# capacity concerns

Topics: Costs, Optimization, Mathematical optimization Pages: 15 (1958 words) Published: December 5, 2013
APMA1210 – Operations Research
Final Project
Introduction

For my project I picked a case out the Hillier textbook, specifically Case 11.1 (Pages 533 – 535). In this case, Communicorp, a leading communication technology company is faced with financial difficulty due to disorganized internal communications. In order to remedy the situation, the CEO instructs us to phase in a corporate intranet to help departments communicate effectively. The schedule for different departments to ‘go live’ on the intranet is set, and we have to purchase the appropriate servers, minimizing cost and making sure that the intranet has enough capacity to handle the employees that start using the intranet each month. I picked this case because it resembles the types of problems that I faced during my summer internship at The CocaCola Company. One of my responsibilities was to assist in the cost analysis of a large software implementation. Different departments would go live in different weeks and I had to cost out the different implementation strategies. At the time, I did not know what went into the decision making process for different strategies, but after taking Operations Research, I know that I am better equipped to understand and formulate optimal implementation solutions.

This case uses mixed integer programming, and to solve the optimization problems, I used LINGO 11.1.

Case Background
We have been given the implementation schedule, as follows:
Month
Department

Month 1
None

Month 2
Sales

Month 3
Manufacturing

Month 4
Warehouse

Month 5
Marketing

In month one, the company plans to educate employees, so we do not have to do anything The company has 365 employees in total. They are divided into the following departments: Department
Sales
Manufacturing
Warehouse
Marketing

Number of Employees
60
200
30
75

To implement the intranet, we need to purchase servers. Each server supports a certain number of employees, and the larger servers cost more (though the cost per employee decreases for larger servers). Server

Server 1 - Standard Intel PC
Server 2 - Enhanced Intel PC
Server 3 - SGI Workstation
Server 4 - Sun Workstation

Server Capacity
Up to 30 employees
Up to 80 employees
Up to 200 employees
Up to 2,000 employees

Cost (\$)
2,500
5,000
10,000
25,000

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Our task is determine which servers to buy and in which month. There are several other factors which complicate our decision making:
1. SGI is willing to offer a 10% discount (i.e. \$9000) on all servers but only if we purchase servers in the first or second month.
2. Sun is willing to discount all servers bought in the first in second month by 25% (i.e. \$18750) 3. Communicorp only has \$9500 in the budget for the first two months 4. The Manufacturing department requires at least one of the 3 most powerful servers.

Buying Month to Month - A Quick Solution
In the first part of the case, we are asked to evaluate it on a month to month basis – minimizing the cost each month, without looking at the implications for the next month. Let: xi = Number of Server i’s (e.g. x2 = Number of Server 2s = Number of Enhanced Intel PCs)

Month 1 – 0 new employees
Minimize

Z = 2500x1 + 5000x2 + 10000(0.9)x3 + 25000(0.75)x4

Subject To:

30x1 + 80x2 + 200x3 + 2000x4 ≥ 0
2500x1 + 5000x2 + 10000(0.9)x3 + 25000(0.75)x4 ≤ 9500

The Z function minimizes overall cost for the month and the costs for servers 3 and 4 are multiplied by their respective discounts. The constraint ensures that the capacity of the servers meets or exceeds the number of employees online in that month and that we don’t exceed our budget. The optimal solution for the first month is:

x1 = 0, x2 = 0, x3 = 0, x4 = 0; Cost = 0
Since we don’t have any employees to support in month one, we don’t need any servers.

Month 2 – Sales, 60 new employees
Minimize

Z = 2500x1 + 5000x2 + 10000(0.9)x3 + 25000(0.75)x4

Subject To:

30x1 +...