Integrated Production Scheduling and Vehicle Routing Problem to Minimum Total Cost

Integrated Production Scheduling and Vehicle Routing Problem to Minimum Total Cost

Student: Bing-Yu GaoStudent ID: M10021024Advisor: Chin-Yao Low, Ph.D.

Outline

• Introduction– Background– Motivation

• Literature review– HVRP– Integration problem (Type I & Type II)

• Research method– MILP/ and verification

• Conclusions

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 chainForecast accurately

Background

Individual IntegrationAdvantage 1. 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.

Defect The mutual cost considerations will be ignored.

The algorithm will be more complexly.

– Comparison as following table:

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.

Research process

Theme direction decided

conclusions

Similar literatures review

Theme decidedSingle machine scheduling

HVRP literature review

Integrated Scheduling and Delivering

Include type I and type II

Literature review

Research method

comparison results

Formula MILP model

Meta-algorithm

Literature review – VRP with heterogeneous fleet

Variety of the meta-algorithm Time windows year reference

Heuristic algorithm x 1984 Golden et al.

Tabu search x 1996 Osman and Salhi

Tabu search x 1999 Gendreau et al.

Tabu search x 2002 Wassan and Osman

B & B v 2007 Choi and tcha

Scatter search v 2007 Belfiore & Favero

Literature review – VRP with heterogeneous fleet

Variety of the meta-algorithm Time windows year reference

Heuristic algorithm v 2007 Dell’Amico et al.

EM-SA v 2008 Oili Bräysy et al.

Memetic algorithm X 2009 Christian Prins

-- V -- This research

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?ANDFixed distance.


meta-algorithm M D Object year reference

Heuristic algorithm1 1

Min makespan 2004 Chang & Lee2 11 2

Heuristic algorithm 1 1 min delivery cost and mean of travel time 2005 Chen &

VairaktarakisHeuristic algorithm 2 1 Min makespan 2009 Su et al.

Heuristic algorithm 1 1Min weighted sum of

the last arrival timeWith independent setup time

2010 T.C.E. Cheng

Heuristic algorithm 1 1 Min makespan 2011 Liu & LuTabu search

Long-term memory 1 1 min Travel time, and lateness time 2012 Condotta et al.

M: number of Parallel Machines.(1 denotes no parallel machine)D: number of Demands.


• Type II: Single machine and deliver to multiple customers with multiple orders but release one time.

Plant

Customer

Customer

Customer

Customer

How to do the production schedule?


• Type II: Single machine and deliver to multiple customers with multiple orders but release one time.

Plant

Customer

Customer

Customer

Customer

When to deliver?How to solve the VRP problem?


meta-algorithm M V Object year referenceTabu search

short-term memory P 1 Max profit of supplier(time windows and travel time) 2005 Garcia &

LozanoDynamic

programming P 1 Min weighted sum of Delivery time and total distribution cost 2005 Chen &

Vairaktarakis

Heuristic algorithm 1 1 Max profit of supplier 2009 Huey-Kuo Chen

Dynamic programming 1 1

Min weighted sum of the last arrival time

With independent setup time2010 T.C.E. Cheng

-- 1 T 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)

Research method– Question description

Plant0

Customer4

Customer3

Customer2

Customer1

Ct01Ct10

d2

Ct23

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.


• Example:

2 4 1 3

0

Production scheduling

stage

VRPstage

02

Time

0 04

e2 l2e4 l4


• If the routing costs are considered, then it may give an integration solution as follow picture.

2 4 1 3

0


stage

VRPstage

2

Time

04

e2 l2e4 l4


• How to scheduling involve HVRP problem is this research want to present mainly.

? … ? ?

0


stage

VRPstage

?

Time

0

0 0? …

…

Research method– Formula the MILP model


Min

Total cost = fixed cost + travel cost + delay penalty + early penalty

Flow constraints

Connection and subtour-breaking constraints

Vehicle capacity constraints


• 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.


• Transportation stage

Arrival time calculation constraints.

Soft time windows constraints.


• Nonnegative constraints:

All decision variables are nonnegative.

But this model has some problems need to modified.In the next chapter will describe in detail.

Research method– MILP model verification

Customer Plant 1 2 3 4

Ei 0 189 198 150 168

Li 630 225 227 180 190

Type of vehicle 1 2 3

Fixed cost 10 15 18

Cij Plant 1 2 3 4

Plant 0 2 4 5 8

1 2 0 7 6 9

2 4 7 0 3 5

3 5 6 3 0 8

4 8 9 5 8 0

Customer Plant 1 2 3 4

EPTi 0 15 7 5 8

LPTi 20 14 9 8 6

Type of vehicle 1 2 3

Capacity 10 50 70

Customer 1 2 3 4

di 50 30 20 15

ti 2 8 2 4

Ctij plant 1 2 3 4

plant 0 17 15 13 15

1 17 0 19 18 21

2 15 19 0 15 8

3 13 18 15 0 6

4 15 21 8 6 0

Customer 1 2 3 4

si 3 2 8 9


• 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


• 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.

Customer 4 3 1 2

Completion of the production time 60 100 140 380


Customer 3 4 1 2

Arrival time 176 190 225 395

• 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


• 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

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

Integrated Production Scheduling and Vehicle Routing Problem to Minimum Total Cost

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