project-example3.pdf

IE6560

PRESENTED TO: PROFESSOR EVRIM DALKIRAN

DONE BY:

WSU HOUSIN DEPARTMENT REVENUE MANAGEMENT

PROJECT

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Contents Introduction .................................................................................................................................................. 2

Overview of the Project ............................................................................................................................ 2

Purpose of the Project .............................................................................................................................. 3

Literature Review .......................................................................................................................................... 3

Model versus Real Life Scenario ................................................................................................................... 7

Model’s Results ............................................................................................................................................. 8

For fall ....................................................................................................................................................... 8

For winter .................................................................................................................................................. 9

Optimal Revenue .................................................................................................................................... 10

Result Analysis ............................................................................................................................................ 10

Xij Constraints ......................................................................................................................................... 10

Fall Capacity Constraints ......................................................................................................................... 11

Winter Capacity ...................................................................................................................................... 12

Quality Constraints ................................................................................................................................. 13

Conclusion and Future Direction ................................................................................................................ 13

Appendix-A .................................................................................................................................................. 15

Appendix-B .................................................................................................................................................. 16

References .................................................................................................................................................. 18

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Introduction

Overview of the Project

Wayne State University ‘Office of Housing & Residential Life’ is responsible for the

management of student housing in and around the main campus. The advantages for students

living on main campus housing provided by the WSU Office of Housing & Residential Life is

that it has close proximity to facilities like classes, libraries, recreational facilities, cafeterias,

student center, etc. These advantages have led to increasing Wayne State University student

community living on-campus, which proved to be having a positive impact in their life styles and

careers with both personal and academic success. With the increasing demand of students to live

on-campus, Wayne State University has increased its available housing options on-campus over

the past decade. There are a total of six housing options for the students to choose from as listed

below.

Chatsworth Apartments University Towers

Towers Residential Suites Ghafari Hall

De Roy Apartments Atchison Hall

The Chatsworth Tower apartment is a historic building from 1929. It is a graceful 9-story

apartment building with turn-of-the-century elegance, which is located in the heart of campus on

Williams Mall. Chatsworth Tower offers three housing unit options to students: (a) studio units,

(b) one-bedroom units, and (c) two-bedroom units. The Towers Residential Suites is an 11-story

apartment building with views as far as the Ambassador Bridge. The Towers Residential Suites

offers mainly suite style rooms, containing up to four bedrooms attached to a shared living space.

There are only a limited number of single rooms in the Towers Residential Suites. The Deroy

apartments, was first built in 1972 and later renovated in 2010. It is a 15-story building located in

the heart of campus near the student center building and undergraduate library. This building

offers two housing unit options to students: (a) one-bedroom units and (b) two-bedroom units.

The University Tower apartment is the newest apartment building on-campus. It was opened in

1995, and comprises of a modern 11-story complex layout located approximately one block

south of Forest Avenue at the southern edge of main campus and just west of the School of

Medicine. The University Towers offers three housing unit options to students: (a) one-bedroom

units, (b) two-bedroom units, and (c) three-bedroom units. The Ghafari Hall opened in 2002,

provides housing for freshmen and upperclass students. The Ghafari Hall offers three housing

unit options to students: (a) one-bedroom units, (b) two-bedroom units, and (c) three-bedroom

units. The Atchison Hall opened in 2003 provides housing for freshmen and upperclass students.

The Atchison Hall also offers three housing unit options to students: (a) one-bedroom units, (b)

two-bedroom units, and (c) three-bedroom units.

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Purpose of the Project

With the above six listed university housing options, thousands of students are now able to

successfully pursue their career interests efficiently by staying on-campus in close proximity to

various resources to on-campus housing. In our project related to ‘Deterministic Optimization

Methods’, we look at the possibility of how we can maximize the revenue of Office of Housing

& Residential Life by deciding how many students to assign for each room type and contract

category, while keeping the student satisfaction rate higher than a certain assigned value. In our

project, we have limited the study to consideration of four apartments: (a) Towers Residential

Suites, (b) De Roy Apartments, (c) Ghafari Hall, and (d) Atchison Hall.

Literature Review Revenue management is the art and science of selling the right product to the right customer at

the right time for the right price, through a combination of inventory controls and pricing (Cross

1997). Thus it is a network of decisions to be made regarding price allocation of each room type,

students’ allocations to rooms, and duration of the allocation. Optimal revenues are normally

obtained by looking at demand requirements and optimal prizing (Song et al. 2013). Hanwu and

Peng (2010) noted that the revenue of an economy hotel with a level ‘k’ at branch ‘b’ may be

maximized using Raeside and Windle (2000) suggested methodology.

Hanwu and Peng (2010) formulated revenue maximization over a booking time-period ‘q’ as

the summation of the products of (a) average revenue gained by bookings and (b) the number

of accepted bookings (decision variables: accept or not),

Subjected to the constraints of

i. the number of rooms available on kth

levels at branch ‘b’,

ii. the number of rooms that branch ‘b’ can provide,

iii. the total number of rooms that the city can provide,

iv. an assumption of no check-outs/stay-overs accumulated on day ‘0’ initially,

v. the number of rooms available on kth

levels at branch ‘b’ limited by extreme (low-

end/high-end) conditions of ‘non-negative’ bookings and ‘maximum allowable’

booking demand in time-period ‘q’, and

vi. the time-period ‘q’ varying between ‘0’ and total time ‘T’.

Refer to the Appendix-A section for the corresponding equations.

However, in the case of Wayne State Housing department, the prices of the rooms must be fixed

throughout the year and are allowed to change in a very small percentage from one year to

another. Thus the decision variables of this type of problems will be restricted to assigning

option ‘j’ for student ‘I’ with contract type ‘n’ to room type ‘m’. Consequently, the formulation

was shifted from revenue management model to an assignment model for room allotments. In

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this context, the study by Mahar et al. (2013) provided further insights into model formulation of

Wayne State Housing department objective function of room allotment.

Mahr et al. (2013) formulated maximizing the proportions of application persons as

the summation of the products of (a) applicant priority based on the user inputs of person ‘i’

with a project ‘j’, and (b) the number of accepted persons ‘i’ to a trip ‘j’ (decision variables:

accept or not),

Subjected to the constraints of

i. the total number of people needed for the trip ‘j’,

ii. lower and upper limits of total no. of applicants from a country ‘k’ to trip ‘j’,

iii. lower and upper limits of total no. of applicants with job ‘k’ to trip ‘j’,

iv. lower and upper limits of total no. of applicants from employee type ‘k’ to trip ‘j’,

v. lower and upper limits of available no. of applicants from a country ‘k’ to trip ‘j’,

vi. lower and upper limits of available no. of applicants with job ‘k’ to trip ‘j’,

vii. lower and upper limits of available no. of female applicants to trip ‘j’,

viii. lower and upper limits of available no. of applicants from region ‘a’ and employee

type ‘k’ to trip ‘j’,

ix. lower and upper limits of total no. of applicants from region ‘k’,

x. lower and upper limits of total no. of applicants from region ‘a’ and employee type

‘k’,

xi. lower and upper limits of available no. of applicants from employee type ‘k’,

xii. lower and upper limits of available no. of applicants from region ‘k’,

xiii. lower and upper limits of available no. of female applicants,

xiv. All non-negative constraints

Refer to the Appendix-B section for the corresponding equations.

Inspired from this formulation, the WSU housing department problem will assume that each

applicant will have 3 choices, and the decision is which choice to accept for student i. The

department has the freedom to reject the student if necessary. However, the difference between

the two formulation lies in the objective function, the ELILILY formulation aims to maximize

the volunteers’ satisfaction level, however in the WSU formulation the aim is to maximize the

revenue subject to a satisfaction constraint that assures a minimum level of student satisfaction.

The fundamental equations related to model formulation of Wayne State Housing allotment

developed on the basis of Mahr et al. (2013) equations are discussed in detail in the Methodology

section.

MODEL FORMULATION Due to high demand for On-Campus housing every year in Wayne State University, the housing

department collaborated with Industrial Engineering department to help them maximize their

revenue using Deterministic Optimization.

The main objective of our model is to maximize the revenue of WSU Housing Department by

allocating the rooms to students according to semester and annual demand during FALL and

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WINTER intake. This is an Assignment INTEGER PROGRAMMING model and is solved for

20 students, 14 of which are applying in the fall and the rest 6 are applying in the winter.

Students have the option of choosing 3 housing Priorities according to annual or semester

contract type among the 13 housing options offered by the university. Below is the table showing

the available housing options and rates according to the contract type.

2013-14 Annual Room Rates (per person)

2013-14

Annual

Fall

2013

Winter

2014

Ghafari & Atchison Halls

Single Occupancy rooms with private bath $7,200 $3,800 $3,800

Double Occupancy rooms with private bath $5,666 $3,033 $3,033

Triple Occupancy rooms with private bath $4,444 $2,322 $2,322

The Towers Residential Suites

Double Occupancy room with shared bath (Type

A)

$5,618 $2,909 $2,909

Single Occupancy room with private bath (Type E

& G)

$7,414 $3,807 $3,807

Double Occupancy room within a suite (Type B &

C)

$6,234 $3,217 $3,217

Single Occupancy room within a regular suite

(Type C, D &F)

$6,462 $3,331 $3,331

Deroy Furnished Apartments

(sophomores/juniors/seniors only)

Efficiency apartment single $7,962 $4,081 $4,081

One bedroom apartment double $6,410 $3,305 $3,305

Two bedroom apartment single $7,600 $3,900 $3,900

These rooms are allotted to students according to the contract choice i.e. Annual or

Semester. We also have a student satisfaction parameter where a certain standard of overall

satisfaction for students has to be maintained.

DECISION VARIABLES

Xij I = 1,2,3,4………….18,19,20

J = 1,2,3,4

Room Type (m) 1 = Single Occupancy Towers

2 = Single Occupancy Atchison

3 = Single Occupancy Ghafari

4 = Single Occupancy Deroy

5 = Single Occupancy within suites(Towers)

6 = Double Occupancy Towers

7 = Double Occupancy Atchison

8 = Double Occupancy Ghafari

9 = Double Occupancy within suites(Towers)

10= Triple Occupancy Atchison

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11= Triple Occupancy Ghafari

12= One bedroom Deroy apartments

13= Two bedroom Deroy apartments

Contract Type (n) 1 = Fall semester only

2 = Annual Fall

3 = Annual Winter

4 = Winter semester only

Rmn Rate for room type m under contract option n.

Eijmn This variable representing the options chosen

by the student and has a value 1 or 0.

Satisfaction rate Qij Qi1= 1 if we give student I choice 1

Qi2= 0.7 if we give student I choice 2

Qi3= 0.5 if we give student I choice 3

Qi4= 0 if we don’t assign student i

CONSTRAINTS

Fall Capacity

Winter Capacity

Fall Satisfaction

rate

>= 0.75

Winter

Satisfaction rate

>=0.75

Decision

Constraint

=1

OBJECTIVE FUNCTION : Maximize ∑i∑j∑m∑n Rmn*Eijmn*Xij

Eijmn

This parameter is the most complicated input to our system. In short it is a mathematical way to

input the students’ choices to our formulation, so that the solver will know all of the student’s

preferences. For example if student 1 has its first priority as room type 3 and contract type 4

parameter E1134=1 and all of the rest E11mn parameters for all m’s and n’s will be equal to

zero. Thus for each student we will have 156 E’s accounting for all 3 options and room type plus

contract type combinations.

∑∑∑𝐸𝑖𝑗𝑚𝑛

4

𝑗=1

∗ 𝑋𝑖𝑗

2

𝑛=1

15

𝑖=1

<= Nm- ∑ ∑ 𝐸𝑖𝑗𝑚34𝑗=1 ∗ 𝑋𝑖𝑗20

𝑖=15

<= Nm- ∑ ∑ 𝐸𝑖𝑗𝑚24𝑗=1 ∗ 𝑋𝑖𝑗15

𝑖=1 ∑ ∑∑𝐸𝑖𝑗𝑚𝑛

4

𝑛=2

4

𝑗=1

20

𝑖=15

∗ 𝑋𝑖𝑗

∑𝑄𝑖𝑗 ∗ 𝑋𝑖𝑗

15

𝑖=1

∗ 𝑋𝑖𝑗

∑ 𝑄𝑖𝑗 ∗ 𝑋𝑖𝑗

20

𝑖=15

∗ 𝑋𝑖𝑗

∑𝑋𝑖𝑗

4

𝑗=1

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Rmn

As there are 13 types of housing options available, the rates are determined by housing

department according to semester or annual contract. The rates chart is listed above.

Rmn denotes the room rate (m) for contract type (n) offered by the department.

Qij

Wayne State University prides itself on its high level of student satisfaction

In all aspects of services. University housing is under no exception in terms of student

satisfaction in allocation of rooms. Satisfaction rate is given on a scale of 0 to 1 where it is 1

when student is assigned to his first choice, 0.7 when assigned to his second choice, 0.5 if

assigned to his third choice and 0 if no choice is allotted. Housing department aim is to maintain

a minimum standard of 0.75 on an average scale.

Difficulties faced in the formulation In our formulation process we have faced many difficulties including:

Time limit, which retained us from performing any surveys with students living on

campus in order to collect reliable data about student preferences, satisfaction levels,

etc…

Lack of responsiveness from the WSU housing department, which refused to give us data

about the exact number of applicants, the most desirable room types and contract types,

and annual rejection rate.

Limited optimization tools, Excel Solver, that cannot solve more than 200 variables and

100 constraints

Numerous number of input parameters, which were randomly assigned and were

manually inputted to the system. More than 3500 input parameters were utilized in our

model, thus this process was very time consuming.

Model versus Real Life Scenario In reality the housing department has thousands of applicants annually. If each student is allowed

to have 3 priorities. The department’s decision is which priority it should accept for each student,

or even not assign this student at all. Therefore, the problem will have 4 decision variables for

each student, in total it will have 4*number of applicants.

However, in excel we cannot solve a model with more than 200 variables. Therefore, we were

obliged to simplify the real life problem by reducing the number of applicants. A random sample

of 20 applicants was generated, each with 3 randomly assigned priorities. 14 of which are

applying in the fall semester and the rest 6 are applying in the winter semester. Consequently we

ended up with a simplified model having 80 variables, Xij’s. Moreover, we assumed that the

model is consistent all over the years. In other words, room capacity, number of applicants,

applicant’s priorities and other conditions affecting the objective function will stay the same

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from year to year. Therefore, the assignment for the current winter semester are the same as that

of the previous winter. The Model will be solved for a time period equal to 1 year, and will be

applied to the rest of the years on a cycle basis.

This simplification has caused us an inaccuracy problem especially when it comes to estimating

the room capacity for each type of rooms. The data we obtained from the housing department

concerning the number of available rooms, can be applied to the real demand which exceeds

2000 students. Therefore, in order to make these parameters applicable to this project’s model,

we need to multiply them by a reducing factor= 20/2000=0.01, and the round up to an integer

value.

Model’s Results

Solving the excel model of this assignment problem had generated the results listed in the table

below.

For fall

Student Name Final Value

1 x11 0 x12 0 x13 1 x14 0 2 x21 0 x22 0 x23 1 x24 0 3 x31 1 x32 0 x33 0 x34 0 4 x41 1 x42 0 x43 0 x44 0 5 x51 1 x52 0 x53 0 x54 0 6 x61 1 x62 0 x63 0 x64 0 7 x71 1 x72 0

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x73 0 x74 0 8 x81 1 x82 0 x83 0 x84 0 9 x91 1 x92 0 x93 0 x94 0 10 x101 1 x102 0 x103 0 x104 0 11 x111 0 x112 0 x113 0 x114 1 12 x121 1 x122 0 x123 0 x124 0 13 x131 1 x132 0 x133 0 x134 0 14 x141 0 x142 0 x143 0 x144 1

Two student from fall applicants 11 and 14 were rejected, as for the rest most of them were given

their first priority, students 3,4,5,6,7,8,9,10,12,13. And only students 1 and 2 were given their 3rd

choice.

Thus the rejection ratio for fall was 2/14 which is interpreted in real life as, from every 14

students applying the department will be rejecting 2. This ratio may defer in real cases depending

on the choices of the students.

For winter Student Name Value

15 x151 1

x152 0

x153 0

x154 0

16 x161 0

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x162 0

x163 1

x164 0

17 x171 0

x172 0

x173 0

x174 1

18 x181 1

x182 0

x183 0

x184 0

19 x191 1

x192 0

x193 0

x194 0

20 x201 1

x202 0

x203 0

x204 0

One winter applicant was rejected which is students 17, students 15,18,19, and 20 were assigned

to their 1st priority, and finally only student 16 was given his 3

rd priority

Thus the rejection ratio for fall was 1/6 which is a realistic ratio, since most of the room

capacities will be already taken by annual fall applicants which are more numerous than those

applying in the winter.

Optimal Revenue And the optimal revenue is 73401 dollars annually. Therefore, if the department follows this

formulation its estimated revenue will be 100*73401= 7340100 dollars, assuming 2000 students

apply annually.

Result Analysis

After generating the answer report in excel, we were able to observe the status of all constraints

to which the objective function is subjected. These information are listed in the table below.

Xij Constraints

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Name Cell Value Formula Status Slack

Xij constraint E153134 1 $AD$678=1 Binding 0

Xij constraint E133134 1 $Z$678=1 Binding 0

Xij constraint E173134 1 $AH$678=1 Binding 0

Xij constraint E193134 1 $AL$678=1 Binding 0

X11 1 Total Fall Capacity 2 $AP$507<=$AR$507 Binding 0

Xij constraint x141 1 $BB$678=1 Binding 0

Xij constraint x151 1 $BF$678=1 Binding 0

Xij constraint Total Fall Capacity 1 $AP$678=1 Binding 0

Xij constraint x161 1 $BJ$678=1 Binding 0

Xij constraint E113134 1 $V$678=1 Binding 0

Xij constraint x181 1 $BR$678=1 Binding 0

Xij constraint i=3 1 $F$678=1 Binding 0

Xij constraint Total Winter Capacity

1 $AT$678=1 Binding 0

Xij constraint E93134 1 $R$678=1 Binding 0

Xij constraint R131 1 $AX$678=1 Binding 0

Xij constraint x201 1 $BZ$678=1 Binding 0

Xij constraint x191 1 $BV$678=1 Binding 0

Xij constraint Q1 1 $B$678=1 Binding 0

Xij constraint i=5 1 $J$678=1 Binding 0

Xij constraint x171 1 $BN$678=1 Binding 0

Xij constraint i=7 1 $N$678=1 Binding 0

Xij constraints are all binding since the housing department is forced to take exactly 1 decision

for each applicant.

Fall Capacity Constraints


X11 1 Total Fall Capacity 2 $AP$507<=$AR$507 Binding 0

Total Fall Capacity 1 $AP$511<=$AR$511 Binding 0



Total Fall Capacity 1 $AP$523<=$AR$523 Not Binding

1


2


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1



1


5


1


In the fall capacity constraints, it’s shown that room types 1, 2, 3, 4, 7, 9, 11 and 13 are binding

which means that they are fully booked for the fall semester. Therefore, according to our results,

the binding constraints represent the most desirable and profitable room options. So, if the

housing department has the choice to increase the capacity of certain room types, it must go with

the above mention options.

Extra capacity was still found in room types 5, 6, 8, 10, and 12, which is not the real life scenario

since the demand will greatly surplus the capacity. Thus rarely will we get empty capacity in any

room.

Winter Capacity


<= Total Winter Capacity 1 $AT$507<=$AV$507 Not Binding 1

<= Total Winter Capacity 1 $AT$519<=$AV$519 Binding 0 <= Total Winter Capacity 0 $AT$511<=$AV$511 Not Binding 1 <= Total Winter Capacity 1 $AT$515<=$AV$515 Binding 0 <= Total Winter Capacity 1 $AT$523<=$AV$523 Not Binding 1 <= Total Winter Capacity 0 $AT$527<=$AV$527 Not Binding 4 <= Total Winter Capacity 0 $AT$539<=$AV$539 Not Binding 1 <= Total Winter Capacity 2 $AT$531<=$AV$531 Not Binding 1 <= Total Winter Capacity 0 $AT$543<=$AV$543 Not Binding 1 <= Total Winter Capacity 0 $AT$535<=$AV$535 Not Binding 1 <= Total Winter Capacity 3 $AT$551<=$AV$551 Not Binding 4 <= Total Winter Capacity 0 $AT$555<=$AV$555 Not Binding 1 <= Total Winter Capacity 1 $AT$547<=$AV$547 Binding 0

As for the winter capacity, room types 3, 4 and 11 are the only fully booked rooms and the rest

have extra empty rooms that are not use. We notice that we have more vacancies in the winter

and thus the housing department must suggest certain offers to attract more students for the

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winter semester, contract types 3 and 4 seeking certain types of rooms that are not currently

occupied by the fall annual students, which are usually much lower than those applying in the

fall semester. Another way to improve this situation, is to accept more students for annual fall

contract type to compensate for the low demand in the winter.

The results we attained are bit exaggerated as compared to real life case, since usually the

number of applying students greatly surpluses the room capacity, so we will rarely end up with

room types that remained unoccupied. This is due to the reduction in the number of students to

only 14 students in the fall and 6 in the winter.

Quality Constraints


Fall Quality Constraint R22 0.785714286 $G$672>=$I$672 Not Binding

0.185714286

Winter Quality Constraint R22 0.75 $G$674>=$I$674 Not Binding

0.15

As shown above both satisfaction rates are very good and higher than our suggested standards.

However, still the satisfaction rate is higher in the fall semester, since the rejection ratio is lower

than the winter. In real life examples this is the case, since students applying in the winter will

have less vacancies due to fall annual applicants.

Conclusion and Future Direction As previously mentioned, the purpose of our project is to maximize profit of all available campus

rooms while also providing the student with their optimal room selection. We have described a

linear program (LP) model that highlights both of these requirements, profit optimization and

student preference constraints. As illustrated above, the model accounts for a selection of rooms

the university has available at the start of the academic school year beginning in the fall

semester. For students that may want housing in the winter semester only or for any student that

may have been rejected for housing in the fall semester, the LP model adjust for the room

availability in the winter semester as well. In addition, the student has the opportunity for

predilection of their first, second, or third housing choice. This allows for optimal room

selection based on the student’s preference. Based on our LP model created in MS Excel, we

were able to simulate the optimal solutions. Using a sample rather than the actual population of

available rooms and student housing applicants, the model illustrates the financial benefit to the

university as well as the ratio of students that would receive their first housing choice. Although

we don’t have data to compare the university’s actual housing profit, if we were to assume 2000

students applied annually to campus housing, this LP model estimates over $7 million total in

annual revenue. For both fall and winter semesters, around 1429 students would receive their

first housing choice, an estimated 285 students would receive their third housing choice, and the

remaining 285 students would be rejected for housing. The rejection percentage is less than

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15%, while the student satisfaction for first choice room selection is over 70%, and all campus

rooms would be completely occupied.

Looking towards the future, we would like to be allowed to use actual revenue data as well as

student applicant data from the WSU Office of Housing & Residential Life to more accurately

develop our LP model to reflect the data. In addition, we are planning to suggest on the

department a student tool whose aim is to allow applying student to optimize his choice between

the different options of campus rooms based on cost, location, roommate preference, dorm

amenities, etc. As a preliminary design for the above mention linear program, our team has

formulated it as follows:

Decision variables are binary variables and are as follows:

Xij Choose fall annual enrolment for room category I in building j

Yij Choose Winter annual enrolment for room category I in building j

Zij Choose fall alone enrolment for room category I in building j

Kij Choose winter alone enrolment for room category I in building j

The table below defines the constant factors required for this model:

aij Annual cost of room category I in building j

cij Semester cost of room category I in building j

qij Fraction of satisfaction of room category I in building j

rij Level of risk associated with each room category

tij Waiting time for room category I and j

Q Required Quality Ratio for category i

T Adequate waiting time for the reply

R Adequate level of risk of rejection

Constraints are as follows:

Objective Function Minimize Z= ∑i∑j aij*(Xij+Yij)+cij*(Zij+Kij)

Constraints

Quality ∑i∑j qij*(Xij+Yij+Zij+Kij)>= Q

Risk ∑i∑j rij*(Xij+Yij+Zij+Kij)<= R

Fall Room ∑i∑j Xij+Yij+Zij=1

Winter Room ∑i∑j Xij+Yij+Kij=1

Also, we would like to allow for a “second round” of room option selection. What we mean, if

the student’s first, second, or third option was not selected, instead of rejecting the student from

campus housing as our current model suggest, we would provide the student with the remaining

available room options to choose from. The student would then select from the remaining

available room options (outside of their first three choices) or decline campus housing. This

option not only allows the student to remain in campus housing but also increases the profit for

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rooms that are less desirable. After obtaining this data and adjusting our LP model to reflect the

changes, we believe our model will maximize WSU’s housing revenue and substantially increase

housing satisfaction amongst student applicants.

Appendix-A

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Appendix-B

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References

1. Jingpu Song, Qingda Yuan, and Shuang Chen. Carlson Rezidor Hotel Group Maximizes

Revenue Through Improved Demand Management and Price Optimization. Interfaces,

Vol. 43, No. 1, 2013, pp. 21–36.

2. Ma Hanwu and Zhang Peng. The Research of Economy Hotel in One City Room Allocation

and Global Optimization Based on Revenue Management. 2010 7th

International

Conference on Service Systems and Service Management (ICSSSM), 28-30 June 2010, pp. 1

– 6, Tokyo, Print ISBN: 978-1-4244-6485-2, INSPEC Accession Number: 11447610, Digital

Object Identifier : 10.1109/ICSSSM.2010.5530181

3. Raeside R, and Windle D. Quantitative aspects of yield management. In: Ingold, et al.,

editors, Yield management: strategies for service industries, 2nd

ed. London: Cassell; 2000.

4. Stephen Mahar, Wayne Winston, and P. Daniel Wright. Eli Lilly and Company Uses Integer

Programming to Form Volunteer Teams in Impoverished Countries. Interfaces, Vol. 43,

No. 3, 2013, pp. 268–284.

http://dx.doi.org/10.1109/ICSSSM.2010.5530181

project-example3.pdf

Documents

main campus housing

fall capacity constraints

management of student

g e introduction overview

xij constraints

quality constraints

winter capacity

g e contents introduction