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

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Presentation on theme: "Integrated Production Scheduling and Vehicle Routing Problem to Minimum Total Cost Student: Bing-Yu Gao Student ID: M10021024 Advisor: Chin-Yao Low, Ph.D."— Presentation transcript:

1 Integrated Production Scheduling and Vehicle Routing Problem to Minimum Total Cost Student: Bing-Yu Gao Student ID: M 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 –H–How to response customer at once In the Past year: –P–Production scheduling. –V–Vehicle routing planning. But most of literatures of above are discussed individually. ‧ Push based supply chain Forecast accurately

4 Background IndividualIntegration Advantage1.It can make the best of object of production scheduling. 2.It can make the best of object of VRP problem. 1.The global optimal solution can be found. 2.Because the mutual cost will be considered Integrally. DefectThe mutual cost considerations will be ignored. The algorithm will be more complexly. – Comparison as following table:

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

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

7 Literature review – VRP with heterogeneous fleet Variety of the meta-algorithm Time windows yearreference Heuristic algorithmx1984Golden et al. Tabu searchx1996 Osman and Salhi Tabu searchx1999Gendreau et al. Tabu searchx2002 Wassan and Osman B & B v 2007Choi and tcha Scatter search v 2007 Belfiore & Favero

8 Literature review – VRP with heterogeneous fleet Variety of the meta-algorithm Time windows yearreference Heuristic algorithm v 2007Dell’Amico et al. EM-SA v 2008Oili Bräysy et al. Memetic algorithmX2009Christian Prins --V This research

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

10 Literature review – Integrated Scheduling and Delivering meta-algorithmMDObjectyearreference Heuristic algorithm 11 Min makespan2004Chang & Lee Heuristic algorithm11 min delivery cost and mean of travel time 2005 Chen & Vairaktarakis Heuristic algorithm21Min makespan2009Su et al. Heuristic algorithm11 Min weighted sum of the last arrival time With independent setup time 2010T.C.E. Cheng Heuristic algorithm11Min makespan2011Liu & Lu Tabu search Long-term memory 11min Travel time, and lateness time2012 Condotta et al. 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. 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. Plant Customer When to deliver? How to solve the VRP problem?

13 Literature review – Integrated Scheduling and Delivering meta-algorithmMVObjectyearreference Tabu search short-term memory P1 Max profit of supplier (time windows and travel time) 2005 Garcia & Lozano Dynamic programming P1 Min weighted sum of Delivery time and total distribution cost 2005 Chen & Vairaktarakis Heuristic algorithm11Max profit of supplier2009 Huey-Kuo Chen Dynamic programming 11 Min weighted sum of the last arrival time With independent setup time 2010T.C.E. Cheng --1T Min total cost With fixed cost of vehicle -- This Research 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 Plant 0 Customer 4 Customer 3 Customer 2 Customer 1 Ct 01 Ct 10 d2 Ct 23

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 VRP stage Time e2e2 l2l2 e4e4 l4l4

17 Research method – Question description If the routing costs are considered, then it may give an integration solution as follow picture Production scheduling stage VRP stage 2 Time e2e2 l2l2 e4e4 l4l4

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

19 Research method – Formula the MILP model

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22 Min Total cost = fixed cost + travel cost + delay penalty + early penalty Flow constraints Connection and subtour-breaking constraints Vehicle capacity 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 CustomerPlant1234 EiEi LiLi Type of vehicle 123 Fixed cost C ij Plant CustomerPlant 1234 EPT i LPT i Type of vehicle 123 Capacity Customer 1234 didi titi 2824 Ct ij plant Customer 1234 sisi 3289

27 Research method – MILP model verification The scheduling result as follows: – The VRP result as follows: – use type 2 – use type 3

28 Research method – MILP model verification All completion of the production time as follows: Hand calculations: – Demands of customer 4: d 4 *t 4 = 60 – And as follow is 3, 20* = 100 – 1 is 20* = 140 – And the customer 2 is 380. Customer4312 Completion of the production time

29 Research method – MILP model verification Customer3412 Arrival time All Arrival time as follows: Hand calculations: Customer 3:140+13=153→176 (it can be accepted) At the same route, customer 4:176 + c 34 + s 3 =190 Customer 1: = 216→225 (Final maturity date) And the customer 2 is another route: Completion time is C 02 = 395

30 Research method – MILP model verification Hand calculations the object as follows: Penalty cost : – only customer 2 is delayed =168 units 168*penalty cost = 168*9=1512 – Route cost is c 03 + c 34 + c 41 + c 10 + c 02 + c 20 =32 – Fixed cost = 15+18=33 – Total cost = =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


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