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