ABSTRACT

The David Adamany Undergraduate Library (UGL) is the most appealing library among

the four libraries on Wayne State University’s campus. All 3 floors in UGL are operational for

24 hours during exam periods and during five days of the week. Many students take advantage of

this operational policy; however, there is a cost to keep the building operating. Sometimes a

certain floor has few or no students; thus, electricity is being wasted to keep the lights and

computers on. We present a mathematical optimization model for the UGL that will advise more

efficient operation. The objective is to minimize the electricity cost of the UGL whilst satisfying

the educational needs of its users.

INTRODUCTION

Located i000t Gullen Mall in Midtown Detroit’s urban research institution and university,

Wayne State, the David Adamany Undergraduate Library (UGL) caters to the needs of

undergraduate, graduate, doctoral students as well as faculty, staff members and alumni.

The library alone provides 2,337 seats, 27 group study rooms, and 3 instruction labs. It has

nearly 500 computer workstations providing students with access to electronic resources. The

learning needs of 1000 and 2000 level undergraduate courses are intended to be supported with

the wide variety of books and magazines. The library also contains the DeRoy Extended Study

Center providing 24-hour access to 140 standard workstations as well as 30 high-end work

stations with specialized software. Also, approximately 8000 videos, DVDs, laser discs and

audiotapes are in the media collection. The Undergraduate Library also provides students with

information on careers, computers, and student survival skills.

With these attractive advantages, an obvious weak point exists in the operational respect.

In order to meet the demand of various users, they are maintaining the policy which is providing

all kinds of energy resources through all library hours. Many students like this policy; however,

there is a cost to keep the building operating. Therefore, the UGL should advise a plan to operate

the electricity more efficiently.

PURPOSE OF MODEL

From using the UGL’s facilities at different points in the day, our group was able to

observe a significant amount of waste in energy resources. Throughout the day, computer

workstations and ceiling lights are on, regardless of whether or not they’re actually being

utilized. Our project goal is to study the consumption of electricity by the UGL facility and use a

mathematical optimization method to minimize the costs associated with it. After having

discussed the issue with the administration authorities, an opportunity was identified to work

towards creation of an optimization model – to minimize electricity consumption and reduce

operational costs. No such study has been conducted before for the building.

OPERATIONAL BACKGROUND

In order to operationalize the project, lighting, seating arrangement and desktop

computers are divided into square regions by our assumption. Each square box represents light

square hanging from the wall and consists of 36 fluorescent lights as shown in the picture below.

Also we classified the light square according to dominant equipment of the light square.

Because square regions include their own different objectives, we need to sort out square regions

according to our uniformed criteria. Shown below are the maps which are further divided into

grids. ‘Pink’ square boxes represent squares containing a combination of lights and desktop

computers and ‘Blue’ boxes represent a combination of lights and tables. ‘Yellow’ boxes

represent just lights.

First floor map:

Second floor map:

Third floor map

LITERATURE REVIEW

Mavrotas, Diakoulaki and Papayannakis (1999) use a mixed 0-1 multiple objective linear

programming (MOLP) model with a branch and bound algorithm and fit it to the Greek

electricity generation sector in an attempt to find the quantity and production of different power

units required to meet the anticipated electricity demand in the future. The electricity demand to

be satisfied is designated by a Load Duration Curve (LDC) which indicates the number of hours

per year that the power demand (in MW) surpasses a specified peak value. In order to use the

branch and bound algorithm, which requires linearity, the LDC is estimated by a piecewise-

constant function. The area under it denotes energy production (in MWh). The suggested

algorithm can contain both integer variables representing the number of each type of power units

considered for subsequent addition to the electricity generation system and continuous variables

signifying the output from each power plant. The proposed mixed 0-1 MOLP algorithm can be

applied in several other actual decision situations. This particular study can provide our case

study with some useful insight and a framework to proceed. The results show combinations of

the power generation units and the electricity production from each unit for each combination

Ren, Gao and Ruan (2009) look at finding an optimal, cost-minimized grid-connected

photovoltaic (PV) system for residential use. A linear programming model is used to achieve

this end. The economic viability of the model is investigated by considering some conditions for

a typical residential building in Japan. It is found that the the optimal system capacity is reliant

on upon the capital cost, interest rate, system efficiency and electricity saleprice, with capital

cost having the most influence. The results of this study provide us with some background on

what to consider if including solar panels in our alternative energy plan.

DATA COLLECTION AND ASSUMPTIONS

An 18-month compilation of data for daily total electricity usage (in KWh) and daily

peak demand (in KW) was obtained for the UGL through the help of Larry S. Fodor, the Director

of Utilities and Energy Management at Wayne State University. For our study, we’re interested

in analyzing a portion of this data corresponding to the 2011-2012 school year, comprising the

fall, winter and summer semesters (see Figure below). Truncation of data and calculation of

parameters such as data minimum, maximum, total and product sum were done with Microsoft ®

Excel. The total cost of electricity was determined by using estimated numbers and

recommendations from DTE Energy and the following formula:

(𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑘𝑊ℎ 𝑥𝑒𝑛𝑒𝑟𝑔𝑦 𝑐ℎ𝑎𝑟𝑔𝑒 𝑐𝑜𝑠𝑡

𝑘𝑊ℎ) + ∑[𝑝𝑒𝑎𝑘 𝑑𝑒𝑚𝑎𝑛𝑑 (𝐾𝑊)𝑖𝑛 𝑚𝑜𝑛𝑡ℎ 𝑖]

12

𝑖=1

𝑥𝑑𝑒𝑚𝑎𝑛𝑑 𝑐ℎ𝑎𝑟𝑔𝑒 𝑐𝑜𝑠𝑡

𝑘𝑊

= 4542911.2 𝑘𝑊𝐻 𝑥$0.04298

𝑘𝑊ℎ+ 10470.4 𝑘𝑊 𝑥

$11.75

𝑘𝑊= $𝟑𝟏𝟕, 𝟐𝟑𝟒. 𝟒𝟖

From this the aggregate cost per kWh was determined to be:

𝑇𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡

𝑇𝑜𝑡𝑎𝑙 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 𝑢𝑠𝑎𝑔𝑒=

($317,234.48)

4542911.2 𝑘𝑊𝐻=

$0.0698

𝑘𝑊ℎ

To simplify our case study, we only consider the consumption of energy by desktop

computers and ceiling lights in the UGL. Furthermore, we only consider ceiling lights that are

arranged in the square grid formation shown previously even though the UGL has some lights in

different arrangements. We also consider desktop computers (monitor and CPU) in their sleep

modes. From walking through the library and making observations, it was determined that

there’re 98 lighting squares total for all three floors, each containing 36 fluorescent tube lights

requiring 35 W of power each. There’re 456 computers and each requires 25 W of power in sleep

mode. Additionally for our calculations, we need to find the number of people during early

morning, day and night periods. We’re considering only the maximum number of people on each

floor during each designated time period. These time periods and the corresponding number of

people during each are shown in the demand constraints table in the ‘Model Formulation’

section.

During the formulation of the problem statement for this case study, our group originally

considered the option of adding solar panels to the roof of the UGL as an alternative energy

generation source. However, through contacting Michigan Solar Solutions and conducting some

analysis and research on our end, we determined that solar panels have a costly initial investment

associated with them and for the purposes of our case study, ultimately omitted it from the

model. The particular solar panels under consideration had a 25 year warranty associated with

them and were each 65” x 39” in dimension. The roof of the UGL was determined to be 6075 m2

through a Google Maps ® estimation. From here, we determined the number of panels to occupy

the roof as 3714. The following is a summary of the analysis conducted in Microsoft Excel ®:

MODEL FORMULATION

- Algorithm

In order to control this project, we needed to make a proper algorithm. Because this

project is a large-scale work and has several steps to arrive at a conclusion, to systematize this

work by making an appropriate algorithm was one of the most important works for us.

WSU UGL 12/6/2012

Panel power production Investment Costs

Payback term Solar Renewable Energy Credits

Annual net income Electric Savings

Estimated Array generation in Kwh's

#Panels Watts Array Watts Annual Kwh's Monthly Kwh's

3714 255 947,070 1,188,201 99,017

Monthly, this system will generate an average electrical savings of…. $6,911.37

Initial investment:

System Design, Parts, Permits & Labor $3,077,977.50

MI sales tax (6%) $184,678.65

Final Project cost $3,262,656.15

30% Federal Tax Credit $978,796.85

Net Cost after Tax Credit $2,283,859.31

Terms:

60% due at contract signing $1,957,593.69

30% due when system inspected & approved $978,796.85

System commissioned by utility company $326,265.62 ** Final payment

Payback term$2,283,859.31

Divided by est. Annual net income $82,936.42

Estimated payback term 27.54 Years

Solar Panels have a 25 year warranty! -$210,448.84

3714 255 watt panels 947070 watts

Angle derating factor X 0.88

833,422

Insolation value X 4.2 avg hrs sunlight/day

3,500,371 watts/day

Per year X 365 days

1,277,635 kwh/yr

Inverter derating factor X 0.93

1,188,201 kwh/yr or

99,017 kwh/month

Electric Savings

Estimated Annual kwh production 1,188,201 kwh/yr

*Current Rate X $0.07 kwh

Annual net savings $82,936.42 yr

Monthly net savings $6,911.37 month

Solar Cost Analysis

Net cost

Power production - estimated

This project can be divided into two parts. One of them is determining the electricity

on/off schedule plan and the other one is analyzing the solar panel adoption. For make sure the

plan for electricity on/off plan, we had to consider both spatial side and temporal side, because

UGL is operating the electricity on the first through the third floor and during timed period. Two

SSA items mean the small scale analysis for spatial operation and temporal operation of

electricity, respectively and large scale analysis means the integrated annual plan analysis.

After determining the electricity on/off schedule plan, we moved on to solar panel

adoption optimization part accompanying with achieved electricity schedule results. For

concluding the suitability of adoption of solar panel, all we needed was sufficient data. To

estimating the monetary benefit and breakeven point for adoption of solar panel was expected by

using collected data and conducting a thorough cost analysis.

- Decision variable and objective function.

Basically, our overriding concern was to determine the optimized operational system for

fluorescent light and desktop computer use in each floor of UGL. In order to set decision

variables, we have investigated the electric system in UGL then, found out 119 binary decision

variables consisting of designated fluorescent light square region term (xij) and designated

desktop computer workstation region term (yij).

1) xij, where ‘i’ represents the floor number in the UGL (i=1, 2 or 3) and ‘j’ represents a

consecutive integer grid number corresponding to the proximity of each light square

region to the central stairwell.

2) yij, where ‘i’ represents the floor number in the UGL (i = 1,2 or 3) and ‘j’ represents a

consecutive integer grid number corresponding to the proximity of each computer

workstation region to the central stairwell.

If certain fluorescent light square region or desktop region’s electricity had to be turned

on, their decision variable value will have a value as 1 in objective function, otherwise 0.

The objective function for this model had to have two kinds of sub-objective functions,

one of them was for light square operation, and the other one was for desktop workstation. We

can make the formulas for these two objective functions as below.

𝑍1 = ∑ ∑ ∑ ∑ 𝑊𝑎𝑡𝑡 × 𝑛𝑜. 𝑜𝑓 𝑓𝑙𝑢𝑜𝑟𝑒𝑠𝑐𝑒𝑛𝑡 𝑙𝑖𝑔ℎ𝑡𝑠 𝑖𝑛 𝑜𝑛𝑒 𝑠𝑞𝑢𝑎𝑟𝑒 × ℎ𝑜𝑢𝑟 × 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑑𝑒𝑐𝑖𝑠𝑖𝑜𝑛 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒

3

𝑙=1

3

𝑘=1

𝑛

𝑗=01

3

𝑖=1

𝑍2 = ∑ ∑ ∑ ∑ 𝑊𝑎𝑡𝑡 × 𝑛𝑜. 𝑜𝑓 𝑑𝑒𝑠𝑘𝑡𝑜𝑝 𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑟𝑠 𝑖𝑛 𝑜𝑛𝑒 𝑠𝑞𝑢𝑎𝑟𝑒 × ℎ𝑜𝑢𝑟 × 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑑𝑒𝑐𝑖𝑠𝑖𝑜𝑛 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒

3

𝑙=1

3

𝑘=1

𝑛

𝑗=01

3

𝑖=1

Minimize Z = Z1 + Z2

First sum is corresponded to sum of each three floors of UGL, second sum is for the

consecutive integer grid number on each floor, third sum is for three time period in a day like

day, night, and early morning, and forth sum is corresponded to sum of each three semester (fall,

winter, and summer).

- Constraints

We have made four major types of constraints to appropriately control the electric

operation system:

If there is no operational order of priority in each electric square, the electric operation

system will have no order about which electric square should be turned on prior to another one

and it will give us a huge confusion to operate the system and students as well. So, we have set

up this order by following the order of the proximity of each light square region to the central

stairwell. This condition can be expressed by these formulas.

𝑥(𝑖,𝑗) ≥ 𝑥(𝑖,𝑗+1)

𝑦(𝑖,𝑗) ≥ 𝑦(𝑖,𝑗+1)

Then, we needed to make sure that certain light square’s fluorescent tubes should be on,

if the desktop computers included in that light square region would be on. This condition could

be formulated by this constraint.

𝑦𝑖𝑗 = 𝑥𝑖𝑗

We also considered the connection between light squares because of the energy

efficiency and convenience for spatial use. This image will be able to help you to understand this

idea.

Additionally, this idea is input to excel solver by using this constraints.

𝑥(𝑖,𝑗(𝑢𝑛𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑏𝑦 𝑑𝑒𝑣𝑖𝑐𝑒)) = 𝑥(𝑖,𝑗+1(𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑏𝑦 𝑑𝑒𝑣𝑖𝑐𝑒))

or

𝑥(𝑖,𝑗(𝑢𝑛𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑏𝑦 𝑑𝑒𝑣𝑖𝑐𝑒)) = 𝑥(𝑖,𝑗−1(𝑜𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝑏𝑦 𝑑𝑒𝑣𝑖𝑐𝑒))

Lastly, we have utilized the collected demand data for making demand satisfaction

constraints. Demand data are as bellow,

Then, we have made demand constraints satisfying this number of population.

𝑎𝑖 × ∑ 𝑥𝑖𝑗

𝑛

𝑗=01

≥ 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 𝑢𝑠𝑖𝑛𝑔 𝑡𝑎𝑏𝑙𝑒 𝑜𝑛 𝑖𝑡ℎ 𝑓𝑙𝑜𝑜𝑟

(′𝑎′𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑒𝑎𝑡𝑠 𝑖𝑛 𝑜𝑛𝑒 𝑠𝑞𝑢𝑎𝑟𝑒)

𝑏𝑖 × ∑ 𝑦𝑖𝑗

𝑚

𝑗=01

≥ 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑜𝑝𝑙𝑒 𝑢𝑠𝑖𝑛𝑔 𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑟 𝑜𝑛 𝑖𝑡ℎ 𝑓𝑙𝑜𝑜𝑟

(′𝑏′𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑟𝑠 𝑖𝑛 𝑜𝑛𝑒 𝑠𝑞𝑢𝑎𝑟𝑒)

OPERATIONAL RESULTS

By using Excel solver, we could get efficient operation systems of electricity. Usually,

UGL operates all electricity system such as fluorescent light and computer during library hour,

however, now we can turn off some useless part among the whole light square region.

Moreover, we have been able to find out the monetary benefit generated from this

operational change. Sensitivity analysis wasn’t applicable to our study and Excel solver didn’t

provide us with a sensitivity report, because our project has been based on 0-1 integer

programming.

The estimated benefit which will be generated by this system is $34,000/year, and this

amount exceeds 10% of total cost of electricity in UGL. By implementing a little change in

energy consumption style of UGL, we can potentially save huge amount of money in one year.

LIMITATION

1. There were a lot of assumptions when we have considered the improvement of

operational system of electricity in UGL, because real electrical system in UGL is too

complicated. This point might make our calculation in project more inaccurate.

2. We have only considered the light square region in the library, because of complexity for

collecting data and making model.

3. We don’t have enough background knowledge about solar panel and other renewable

sources, so we have considered only technical part for estimating cost, excluding a

regulatory consideration.

RECOMMENDATIONS

Different days, students arrive at the library that are outside the mean data number of

students calculated by our team. For example, if a very large study groups wishes to use the 3rd

floor but it is already filled, management will have to come in and make room to accommodate

these students. Likewise, management should continuously monitor the number of students each

month to ensure students' needs are met and having a mindset of what is going on academically

throughout the semesters like when finals are and when students usually leave for break. We

recommend that management should use waiting line black posts to designate where students

should study.

CONCLUSION

For our data, we concluded that we would save the library approximately $34,000 of

electricity. That would be half the amount of electricity that the library would typically use for

ceiling lights and computers.

The achievement of this project took many trials and difficulties. One of them was

estimating the cost of installation of solar panels and wind turbines. One team member was

assigned to determine the cost through quotes of nearby companies. A reputable company

cannot determine the cost without knowing the annual cost of the electric demand and annual

usage. Another team member's job was to find the management of the building to see if he

knows but it took nearly 3 weeks for a response from the manager and from there on, the data

was given to a sales manager of the solar panel company. After receiving the quote from the

manager, we performed an analysis to see how much it would cost and how many solar panels

the library's roof can accommodate a number. The conclusion was that solar panels and wind

turbines is not cost effective (10 to 15% efficient of converting solar energy into pure electricity,

$25,000,000 for initial investment (which the library does not have a budget for) at a 25 year

return) is not a reasonable choice as a return on investment. Thus, this was an issue for us as part

of the project. Had we known sooner that solar panels is not cost effective, we would have not

gone through so much hassle and wasted efforts.

With the objective function solution for the period of 2011 to 2012 at $34,000, this the

objective solution will vary from time to time. For example, because population and enrollment

increases every year, more students will be using the library and thus we will see a possible

decrease in the objective function.

Do we believe that this project is something practical the library can put into practice?

From a student's standpoint we do not believe so. Constant lights turning on and off and

designating students to other areas of the floor is too much of an annoyance to the students. This

project also causes a lot of restrictions to students to roam freely around the library wherever

they want to study and decide a private room to study. There are other ideas for energy cost

saving, like installing a motion sensor light activation system where the slightest movement is

detected, will activate the lights and turn off after about an hour. Last even though it will save

$34,000 of the $60,000 spent on ceiling lights and computers, it is just only 10% of the overall

electricity usage of $300,000 (other electrical costs were spent on elevators, air conditioning,

heating, etc. Therefore the management effort of saving $34,000 is not worth the investment to

go through.

This project can be expanded to other areas of the campus as well where enormous

amount of electricity is observed to be wasted. For example, we see an opportunity for parking

structures, recreation center, and other libraries.

REFERENCES

1. Mavrotas, G., Diakoulaki, D., & Papayannakis, L. (1999). An energy planning approach based

on mixed 0–1 Multiple Objective Linear Programming. International Transactions in

Operational Research, 6(2), 231-244.

2. Ren, H., Gao, W., & Ruan, Y. (2009). Economic optimization and sensitivity analysis of

photovoltaic system in residential buildings. Renewable Energy, 34(3), 883-889.