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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. Outline. Introduction Background Motivation Literature review HVRP Integration problem (Type I & Type II) Research method

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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 Gao

Student ID: M10021024

Advisor: Chin-Yao Low, Ph.D.


Outline
Outline to Minimum Total Cost

  • Introduction

    • Background

    • Motivation

  • Literature review

    • HVRP

    • Integration problem (Type I & Type II)

  • Research method

    • MILP/ and verification

  • Conclusions


Background
Background to Minimum Total Cost

  • 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


Background1
Background to Minimum Total Cost

  • Comparison as following table:


Motivation
Motivation to Minimum Total Cost

  • 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

Literature review to Minimum Total Cost

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


Literature review vrp with heterogeneous fleet
Literature review to Minimum Total Cost– VRP with heterogeneous fleet


Literature review vrp with heterogeneous fleet1
Literature review to Minimum Total Cost– VRP with heterogeneous fleet


Literature review integrated scheduling and delivering
Literature review to Minimum Total Cost– 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.


Literature review integrated scheduling and delivering1
Literature review to Minimum Total Cost– Integrated Scheduling and Delivering

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

D: number of Demands.


Literature review integrated scheduling and delivering2
Literature review to Minimum Total Cost– 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?


Literature review integrated scheduling and delivering3
Literature review to Minimum Total Cost– 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?


Literature review integrated scheduling and delivering4
Literature review to Minimum Total Cost– 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)


Research method question description
Research method to Minimum Total Cost– Question description

Customer

2

Ct23

d2

Customer

3

Plant

0

Ct01

Customer

1

Ct10

Customer

4


Research method another question restrict
Research method to Minimum Total Cost– 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.


Research method question description1
Research method to Minimum Total Cost– Question description

  • Example:

Production scheduling

stage

2

4

1

3

2

0

0

VRP

stage

4

0

0

e4

l4

e2

l2

Time


Research method question description2
Research method to Minimum Total Cost– 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


Research method question description3
Research method to Minimum Total Cost– 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


Research method formula the milp model
Research method to Minimum Total Cost– Formula the MILP model


Research method formula the milp model1
Research method to Minimum Total Cost– Formula the MILP model


Research method formula the milp model2
Research method to Minimum Total Cost– Formula the MILP model


Research method formula the milp model3
Research method to Minimum Total Cost– 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


Research method formula the milp model4
Research method to Minimum Total Cost– 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.


Research method formula the milp model5
Research method to Minimum Total Cost– Formula the MILP model

  • Transportation stage

Arrival time calculation constraints.

Soft time windows constraints.


Research method formula the milp model6
Research method to Minimum Total Cost– 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.


Research method milp model verification
Research method to Minimum Total Cost– MILP model verification


Research method milp model verification1
Research method to Minimum Total Cost– 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


Research method milp model verification2
Research method to Minimum Total Cost– 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.


Research method milp model verification3
Research method to Minimum Total Cost– 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


Research method milp model verification4
Research method to Minimum Total Cost– 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


Conclusions
Conclusions to Minimum Total Cost

  • 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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