The document describes a capacity planning problem for Communicorp using integer programming to determine the optimal server configuration over multiple periods. It presents three models: 1) A monthly analysis model that examines each month individually and finds the optimal servers for each. 2) A two-phase analysis that considers setup and operating costs over two periods and constraints like budget and capacity. 3) A two-period model that also incorporates server life expectancies and constraints to ensure servers from the first period are replaced in the second if needed. The three-sentence summary compares the optimal costs of each model.

1. CAPACITY CONCERNS FOR
COMMUNICORP
AN INTEGER PROGRAMMING PROBLEM
by
Diego Hererra Ceron
Diana Caro
Catherine Dela Cruz
Ramon Savinon

2. PROBLEM DESCRIPTION
$ INTERNAL
COMMUNICATION
INVENTORY
CONTROL
NEW SERVER DESCISION

3. OUR APROACH
2 PHASES
MONTHLY 2 PHASES WITH LIFE
EXPECTANCY

4. Model 1 - Monthly Analysis
Month 1 Month 2 Month 3 Month 4 Month 5
Education
Sales -60
Accounting-30
Manufacturing-200
HR -10
Warehouse -30
Marketing -75
Legal-15

5. Model 1 - Monthly Analysis
Server Type Capacity Setup Cost & Variable Unit Cost & Variable
IBM 1000 X1 $1,500 X8 $20,000
Standard Intel 30 X2 $400 X9 $2,500
Enhanced Intel 80 X3 $800 X10 $5,000
SGI workstation 200 X4 $1,000 X11 $10,000
Sun Workstations 2000 X5 $2,500 X12 $25,000
Lenovo 10 X6 $200 X13 $1,300
Dell 30 X7 $800 X14 $2,600

6. MIN Z = 1500X1 + 400X2 + 800X3 + 1000X4 + 2500X5 + 200X6
+ 800X7 + 20000X8 + 2500X9 + 5000X10 + 10000X11 +
25000X12 + 1300X13 + 2600X14
•Employees: 90
Month 2 •Budget: $12,000 & Discounts offered
•Objective Function: $7300
•Servers: Enhanced Intel and Lenovo
•Employees: 75
Month 3 •Buy one of the two most powerful servers (IBM or SUN)
•Objective Function: $21,500
•Server: IBM
•Employees: 40
Month 4 •Objective Function: $4,400
•Servers: Standard Intel, Lenovo
•Employees: 100
Month 5 •Objective Function: $8,600
•Servers: Enhanced Intel and Lenovo (2)

7. TWO PHASE ANALYSIS
k= 1 to 7 set up cost (BINARY)
K=8 to 14 the quantity
For j=1 first phase
For j=2 the second phase

8. TWO PERIOD ANALYSIS
Objective Function:
min Z = 1500X12 + 400X21 + 400X22 + 800X31 +800X32
+ 1000X41 +1000X42+ 2500X52 + 200X61+ 200X62 +
800X71+800X72 + 20000X82 + 2500X91+2500X92 +
5000X101+5000X102 + 9000X111+10000X112 +
25000X122 + 1300X131+1300X132 + 2600X141+2600X142

9. Constraints
First Phases’ Budget
400X21 + 800X31 + 1000X41 + 200X61 + 800X71 + 2500X91
+ 5000X101 + 9000X111 + 1300X131 + 2600X141<=12000
Capacity for the First phase:
30X91 + 80X101 + 200X111 + 10X131 + 20X141 >= 90
Capacity for the Second phase:
100X82+30X92+80X102+200X112+2000X122+10X132+20X142
>=340

10. Constraints
Manufacturing department power constraint: X142+X82>=1
Relationship constraints:
X82<=Mx1z

11. Model 3 – Two Period Life
Expectancy
SERVER TYPE LIFE EXPECTANCY
IBM – X1 5
Standard Intel - X2 2
Enhanced Intel – X3 3
SGI workstation – X4 3
Sun Workstations – X5 4
Lenovo – X6 3
Dell- X7 3

12. Model 3 – Two Period Life
Expectancy
NEW CONSTRAINTS
10X12 + 4X21+ 4X22 + 6X31 + 6X32 + 6X41 + 6X42 + 8X52 + 6X61 + 6X62 +
6X71 + 6X72 -7X12- 7X21- 7X22- 7X31- 7X32- 7X41- 7X42- 7X52- 7X61-
7X62- 7X71- 7X72 >= 0
Safeguard constraint 1: X12 - X82 <=0
Safeguard constraint 2: 100000(1-X12)>= X22+ X32+X42+X52+X62+X72

13. Analysis of Results
Optimal Cost
Model 1 •$41,800
Model 2 •$31,500
Model 3 •$28,800

14. Thank you !!