integrated production and inventory policy in a supply chain student: huynh minh tri id: st 105050...
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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
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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.
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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)
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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
Figure 3: Outgoing inventory of manufacturer i (Upper graph)
Incoming Inventory of manufacturer j (Lower graph)
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
qi/pi 2qi/pi (nj-k-1)qi/pi
Inventory at manufacturer i
Time
Time
Inventory at manufacturer j
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
Figure 4: Outgoing inventory of manufacturer i (Upper graph)
Incoming Inventory of manufacturer j (Lower graph)
III. Case 2.1: pi>pj, hi>hj
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
Figure 5: Outgoing inventory of manufacturer i (Upper graph)
Incoming Inventory of manufacturer j (Lower graph)
IV. Case 2.2: pi<pj, hi<hjInventory at manufacturer i
Time
Inventory at manufacturer j
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
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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.
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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
Figure 3: Outgoing inventory of manufacturer i (Upper graph)
Incoming Inventory of manufacturer j (Lower graph)
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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
knkn
p
pkq
p
qk
p
qkq
p
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
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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
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
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.
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
1. Sensitivity analysis of the model with respect to small variation of higher production rate
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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
INTEGRATED PRODUCTION AND INVENTORY POLICY IN A SUPPLY CHAIN
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