INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN STUDENT: HUYNH MINH TRI ID: St 105050 THESIS ADVISOR: ASSISTANT PROFESSOR HUYNH TRUNG LUONG

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN

STUDENT: HUYNH MINH TRI

ID: St 105050

THESIS ADVISOR:

ASSISTANT PROFESSOR HUYNH TRUNG LUONG

PROGRAM COMMITTEE:

DR. HUYNH TRUNG LUONG (CHAIRPERSON)

DR. VORATAS KACHITVICHYANUKUL

DR. PISUT KOOMSAP

CONTENTS:

- THE OBJECTIVES & THE SCOPES OF THIS THESIS

- MULTI DELIVERY IN JUST IN TIME ENVIROMENT

- ASPESTS CONSIDERED IN CHOOSING DELIVERY POLICIES

- MODELINGS & RESULTS OF THIS STUDY- CONCLUSIONS AND RECOMMENDATIONS



Objectives of the study

Determine the optimal order lot size Q* for an integrated production and inventory system

In particular, the models developed in this research will take into consideration decisions of where to hold the inventory (upstream or downstream echelon) and when to ship the product between them

The following assumptions are used in the development of the two-echelon inventory model in this thesis:

Demand rate is constant. Two manufacturers with one product are considered Production rates are constants Lead-time to deliver products from one echelon to another

echelon is negligible. No deterioration occurs in the stock.


THE CONFIGURATION OF THE SYSTEM

Transfer qi, nj, Tri

Manufacturer i qi, pi, hi,Ai

Manufacturer j qj, pj, hj

Demand D

Outgoing inventory of manufacturer i

Incoming inventory of manufacturer j


Figure 1: Two-echelon Inventory-Production System

Lot size Q*=qinj

NOTATIONS: Q: lot size D: demand rate of the customer (product/unit time) qi: production batch size (product) pi: production rate of manufacturer i (product/unit time) pj: using rate of manufacturer j (product/unit time) nj :the number of batch needed for one lot of size hi: outgoing inventory holding cost of manufacturer i ($/period) hj: incoming inventory holding cost of manufacturer j($/period) Tri : transportation cost per batch from manufacturer i to manufacturer j ($/ batch)



I. Case 1.1: pi > pj, hi>hj

Figure 2: Outgoing inventory of manufacturer i (Upper graph)

Incoming Inventory of manufacturer j (Lower graph)

qi/pi 2qi/pi

Inventory at manufacturer i

Time

Time

Inventory at manufacturer j

qi/pi 2qi/pi (nj-2)*qi/pi (nj-1)qi/pi nj*qi/pi

(nj-2)*qi/pi (nj-1)qi/pi nj*qi/pi

O1

O2

A

B

D

C

E

F

H

G K

i

ji p

pq 1


II. Case 1.2: pi > pj, hi<hj

qi/pi

qi/pi

qi/pj+qi/pi

2qi/pj+qi/pi

qi/pj+qi/pi

2qi/pj+qi/pi

3qi/pj+qi/pi

Inventory at i

Inventory at i

Time

Time

3qi/pj+qi/piO

H

AM

N

K

L

(k-1)qi/pj+qi/pi

kqi/pj+qi/pi

(k+1)qi/pj+qi/pi

(nj-2)qi/pj+qi/pi

(nj-1)xqi/pj+qi/pi

(nj-2)qi/pj+qi/pi

(nj-1)xqi/pj+qi/pi

njqi/pj+qi/pi

(k+1)qi/pj+qi/pi

kqi/pj+qi/pi

(k-1)qi/pj+qi/pi

P

T

Q

S

D

E




qi/pi 2qi/pi (nj-k-1)qi/pi

Inventory at manufacturer i

Time

Time


qi/pi 2qi/pi

Production start

(nj-1)qi/pi njqi/pi

njqi/piO A K L N

Production delay time

B

C

D E

F

G

M

H

I

(nj-2)qi/pi(nj-k-1)qi/pi (nj-k)qi/pi (nj-k)qi/pi

(nj-1)qi/pi(nj-2)qi/pi(nj-k)qi/pi



III. Case 2.1: pi>pj, hi>hj




IV. Case 2.2: pi<pj, hi<hjInventory at manufacturer i

Time


Production start

Time

Start transferring, Ts

Ts+(nj-1)qi/pi

qi/pj

0

A

B

C

D

E

F

Ts

Ts+njqi/piTs+(nj-1)qi/pi


Develop the joint total cost case 1.2

ijj

ii qkn

p

pqk 11

1j

i

j np

pk

- After the (k+1)th shipment, manufacturer i may or may not need to produce, and it should stop before the (k+2)th shipment.

- After the (k+1)th shipment, manufacturer j needs (nj-k-1) shipments more in order to fulfill the lot size Q.


qi/pi

qi/pi

qi/pj+qi/pi

2qi/pj+qi/pi

qi/pj+qi/pi

2qi/pj+qi/pi

3qi/pj+qi/pi

Inventory at i

Inventory at i

Time

Time

3qi/pj+qi/piO

H

AM

N

K

L

(k-1)qi/pj+qi/pi

kqi/pj+qi/pi

(k+1)qi/pj+qi/pi

(nj-2)qi/pj+qi/pi

(nj-1)xqi/pj+qi/pi

(nj-2)qi/pj+qi/pi

(nj-1)xqi/pj+qi/pi

njqi/pj+qi/pi

(k+1)qi/pj+qi/pi

kqi/pj+qi/pi

(k-1)qi/pj+qi/pi

P

T

Q

S

D

E




The outgoing inventory cost of manufacturer i is

i

ijji

j

j

iij

j

ii

j

ij

i

j

j

ii

jj

j

ii

j

i

j

ii

i

ii

i h

qknnp

pk

p

qqkn

p

pkq

p

qkn

p

p

p

qq

knkn

p

pkq

p

qk

p

qkq

p

qq

H

1111112

1

2

121

2

1

2

1

2

1

Joint total cost per unit timej

ij

i

jj

i

jji p

qh

p

pn

p

pnH

22

2

11

2

Simplify the above expression, we have

2

11

22,

i

j

j

ii

i

j

j

jii

j

ji

i

i

ij

iji p

p

p

Dhq

p

p

p

Dnhq

p

Dhq

q

DTr

qn

DAnqTC

The accumulated outgoing inventory level at manufacturer i

ILi=SOHA+k*SAMN+SALK+SKLPT+SPQST+SDSE


2. Determine the solution

Take the first partial derivative of TC(qi,nj) with respect to qi, nj

and let them equal to zero

i

j

j

ii

i

i

jj p

p

p

hq

q

A

nn

TC1

2

10

2

2

11

22

10

2i

j

j

i

i

j

j

ji

j

ji

j

i

ii p

p

p

h

p

p

p

nh

p

hTr

n

A

qq

TC

Solve the above equations, we obtain the exact solution

i

i

j

i

j

j

ii

p

h

p

h

p

hTr

q

22

i

j

i

j

ji

i

i

ij p

p

h

h

pp

p

Tr

An

21



NUMERICAL EXPERIMENT


NUMERICAL EXPERIMENT

Conclusions

This thesis achieved all the objectives proposed.

1. Exact mathematical models, based on the analytical technique have been developed to help find the optimum solution.

2. Exact solution expressions for all considered cases are obtained.

3. Numerical experiments and sensitivity analysis have been conducted to illustrated the applicability of the proposed models.

4. It is also noted that although the models are developed under the assumption that transportation time is negligible, we also can apply these results if there exists a constant lead time for transportation between two manufacturers by shifting the inventory graphs by an amount of time equals to the lead time.


Recommendations

Although this research gains satisfactory results, the solution expressions

are simple and easy to be employed. There are still some limitations exist

that need to be addressed in future researches.

1. The models are developed under an implicit assumption of unlimited capacity of the transport facility

2. The results here are applicable for a two-stage supply chain with two manufacturers and one product. Further researches should be conducted so that the models developed here can be expensed for a general supply chain with more than two manufacturers


THANK YOU FOR YOUR KIND LISTENING!

Question and Answer


SENSITIVITY ANALYSISI. Preliminary analysis- Decision variables are independent of demand - qi is independent of production setup cost Ai

II. Parameters- Variation of higher production rate and variation of lower

production rate - Variation of higher inventory holding cost and lower inventory

holding cost- Other parameters used in the numerical examples are kept intact


1. Sensitivity analysis of the model with respect to small variation of higher production rate


nj vs p

3

5

7

9

11

13

15

17

19

21

1510

0

1560

0

1610

0

1660

0

1710

0

1760

0

1810

0

1860

0

1910

0

1960

0

2010

0

2060

0

2110

0

nj-case 1.1 nj-case 1.2 nj-Case 2.1 nj-Case 2.2


qi vs p

400

450

500

550

600

650

700

750

800

1510

0

1560

0

1610

0

1660

0

1710

0

1760

0

1810

0

1860

0

1910

0

1960

0

2010

0

2060

0

2110

0

qi-Case 1.1 qi-Case 1.2 qi-Case 2.1 qi-Case 2.2



TC vs p

1500

1700

1900

2100

2300

2500

2700

1510

0

1560

0

1610

0

1660

0

1710

0

1760

0

1810

0

1860

0

1910

0

1960

0

2010

0

2060

0

2110

0

TC-case 1.1 TC-case 1.2 TC-Case 2.1 TC-Case 2.2


T vs p

15

20

25

30

35

40

45

1510

0

1560

0

1610

0

1660

0

1710

0

1760

0

1810

0

1860

0

1910

0

1960

0

2010

0

2060

0

2110

0

T-Case 1.1 T-Case 1.2 T-Case 2.1 T-Case 2.2

Documents

INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN STUDENT: HUYNH MINH TRI ID: St 105050 THESIS ADVISOR: ASSISTANT PROFESSOR HUYNH TRUNG LUONG