customer 4:176 + c34+ s3 =190 • Customer 1: 190 + 8 + 18 = 216→225(Final maturity date) • And the customer 2 is another route: Completion time is 380 + C02 = 395

30. Research method– MILP model verification • Hand calculations the object as follows: • Penalty cost : • only customer 2 is delayed 395-227=168 units • 168*penalty cost = 168*9=1512 • Route cost is c03+ c34 + c41+ c10 + c02 + c20 =32 • Fixed cost = 15+18=33 • Total cost = 1512+32+33=1577

31. Conclusions • The model still has shortage, and needs to be modified. • Design of meta-heuristic algorithm: • Literature review • Design and application to solve in this problem