Let's define binary decision variables for each site, such that:
X1 = 1 if site S1 is selected, 0 otherwise
X2 = 1 if site S2 is selected, 0 otherwise
...
X10 = 1 if site S10 is selected, 0 otherwise
The objective is to minimize the total exploration cost, which can be formulated as:
Minimize: C1*X1 + C2*X2 + ... + C10*X10
Subject to the following constraints:
1. Exploring sites S1 and S7 prevents exploring site S8:
X1 + X7 <= 1
2. Evaluating site S3 or S4 prevents exploring site S5:
X3 + X4 <= 1
3. Only two sites from the group S5, S6, S7, S8 can be explored:
X5 + X6 + X7 + X8 <= 2
4. The number of selected sites must be 5:
X1 + X2 + ... + X10 = 5
Also, it is important to note that X1, X2, ..., X10 should be binary variables.
1. As the leader of an oil-exploration drilling venture, you must determine the leastcost selection of 5 out of 10 possible sites. Label the sites S 1
,S 2
,…,S 10
, and the exploration costs associated with each as C 1
,C 2
,…,C 10
. Regional development restrictions are such that: (a) Exploring sites S 1
and S 7
will prevent you from exploring site S 8
; (b) Evaluating site S 3
or S 4
prevents you from exploring site S 5
; and (c) Of the group S 5
,S 6
,S 7
,S 8
, only two sites may be explored. Formulate this problem as an integer programming problem.
1 answer