Efficient allocation of IT resources.

ABSTRACT

Technology spending has risen sharply over the past 40 years, in 2001 spending approached $906 billion of which computer hardware expenditures amounted to about 20%. In the past, companies have replaced PCs every three years. Budget constraints are expected to lengthen this cycle. As a result, IT managers are faced with the complex, and sometimes political, decision of how to distribute new and/or redistribute existing PCs to staff. The decision must be based on getting the largest value from each IT dollar spent on PC replacement. To answer this need, we develop a model to assist IT managers in allocating PC resources. The model is illustrated with a real world application of allocating PCs to faculty members in a business school.

1. INTRODUCTION

Corporate belt-tightening has put the pinch on purchases of personal computers by companies worldwide. Alter a 40 year period of growth in information technology spending, which jumped from $30 billion in 1960 to $227 billion in 1980 to $979 billion in 2000, spending fell back to an estimated $906 billion in 2001. According to research group IDC, sales of PCs to businesses have remained flat at roughly 87 million units annually since 2000 (Delaney, 2003). Spending on information technology in 2002 declined or stayed the same for many firms and is expected to remain flat or only increase slightly in 2003 (Van Arnum, 2003). Software continues to eat up the largest percentage of overall technology spending and approaches 50%; computer hardware expenditures amount to about 20% (Savitz, 2002).

Meta Group Chief Executive Dale Kutnick notes that over the past six years, the percentage of corporate revenues spent on information technology has increased 50%, a trend that will not likely continue at the same pace. Although corporate America is due for a major PC replacement cycle, the demand for PCs is expected to remain soft. In the past, companies have tossed their old hardware every three years, and many PCs were purchased in 1999 ahead of Y2K. But due to budget constraints and a lack of new applications the cycle is expected to stretch out (Savitz, 2002).

A recent survey by Gartner Data-quest of 589 companies worldwide with average revenue of $2.3 billion found that 56% of the respondents planned to increase spending in 2001. The survey showed however, that IT capital budgets, including hardware purchases have been affected more severely by the economic downturn than operating budgets. In 2002, it is expected that while IT services expenditure will increase by 18-20%, hardware budgets will decrease by about 15%. Businesses are taking a hard look at how they can get more out of their current equipment. Instead of replacing systems they may upgrade. In a recent Merrill Lynch survey, only 38% of respondents believe that a PC replacement cycle will kick in beginning in the second quarter of 2002; just 35% expect their PC spending growth to accelerate next year (Lamb, 2001).

Private corporations are not alone in their battle to fund technology projects. Local governments are expected to spend $39.4 billion on IT purchases in 2002. Funding may come from traditional methods, such as issuing bonds or using general funds, or alternative methods, like leasing and using special technology funds, that acknowledge the short lifecycle and constant need for updating computer systems (Isaacs, 2001). Organizations must demonstrate that $1 spend on IT has as much value as $1 spent on anything else. In Tucson, Arizona, the city's IT department meets annually with representatives of other departments to determine where to allocate IT dollars. Their goal is to update 25% of the PCs each year. "If one department got replacements two years ago, but they can demonstrate that they need new equipment, they might get money before someone else", CIO and Director of IT Todd Sander says.

To avoid large yearly capital expenditures on PC replacement, some organizations have looked to leasing programs to assist in the budgeting process. Instead of having spikes every few years, departments can budget monthly payments on its computers that are leased for 24-36 months. At the end of the leases, the vendor replaces the computers with newer models. Second only to setting up the master lease agreements, managing leases poses a big challenge to upgrading computers. In addition, under leasing programs, organizations do not retain as much flexibility to determine when to replace computers--it is expensive to terminate leases, so they have to keep machines for the duration (Isaacs, 2001).

In all types of organizations, IT managers, analysts, and third party vendors consistently report that fast-paced PC replacement cycles are wearing them out. Many organizations are on a three-year PC replacement cycle. Among companies that have shortened desktop PC replacement cycles 46% report the primary reason as the promise of improved performance. Overwhelmingly, though, they are driven by the appeal of new applications and operating systems (Anonymous, 2001). Due to the high cost of PC replacement, many managers are looking for solutions to lower these costs.

IT managers are faced with the complex, and sometimes political, decision of how to distribute new and/or redistribute existing PCs to staff. The decision must be based on getting the largest value from each IT dollar spent on PC replacement. To answer this need, we develop a model to assist IT managers in allocating PC resources.

Resource allocation models attempt to optimize the distribution of a scarce resource subject to a set of constraints. Resource allocation models have been applied in many areas including the airline industry, financial planning, hospital administration, worker-job assignments, production scheduling, and inventory models.

This paper is organized as follows: In Section 2 we describe the PC replenishment resource allocation model. In Section 3, we apply our model to the real world problem of allocating IT PC replacement resources in a small organization. In Section 4, we discuss the solution process and an analysis of the results from our model. We end the paper with concluding remarks in Section 5.

2. PC Replenishment Resource Allocation Model

This section presents the PC replenishment resource allocation model. The impetus for this model is the need for an efficient methodology to determine the best distribution of a limited number of PCs to a larger set of users. Solutions to the model allow IT managers to evaluate the impacts of various PC allocation schemes on the organization. The objective of the model is to develop a plan that maximizes the total increase in utility obtained by computer users while maintaining a reasonable number of PC replacements. A study by Wierschem and Brodnax investigated the impact of processor speed (captured by age of computer in our model) and end-user productivity; they observed that end-user productivity improved with an increase in processor speed (Wierschem and Brodnax, 2003).

Prior to outlining the mathematical details of the model, it is useful to provide a brief description of utility. We define utility as a function of computer productivity level of a user and class of computer used. Each member of an organization is assigned a score for "computer productivity level" based on his or her level of computer usage (i.e., level 1--technology is integral to both teaching and research to level 5--no usage of technology). Each computer in an organization is categorized according to its class. For simplicity, we will assume that each class represents a different age (generation) of computers and all computers of the same age (generation) are equivalent. For example, if there are three classes then all the computers are either brand-new (0-years old), 1-year old, or 2-years old.

For each class of computers, a unique utility value is assigned for each computer productivity level. For example, a class 1 computer is assigned a utility score of XX for a user with a computer productivity level of 1 and a utility score of YY for a user with a computer productivity level of 2, and so on. Scores are assigned for every class of computer and productivity level combination.

For each person, the gain in utility is the difference between the utility score with their new computer assignment and the utility score with their current computer. Obviously, if a person's computer is not replaced, then there is no change in utility. The overall increase in utility in an organization is the sum of all users' increases.

The purpose of the PC replenishment resource allocation model is the assignment of computers to users within the organization. The objective is two-fold: to maximize the overall gain in utility across the organization obtained from strategically reassigning computers and to limit the total number of computer replacements. This ensures that users who will achieve the highest gain in utility from a new computer assignment--will have computers replaced; and limits the time and capital spent in not only physically moving and installing the computer, but in transferring files and configuring new machines. It may be optimal to not replace a computer if the new computer provides the user only a minimal increase in utility.

The mathematical model is represented by a linear, assignment-type, mixed-integer programming (MIP) problem. In order to describe the situation mathematically, it is first necessary to make the following definitions:

2.1 Decision Variables:

Two types of decision variables are utilized in the model:

* [x.sup.new.sub.cp] = { 1 if a computer in class c will be assigned to person p 0 otherwise

* [y.sup.+.sub.ep] and [y.sup.-.sub.ep] = denote a change in assignment of a computer to a person

2.2 Parameters:

The model utilizes the following parameters:

* P = number of people assigned a computer. Each person is represented by p, (1,2..... P)

* S = number of computer productivity levels

* C = number of classes of computers. Each class is represented by c, (1,2..... C)

* [N.sub.c] = number of computers in class c.

* B = penalty value associated with a replacing a computer.

* [u.sub.cp] = utility a person p would derive from a computer in class c.

* [X.sup.old.sub.ep] {1 if a computer in class c is currently assigned to personp 0 otherwise

2.3 Objective function:

The objective function in equation (1) consists of two components. The first maximizes overall incremental gain in utility obtained from computer reassignments; the second limits the number of computer replacements by assigning a penalty for each replacement.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

2.4 Constraints

The objective function is maximized subject to six sets of constraints as shown in Equations (2) through (7).

Equation (2) requires that each person is assigned exactly one computer.

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Equation (3) requires that the number of computers from each class assigned cannot exceed the number of computers available in that class.

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Equation (4) prevents a situation in which a person's existing computer is replaced with an "older" computer (i.e. a computer that would provide less utility).

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Equation (5) ensures that a penalty is assigned each time a computer is replaced. If a new assignment is made, values are set for the decision variables [y.sup.+.sub.cp] and [y.sup.-.sub.cp].

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Equation (6) ensures that [x.sup.new.sub.cp] is a binary variable and can only take on the values of 0 or 1.

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Equation (7) requires that [7.sup.+.sub.cp] and [y.sup.-.sub.cp] are non-negative.

(7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The solution to the MIP problem determines the optimal assignment of computers to all users in the organization, including both those whose assignments remain unchanged and those who receive a new or improved computer.

4. Real World Application: Allocating IT Resources in a Business School

To illustrate its effectiveness, our model is demonstrated in the real world environment of the School of Business at Montclair State University. Montclair State University (MSU) is the second largest university in New Jersey with an enrollment of 13,500. MSU is comprised of six schools; among these is the School of Business (SBUS). The SBUS has a current enrollment of approximately 1,500 and a faculty of 50 (Institutional Research, 2002).

Currently, each faculty member in the SBUS has a PC on their desk. in 1998, the SBUS instituted a program to systematically replace PCs on a three-year cycle. The SBUS was the first, and remains the only, school at MSU to have such a program in place. Up to and including the 2001-2002 academic year, the program was implemented as planned with one-third of the computers replaced. Unfortunately, due to state budget problems, the budget for PC replacements within the SBUS will be reduced. The IT coordinator for the SBUS is faced with the challenge of how to allocate a reduced number of PCs to faculty.

Our case study considers the allocation of new PC's to 50 current faculty members and 2 new, incoming faculty members. Each faculty member was assigned a computer productivity level describing the level of productivity they derive from utilizing a PC for both teaching and research. Table 1 describes each of the five (5) computer productivity levels. An inventory of the current type of computer assigned to each faculty member was conducted. Currently, faculty members are assigned one of three types of computers; in the model a fourth type of computer is added representing new PC's purchased by the SBUS. Table 2 lists each type of computer and the total number of each type currently assigned to faculty and the number of new computers to be purchased fewer than two different model scenarios, as explained at the end of this section.

As described in the previous section, the PC replacement model maximizes the total utility that faculty members achieve from using PC's. Based upon each faculty member's computer productivity level, a utility value is calculated for each of the four classes of computers. Utility values are an increasing function of both computer type and computer productivity level. A user's computer productivity level is fixed for the model period; any increases in utility stem from an upgrade in the computer assigned to a specific user. Table 3 lists the utility values associated with each computer productivity level and each class of computer. In the model, each user has a current utility associated with their existing computer assignment. During the solution process, a new utility value is calculated based upon a change, if any, in computer assignment (class). The model seeks to maximize the total increase in utility among all users while minimizing the number of reassigned PCs.

A computer inventory and computer productivity level assessment survey was conducted on all faculty members in the SBUS. Table 4 lists each faculty member, by coded number, the current class of computer they are assigned, and their computer productivity level. It should be noted that no faculty members are assigned class 1 (new) computers, the assignment of these computers will be determined by the model solution.

In developing model solutions, two scenarios are considered. Both scenarios use the data presented in this section and develop solutions for the optimal assignment of computers to the fifty (50) existing faculty members in the SBUS and two (2) new faculty members joining the SBUS in the fall of 2003. The scenarios differ only in the number of new (class 1) computers to be allocated among faculty members. In Scenario 1--ten (10) new computers are available for distribution; in Scenario 2--seventeen (17) or one-third of the number of existing computers are available for distribution. The following section details both the solution process and an analysis of our results.

5. Results

The mixed-integer programming model was written in the GAMS programming language and solved using the MINOS5 solver. The solution to the MIP problem determines the optimal assignment of computers to all users in the organization, including both those whose assignments remain unchanged and those who receive a new or improved computer.

As mentioned in the previous section, two scenarios are considered; the scenarios differ only in the number of new computers purchased for the SBUS. In the first scenario, ten (10) new computers are purchased and in the second scenario, (19) nineteen new computers are purchased.

Solutions to the model are generated by varying B, the penalty associated with replacing a computer. Each solution generates an alternative PC rollout pattern.

4.1 Scenario 1

The model is solved under the assumption ten (10) new computers are purchased for the SBUS. As the penalty B is increased, the number of computer changes decreases. Results are shown in Table 5.

When the penalty value, B, is greater than or equal to 2.5, no computers were reissued. Only people receiving brand new computers had a replacement. 19% of the faculty received a computer change. In particular, the following changes were made:

* The two new faculty members were assigned new computers.

* Eight people with 3-year old systems were upgraded to brand new computers.

On the other extreme, when the penalty value was set to zero, 16 changes were made, resulting in 31% of the faculty members received a computer change. These changes incorporated 10 new computers into the system and the reissuing of 6 other computers. In particular the following assignments were made:

* The two new faculty members were assigned new computers.

* Three people with 3-year old computers received brand new computers.

* Two people with 2-year old computers received brand new computers.

* Three people with 1-year old computers received brand new computers.

* One person with a 2-year old computer was upgraded to a 1-year old computer.

* Two people with 3-year old computers were upgraded to 1-year old computers.

* Three people with 3-year old computers were upgraded to 2-year old computers.

Regardless of the penalty value, 9 of the original 17 three-year-old computers remain in operation.

Graph 1 shows the percentage of faculty with computer replacements as the penalty weight on B increases, when 10 new computers are introduced into the SBUS.

4.2 Scenario 2

The model is solved under the assumption (19) nineteen new computers are purchased for the SBUS. As in scenario 1, the number of computer changes decreases as the penalty on replacements, B, is increased as shown in Table 6.

When the penalty value, B, is greater than or equal to 3.5, no computers were reissued. Only people receiving brand new computers had a replacement. 37% of the faculty received a computer change. In particular, the following changes were made:

* The two new faculty members were assigned new computers.

* Twelve people with 3-year old computers received brand new computers.

* Five people with 2-year old computers received brand new computers.

Because of the high penalty associated with replacing a computer, 5 of the original 17 three-year old computers remain in operation. Twelve of the original three-year old computers and five of the original two-year old computers are removed from operation. When the penalty associated with replacing a computer is reduced, the number of the three-year old computers in operation decreases.

When the penalty value was set to zero, 29 changes were made, resulting in 56% of the faculty members receiving a computer change. These changes incorporated the 19 new computers into the system and the reissuing of 10 other computers. In particular the following assignments were made:

* The two new faculty members were assigned new computers.

* Ten people with 3-year old computers received brand new computers.

* Three people with 2-year old computers received brand new computers.

* Three people with 1-year old computers received brand new computers.

* Three people with a 2-year old computer were upgraded to a 1-year old computer.

* Six people with 3-year old computers were upgraded to 2-year old computers.

* None of the original 17 three-year old computers remain in operation.

Graph 2 shows the percentage of faculty with computer replacements as the penalty weight on B increases, when 19 new computers are introduced into the SBUS.

6. CONCLUSION

Given the current state of the economy, organizations are confronted with the challenge of increasing productivity while working with reduced resources. It is likely that this scenario will continue. Contrary to the past, IT managers no longer have the luxury of replacing PC's every three years. IT managers are faced with the complex decision of how to distribute new and/or redistribute existing PCs to staff.

In response to this challenge, we developed a mathematical model to assist IT managers in making PC allocation decisions. Our model determines the optimal assignment of computers to all users in the organization, including both those whose assignments remain unchanged and those who receive a new or improved computer.

We illustrate the effectiveness of our model in the real world environment of the SBUS at Montclair State University, where state budget cuts have reduced the funds available for PC replacements.

By implementing our model, the school's IT coordinator was able to model multiple scenarios for the distribution of a reduced number of new PCs to faculty and the redistribution of existing PCs such that the total increase in utility achieved by the new or improved computer assignments was maximized while minimizing the number of reassigned PCs.

As with all smart IT decisions, getting the largest value from each IT dollar spent on PC replacement requires an efficient algorithm for distributing the PCs within an organization.

TABLE Level 1--COMPUTER PRODUCTIVITY LEVEL

Level   Description

1       Technology is integral in both teaching and research
2       Technology is used frequently for some teaching and research
3       Technology is used occasionally for teaching and research
4       Technology used infrequently for non-teaching and non-research
        activities
5       No usage of technology

TABLE 2--COMPUTER TYPES

Type   Description                                 Total Number

1      New computers to be purchased--Dell GX150   10 Scenario 1
       1.2Ghz PIII                                 19 Scenario 2
2      1 year old Dell GX110 933Mhz PIII           17
3      2 year old Dell GX110 667Mhz PIII           16
4      3 year old Dell Dimension 500Mhz PIII       17

TABLE 3--UTILITY VALUES

               Computer Class
                   4    3    2    1
Computer       1   40   45   50   55
Productivity   2   45   52   59   66
Level          3   50   59   68   77
               4   55   66   77   88
               5   60   73   86   99

TABLE 4--CURRENT--PC ASSIGNMENT AND COMPUTER
PRODUCTIVITY LEVEL FOR SBUS FACULTY

User   Computer Productivity   Current Computer
       Level                   Class Assigned

A1     3                       2
B1     3                       2
C1     5                       3
D1     1                       4
0      2                       4
F1     3                       2
G1     2                       2
H1     4                       3
I1     3                       2
J1     4                       4
K1     3                       3
L1     1                       2
M1     3                       3
N1     4                       4
O1     2                       4
P1     1                       3
Q1     4                       4
R1     5                       3
S1     4                       2
T1     2                       2
U1     1                       4
V1     1                       3
W1     5                       4
X1     1                       2
Y1     3                       3
Z1     1                       2
A2     3                       3
B2     2                       2
C2     2                       3
D2     4                       3
E2     2                       3
F2     2                       4
G2     4                       4
H2     2                       3
12     5                       2
J2     1                       2
K2     4                       2
L2     3                       3
M2     2                       4
N2     3                       4
O2     5                       4
P2     4                       4
Q2     2                       3
R2     5                       2
S2     5                       2
T2     3                       2
U2     4                       4
V2     4                       3
W2     5                       4
X2     4                       4

TABLE 5

(a)          (b)           (c)         (d)            (e)
             % of people
             with a                    %
Weight       --computer    total       of computers   # computers that
Value of B   change        changes #     reissued         reissued

0.0          31%           16          12%            6
0.5          29%           15          10%            5
1.0          25%           13          6%             3
1.5          23%           12          4%             2
2.0          23%           12          4%             2
2.5          19%           10          0%             0
3.0          19%           10          0%             0
3.5          19%           10          0%             0
4.0          19%           10          0%             0
4.5          19%           10          0%             0
5.0          19%           10          0%             0

             (f)
             changes
Weight       are
Value of B   reissues

0.0          38%
0.5          33%
1.0          23%
1.5          17%
2.0          17%
2.5          0%
3.0          0%
3.5          0%
4.0          0%
4.5          0%
5.0          0%

TABLE 6

(a)          (b)           (c)         (d)            (e)
             % of people
             with a                    %
Weight       --computer    total       of computers   # computers that
Value of B   change        changes #     reissued         reissued

0.0          56%           29          20%            10
0.5          54%           28          13%            9
1.0          50%           26          14%            7
1.5          50%           26          14%            7
2.0          50%           23          14%            7
2.5          44%           23          8%             4
3.0          44%           19          8%             4
3.5          37%           19          0%             0
4.0          37%           19          0%             0
4.5          37%           19          0%             0
5.0          37%           19          0%             0

             (f)
             changes
Weight       are
Value of B   reissues

0.0          34%
0.5          32%
1.0          27%
1.5          27%
2.0          27%
2.5          17%
3.0          17%
3.5          0%
4.0          0%
4.5          0%
5.0          0%

REFERENCES

1. Anonymous, "Performance is Equally Important," Information Week, 172 (May 22), 2000, 172.

2. Delaney, Kevin J., "Old Computer Don't Fade Away Anymore," Wall Street Journal, May 1, 2003.

3. Isaacs, Lindsay, "Financing Computer Upgrades," The American City & County, 116(2), 2001, 30-40.

4. Lamb, Robin. "The Economy-IT Hardware Spending To Fall as Corporate Budgets Get Cut--Conflicting Forecasts Mean Poor Visibility," Ebn, 1273, 2001, 1-3.

5. Savitz, Eric J., "Wave Theory," Barrons, 82(3), 2002, 15-17.

6. Van Arnum, Patricia, "Information Technology insights: Outlook 2003: What's in store for the chemical industry," Chemical Market Reporter, 263(4), 2003, 17-19.

7. Wierschem, David C. and Brodnax, Thomas L., "The impact of computer processor speed on end-user productivity," Journal of End User Computing, 15(2), 2003, 23-36.

Kimberly Killmer Hollister, Montclair State University

Nicole B. Koppei, Montclair State University

Author Profiles:

Dr. Kimberly Killmer Hollister earned her Ph.D. at the University of Pennsylvania. Currently, she is an Assistant Professor of Information and Decision Sciences. Dr. Killmer Hollister is on the Board of Directors of the Northeast Business & Economics Association and has recently published in European Journal of Operational Research, Journal of Accountancy, Journal of Informatics and Education Research, and the THE Journal.

Dr. Nicole Koppel earned her Ph.D. at Rutgers University. Currently, she is an Assistant Professor of Information and Decision Sciences. Dr. Koppel has recently published in the Journal of Informatics and Education Research and the THE Journal.