A governmental agency needs to decide suppliers for fuel to be used in its n depots. The

agency takes bids from m different oil companies. The facility capacity of oil company

i is ai

liters, and depot j demands bj

liters. Suppose that cij is the unit delivery cost

of oil company i to the depot j$.$ The closed form formulation is given as follows:

I $=\{1,2,...,$ n$\}$ Set of oil companies.

J$=\{1,2,...,$ m$\}$ Set of depots.

xij : The number of unit oil deliver from company i to the depot j

$3$ of $4$

ISL $323$ Assignment #$2$ Dr$.$ Fuat Kosanoglu

M inimizeZ $=$

Xn

i$=1$

Xm

j$=1$

cijxij

subject to

Xm

j$=1$

xij $<=$ ai $$i in I

Xn

i$=1$

xij $>=$ bj $$j in J

xij $>=0$i in I and $$j in J

Solve the problem using GAMS for the given data.

Table $8$: Distances, capacity and demand

Depots

Company D$1$ D$2$ D$3$ D$4$ Capacity

C$18010085901500$

C$29585801001500$

C$3908095901500$

Demand $1000120013001000$