models for faqcitlity loacation and capactiy planning20
TRANSCRIPT
1
Models For Facility Location
And Capacity Allocation
4/24/2011 2
Contents:-1. Need2. Types of Models3. Network Optimization Model4. Gravity Location Model5. Allocation and location6. References
4/24/2011 3
Total Revenu
esProduct Sale
Facilities
Labor
Transportation
Materials
Inventories
Profit + Taxes
Increasing Facilities and capacity decreases transportation costs but increases inventory costs.
1. Need:-Aim is to design a network which increases Profitability with apt. Responsiveness.
4/24/2011 4
Phases in network design:-Phase I Phase II Phase III Phase IV
A. Network Optimization ModelB. Gravity Location Models
2. Types of Models:-
4/24/2011 5
3. Network Optimization Model.
4/24/2011 6
Steps:-
4/24/2011 7
Example:- Capacitated Plant location modelCapacities of plants are known.
n = Number of Potential Plant Locations
m = Number of markets or demand points
Dj = annual demand from market j
Ki = potential capacity of plant i
Fi = annualized fixed costs for keeping factory i open
Cij = cost of producing and shipping one unit from factory i to market j
4/24/2011 8
Yi = 1 if plant i is open , else 0.Xij = quantity shipped fron plant i to market j.So,
Min ∑ Fi*Yi + ∑∑ Cij*Xij
Subject to:
∑ Xij = Dj For j= 1 to m
∑ Xij ≤ Ki * Yi For i = 1 to n
Yi є {0,1} For i = 1 to n, Xij ≥ 0
n mn
i=1 i=1j=1
m
j=1
n
i=1
4/24/2011 9
4. Gravity Location Model.
4/24/2011 10
Basic Model:
F1
S1
S2
S3
M2M3
M1
(Xn,Yn) = Co ordinate location of either market or supply source n
Fn = Cost of Shipping One unit for one mile between facility and either market or supply source n
Dn = Quantity to be shipped between facility and either market or supply source n
4/24/2011 11
Let,(X,Y) = location selected for the facilitydn = distance between the facility at location (X,Y) and Supply source or market n is given by:-dn = √(X-Xn) + (Y-Yn)
The total Transportation cost TC:-
TC = ∑ (dn * Dn * Fn)
The optimal location is one that minimizes TC.
2 2
k
n=1
4/24/2011 12
5. Allocation And Location:-a.Allocating Demand to production facilities:
Find Xij sb. Locating Plants
Find Yi=1sc. Locating Plants and Warehouses
SimultaneouslyIntroducing new decision variablesIntroducing new constraintsIntroducing certain changes in the objective function
4/24/2011 13
6. References:-a.Supply Chain Management By Sunil
Chopra , Third Edition.
b. citeseerx.ist.psu.edu
c.www.dms.umontreal.ca
4/24/2011 14
4/24/2011 15