Descripción del problema

On April 16, 2016, a hot and humid afternoon, Srikanth Rao, the owner of Apoorva Mess 1
(Apoorva) in Manipal, India, looked out his office window, lost in thought. The ever-increasing
competition in the fast food industry was taking its toll on his business, a fact that was reflected
in falling sales figures over the past couple of months. As in the past few years, Rao worried that
this year his business would again be affected by upcoming summer vacations in Manipal. He
was constantly thinking about opening a full-service economical restaurant and taking Apoorva
closer to his customers. He had six potential locations in mind, and he had even visited them
along with Apoorva’s manager, Avinash Poojari. However, he had not been able to pinpoint the
final location. He now had less than 48 hours to finalize the location, as he had to inform
investors of his decision during the much-awaited investor meeting scheduled for April 18. Rao
wanted an in-depth evaluation of these potential locations before the meeting.

BACKGROUND

Apoorva started operations in early 1993 with a single outlet near Tiger Circle, Manipal. Rao
partnered with one of his friends to set up a food business catering to the students of T. A. Pai
Management Institute (TAPMI). Apoorva’s focus on hygiene and food quality won over the
students, and soon the business took off. Rao took care to provide personalized services, a fact that
was well appreciated by his customers. Within a short period, Apoorva’s customer base rose to 900.
Soon, Rao was able to set up two more cafés near the Manipal Institute of Technology campus.
Apoorva experienced a steady growth in revenue (see Exhibit 1).

In 2009, TAPMI relocated to a spacious, lush, and green 40-acre campus, 5 kilometres
from Manipal. By then, Rao had increased his customer base to 1,800 on the Manipal
Institute of Technology campus and added another 300 customers from the new TAPMI
campus. Poojari, a young, dynamic management graduate, joined him to look after the
three facilities at the two different locations. Unfortunately, in 2010, Rao suffered a road
accident and was confined to bed for almost a year. The business began to suffer a dip
in sales. To make matters worse, the contracts with both the Manipal Institute of
Technology women’s and men’s hostels were not renewed. Poojari was asked to run
Rao’s business at Manipal.
On April 16, 2016, a hot and humid afternoon, Srikanth Rao, the owner of Apoorva Mess 1
(Apoorva) in Manipal, India, looked out his office window, lost in thought. The ever-increasing
competition in the fast food industry was taking its toll on his business, a fact that was reflected
in falling sales figures over the past couple of months. As in the past few years, Rao worried that
this year his business would again be affected by upcoming summer vacations in Manipal. He
was constantly thinking about opening a full-service economical restaurant and taking Apoorva
closer to his customers. He had six potential locations in mind, and he had even visited them
along with Apoorva’s manager, Avinash Poojari. However, he had not been able to pinpoint the
final location. He now had less than 48 hours to finalize the location, as he had to inform
investors of his decision during the much-awaited investor meeting scheduled for April 18. Rao
wanted an in-depth evaluation of these potential locations before the meeting.

BACKGROUND

Apoorva started operations in early 1993 with a single outlet near Tiger Circle, Manipal. Rao
partnered with one of his friends to set up a food business catering to the students of T. A. Pai
Management Institute (TAPMI). Apoorva’s focus on hygiene and food quality won over the
students, and soon the business took off. Rao took care to provide personalized services, a fact that
was well appreciated by his customers. Within a short period, Apoorva’s customer base rose to 900.
Soon, Rao was able to set up two more cafés near the Manipal Institute of Technology campus.
Apoorva experienced a steady growth in revenue (see Exhibit 1).

In 2009, TAPMI relocated to a spacious, lush, and green 40-acre campus, 5 kilometres from
Manipal. By then, Rao had increased his customer base to 1,800 on the Manipal Institute of
Technology campus and added another 300 customers from the new TAPMI campus. Poojari, a
young, dynamic management graduate, joined him to look after the three facilities at the two
different locations. Unfortunately, in 2010, Rao suffered a road accident and was confined to
bed for almost a year. The business began to suffer a dip in sales. To make matters worse, the
contracts with both the Manipal Institute of Technology women’s and men’s hostels were not
renewed. Poojari was asked to run Rao’s business at Manipal.
Poojari was a conscientious worker, and was admired by both employees and customers. To
improve sales, he experimented with different flavours and dishes on the menu. He ushered in
some tactical changes, all of which translated into a steady growth in revenue. He introduced
innovations such as sponsoring food and beverages for participants in social events, which
further increased Apoorva’s visibility and brought in more customers. He went the extra mile to
please customers and often interacted with them to understand their requirements, even
customizing some dishes to their tastes. This led to the creation of one of Apoorva’s signature
dishes, the Bombay Tawa Sandwich, which was popular with customers.

Ninety per cent of Apoorva’s customers were undergraduate and postgraduate students of
Manipal. The average ticket price for registered members at Apoorva was ₹135,2 whereas for
others it was ₹170. Most of the un-registered members were medical patients, labourers, and
friends of members from around the Manipal–Udupi region. While they enjoyed the food and
services of the mess, they often complained that the distance from the town was a major factor
that dissuaded them from visiting more frequently. Some of them even requested that Rao bring
Apoorva closer to their locations.

ABOUT MANIPAL

Manipal was a small suburb in the district of Udupi, Karnataka, with an area of 26 square
kilometres and a population of just over 37,000 (see Exhibit 2). Known as the “university town,”
Manipal housed some of the leading educational institutes in the country, including the Manipal
Institute of Technology, Kasturba Medical College, and TAPMI. The student community
constituted over 75 per cent of the town’s population, with around 7,000 international students
from 60 different countries (see Exhibit 3).3 The average student age was 22, and most students
belonged to the upper middle class of society.

Besides their diverse student population, Manipal and Udupi (3.5 kilometres from Manipal) had
witnessed a surge in medical tourism, as both of these towns attracted many patients from India
and the South Asian Association for Regional Cooperation (SAARC) countries, who came for
allopathic and alternative medicine treatments. In addition, the government and corporate
businesses invested in infrastructure projects in this region, which brought a huge migratory
labour force to the region, mostly from the northern and eastern states of the country. The
ancient Udupi Krishna temple and other spiritual places also brought in their share of domestic
and international tourists.4
Since Manipal was located near the Western Ghats and the western coast, it witnessed tropical
weather conditions, with a hot and humid summer and heavy rainfall from June to September.
The rainy season generally affected the public transport system, resulting in the closure of
schools and colleges.

COMPETITION

In the past few decades, Apoorva had enjoyed a distinct advantage in catering to the Manipal
Institute of Technology students, and a monopoly with respect to TAPMI. However, in recent
years, many domestic and international fast-food restaurant chains such as Mavalli Tiffin Room,
Sagar Ratna, Kentucky Fried Chicken, Subway, Pizza Hut, Domino’s Pizza Inc., and Café
Coffee Day had opened outlets in the region, causing a temporary dip in business for Apoorva.
After each such dip, Apoorva had managed to bounce back. Yet the pressure was beginning to
grow, especially considering that these established brands had better logistics, including home
delivery, that were denting Apoorva’s business. Online food aggregators, too, had entered into
the arena, further harming Apoorva.

With a change in TAPMI leadership in January 2016, the institution insisted on giving more
options to its 900+ students and allowed three more vendors to cater to the same set of
customers. In February 2016, the monthly subscription plan also underwent a change. It was
replaced by a daily plan that gave students the power to choose from one of the four vendors for
a day. Though Rao kept the day’s price reasonable (₹140) compared to Madhuvan Serai (₹180)
and the other two vendors (₹200), the daily plan affected Apoorva’s revenue in these two
months.

SELECTING A FACILITY LOCATION

Rao had always wanted to open a full-service economical restaurant in the Manipal–Udupi
region, but was unable to give shape to his dream as he was bed-ridden from the accident. Over
the years, Rao had served the students of Manipal; however, he had always wanted to cater to
the needs of the lower middle class by providing them with hygienic food at affordable rates.
For these people—daily wage workers, patients, and budget tourists—high-priced domestic and
international food venues were out of their budgets; also, roadside food stalls offered unhygienic
food that could have adversely affected their health.

Now that Poojari was successfully taking care of his existing business, Rao turned his attention
to fulfilling his dream. With the price of land in Manipal reaching a very high level, he felt that
places around Udupi or Parkala–Hiriadka would be more reasonable, and that the competition
would be more manageable. Also, apart from fulfilling the demands of his existing customers in
this region, he would be able to fulfill his dream of serving quality food to a lower demographic.
Over the past year, he had contacted several property dealers and shortlisted six potential
locations around the area. In January 2016, he visited all six locations to identify the one that
would be best for his new restaurant (see Exhibit 4).

Based on his 20 years of experience running the mess and café, Rao knew that the three most
important criteria for setting up a restaurant were space within the facility, parking space outside
the facility, and the ability to serve hot and fresh food to customers not only in the restaurant but
also through home delivery. He believed that a good facility should have around 1,000 square
feet of carpeted area and a parking lot one and a half times the size of the facility. He also
believed the average time required for home delivery should not be long. However, he still felt
unsure, because all of his experience was based on running a mess for students at a university.
Would it be sufficient to launch a successful business with a different clientele and a different
location? He knew his strength was not in the local cuisine, so he would have to focus more on
tourists, patients, students, and migratory labourers from other states rather than on locals.

In February, he approached a market research agency in Manipal, BrandScan, to help him

identify the best location. He knew that the cost of land across these six potential locations
might vary a little. However, he believed that a prominent location was the key to success for
this type of business, and asked that the agency not focus on the land cost.

After conducting a two-phase survey—one with restaurant owners in Manipal–Udupi and

nearby regions, and the other with the customers in these locations—the BrandScan team
submitted a report to Rao in the first week of April. The report detailed the customer segments
(see Exhibit 5A) and the set of criteria for evaluation, along with their importance in selecting
the restaurant location (see Exhibit 5B). Rao wanted a thorough assessment of these six
potential locations before making the final decision, understanding fully
that the wrong choice would spell disaster for his business in the long run. He asked Poojari to
gather the details of the locations corresponding to the criteria recommended by the survey
report and submit it to him by April 16, 2016.

Rao was apprehensive about giving equal weight to the criteria in evaluating these locations.
However, the research report recommended differential weights to be given to the criteria in
selecting the best location. With only one day to evaluate and pinpoint the final location before
the investor meeting, he knew he would have to work late.

Rao’s chain of thoughts was broken by the sudden entry of Poojari carrying the assessment
report (see Exhibit 6). Looking anxious, he told Rao, “Sir, we have to decide fast. I just heard
that a couple of restaurants are opening up by the end of this monsoon season.”

Justificación y supuestos del problema

Como se señaló en la descripción, el contexto de la situación se basa en los siguiente supuestos
que se utilizarán para la construcción del modelo:
o Se cuenta con un reporte de análisis de mercado realizado por una empresa tercera en el
que se detallan 8 factores críticos para identificar la mejor ubicación; de ahí que se ha
seleccionado un modelo de programación lineal por metas.
o En dicho reporte, la empresa tercera asignó pesos a cada criterio; por ello, se ha optado
por una solución por ponderaciones.
o Asimismo, el dueño del restaurante considera que las ponderaciones deberían ser
iguales; de esta forma se formulará otro modelo considerando que todas valen lo mismo
y se compararán los resultados.
 o El reporte también incluye la media de cada criterio; por ende, se construirán las metas
considerando a las medias como el mínimo o el máximo deseado según sea el caso
de optimización.
o Asimismo, las desviaciones estándar que se proveen serán consideradas durante la
interpretación de los resultados del modelo. La desviación estándar fungirá como
un intervalo de aceptación para las variables de desviación que se pretenden
minimizar. Por ejemplo, si no fue posible minimizar una variable de desviación pero su
valor quedó dentro de la desviación estándar para ese criterio, la interpretación será que la
meta sí se cumplió.
o El reporte de Poojari muestra la medición de cada criterio para cada ubicación; de ahí que
es posible utilizar dichos valores como coeficientes de cada término en la
construcción de las metas.
o Debido a que se tiene que decidir la ubicación óptima, las variables de decisión
serán dichas ubicaciones y pueden adquirir sólo dos valores (1 si se selecciona, 0 si
no se selecciona).
o Debido a que sólo se puede seleccionar una ubicación, se construirá una
restricción dura que asegure que las variables de decisión sumadas sean igual a 1.
Variables de decisión
0 𝐿𝑎 𝑢𝑏𝑖𝑐𝑎𝑐𝑖ó𝑛 𝑖 𝑛𝑜 𝑒𝑠 𝑠𝑒𝑙𝑒𝑐𝑐𝑖𝑜𝑛𝑎𝑑𝑎
𝑋𝑖 {
1 𝐿𝑎 𝑢𝑏𝑖𝑐𝑎𝑐𝑖ó𝑛 𝑖 𝑒𝑠 𝑠𝑒𝑙𝑒𝑐𝑐𝑖𝑜𝑛𝑎𝑑𝑎
𝑖=
1: 𝑇ℎ𝑒𝑛𝑘𝑝𝑒𝑡𝑒
2: 𝐾𝑢𝑛𝑗𝑖𝑏𝑒𝑡𝑡𝑢
3: 𝐻𝑖𝑟𝑖𝑎𝑑𝑘𝑎
4: 𝐶ℎ𝑖𝑡𝑝𝑎𝑑𝑦
5: 𝐴𝑚𝑏𝑎𝑙𝑝𝑎𝑑𝑖
6: 𝑃𝑎𝑟𝑘𝑎𝑙𝑎
Restricciones (duras y flexibles)
R. flexible: Espacio dentro de las instalaciones (𝑓𝑡2)

7.2𝑋1+10.4𝑋2+12.5𝑋3+10.5𝑋4+9.5𝑋5+11.7𝑋6 ≥10.01
R. flexible: Espacio de estacionamiento fuera de las instalaciones(𝑓𝑡2)
8𝑋1+12𝑋2+15𝑋3+8.5𝑋4+12𝑋5+15𝑋6 ≥14.2
R. flexible: Tiempo de respuesta para entregar a domicilio (𝑚𝑖𝑛)

16𝑋1+16𝑋2+18𝑋3+16𝑋4+14.5𝑋5+18𝑋6 ≤13.50
R. flexible: Disponibilidad de infraestructura (1 − 10 𝑑𝑜𝑛𝑑𝑒 1 𝑒𝑠 𝑚𝑢𝑦 𝑏𝑎𝑗𝑜 𝑦 10 𝑒𝑥𝑐𝑒𝑙𝑒𝑛𝑡𝑒)
8.5𝑋1+ 9.5𝑋2+7𝑋3+8.5𝑋4+8.5𝑋5+7𝑋6 ≥7.25
R. flexible: Tamaño de población (𝑚𝑖𝑙𝑒𝑠 𝑑𝑒 𝑝𝑒𝑟𝑠𝑜𝑛𝑎𝑠)

20𝑋1+16𝑋2+15𝑋3+12.5𝑋4+13𝑋5+14𝑋6 ≥12.3
R. flexible: Disponibilidad de la red de carreteras (1 − 10 𝑑𝑜𝑛𝑑𝑒 1 𝑒𝑠 𝑚𝑢𝑦 𝑏𝑎𝑗𝑜 𝑦 10 𝑒𝑥𝑐𝑒𝑙𝑒𝑛𝑡𝑒)
9𝑋1+8𝑋2+6.5𝑋3+8.5𝑋4+8.5𝑋5+7𝑋6 ≥8.5
R. flexible: Número de competidores
9𝑋1+3𝑋2+5𝑋3+2𝑋4+1𝑋5+2𝑋6 ≤3.2
R. flexible: Distancia al mercado (𝑘𝑚)
2𝑋1+3.2𝑋2+15.4𝑋3+4𝑋4+2.5𝑋5+10.5𝑋6 ≤5.5
R. dura: Sólo es posible seleccionar una ubicación
𝑋1+𝑋2+𝑋3+𝑋4+𝑋5+𝑋6 =1

Metas y Restricciones
Espacio dentro de las instalaciones (𝑓𝑡2)
7.2𝑋1+10.4𝑋2+12.5𝑋3+10.5𝑋4+9.5𝑋5+11.7𝑋6 + 𝑠− −1 𝑠+ =10.01
1

Espacio de estacionamiento fuera de las instalaciones (𝑓𝑡2)

8𝑋1+12𝑋2+15𝑋3+8.5𝑋4+12𝑋5+15𝑋6 + 𝑠− − +
2 𝑠 =14.2
2

Tiempo de respuesta para entregar a domicilio (𝑚𝑖𝑛)

16𝑋1+16𝑋2+18𝑋3+16𝑋4+14.5𝑋5+18𝑋6 + 𝑠− − +
3 𝑠 =13.5
3

Disponibilidad de infraestructura (1 − 10 𝑑𝑜𝑛𝑑𝑒 1 𝑒𝑠 𝑚𝑢𝑦 𝑏𝑎𝑗𝑜 𝑦 10 𝑒𝑥𝑐𝑒𝑙𝑒𝑛𝑡𝑒)

8.5𝑋1+ 9.5𝑋2+7𝑋3+8.5𝑋4+8.5𝑋5+7𝑋6 + 𝑠− 4− 𝑠+ =7.25
4

Tamaño de población (𝑚𝑖𝑙𝑒𝑠 𝑑𝑒 𝑝𝑒𝑟𝑠𝑜𝑛𝑎𝑠)

20𝑋1+16𝑋2+15𝑋3+12.5𝑋4+13𝑋5+14𝑋6 + 𝑠− − 𝑠+ =12.3
5 5

Disponibilidad de la red de carreteras (1 − 10 𝑑𝑜𝑛𝑑𝑒 1 𝑒𝑠 𝑚𝑢𝑦 𝑏𝑎𝑗𝑜 𝑦 10 𝑒𝑥𝑐𝑒𝑙𝑒𝑛𝑡𝑒)

9𝑋1+8𝑋2+6.5𝑋3+8.5𝑋4+8.5𝑋5+7𝑋6 + 𝑠− −
6
𝑠+ =8.5
6

Número de competidores
9𝑋1+3𝑋2+5𝑋3+2𝑋4+1𝑋5+2𝑋6 + 𝑠− − 𝑠+ =3.2
7 7

Distancia al mercado (𝑘𝑚)

2𝑋1+3.2𝑋2+15.4𝑋3+4𝑋4+2.5𝑋5+10.5𝑋6 + 𝑠− − +
8 𝑠 =5.5
8
Sólo es posible seleccionar una ubicación
𝑋1+𝑋2+𝑋3+𝑋4+𝑋5+𝑋6 =1

Objetivos
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑟 𝐺1 = 𝑠1−
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑟 𝐺2 = 𝑠2−
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑟 𝐺3 = 𝑠3+
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑟 𝐺4 = 𝑠4−
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑟 𝐺5 = 𝑠5−
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑟 𝐺6 = 𝑠6−
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑟 𝐺7 = 𝑠7+
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑟 𝐺8 = 𝑠8+

Modelo
𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑟 𝑧 = 25𝑠− + 16𝑠− + 14𝑠+ + 9𝑠− + 12𝑠− + 10𝑠− + 10𝑠+ + 4𝑠+
1 2 3 4 5 6 7 8

s.a.:
7.2𝑋1+10.4𝑋2+12.5𝑋3+10.5𝑋4+9.5𝑋5+11.7𝑋6 + 𝑠− − 𝑠+ =10.01
1 1
8𝑋1+12𝑋2+15𝑋3+8.5𝑋4+12𝑋5+15𝑋6 + 𝑠 2− 𝑠 =14.2
−
2
+

16𝑋1+16𝑋2+18𝑋3+16𝑋4+14.5𝑋5+18𝑋6 + 𝑠 − − +
3 𝑠 =13.5
3
8.5𝑋1+ 9.5𝑋2+7𝑋3+8.5𝑋4+8.5𝑋5+7𝑋6 + 𝑠 −4− 𝑠 +4=7.25
− +

20𝑋1+16𝑋2+15𝑋3+12.5𝑋4+13𝑋5+14𝑋6 + 𝑠 − 𝑠 =12.3
5 5
9𝑋1+8𝑋2+6.5𝑋3+8.5𝑋4+8.5𝑋5+7𝑋6 + 𝑠 6− 𝑠 6=8.5
− +

9𝑋1+3𝑋2+5𝑋3+2𝑋4+1𝑋5+2𝑋6 + 𝑠−7− 𝑠+ 7=3.2

2𝑋1+3.2𝑋2+15.4𝑋3+4𝑋4+2.5𝑋5+10.5𝑋6 + 𝑠− − 𝑠+ =5.5
8 8
𝑋1+𝑋2+𝑋3+𝑋4+𝑋5+𝑋6 =1
𝑥−𝑖 ≥ +0, 𝑖 = 1,2,3,4,5,6
𝑠 , 𝑠 ≥ 0, 𝑖 = 1,2,3,4,5,6,7,8
𝑖 𝑖
Solución (ponderaciones distintas)
Solución (ponderaciones iguales)
Interpretación
Como es posible observar, para este problema no importa si el modelo tiene ponderaciones
diferentes o iguales pues se obtiene exactamente el mismo resultado. Es decir, en ambos casos
seleccionar 𝑋5 optimiza el modelo. Por ello, se dará una sola interpretación de los resultados por
variable.
Resulta Interpretaci
do ón
No fueron seleccionadas las ubicaciones (en el mismo orden que
𝑋1, 𝑋2, 𝑋3, 𝑋4, 𝑋6 las variables): Thenkpete, Kunjibettu, Hiriadka, Chitpady y
=0 Parkala

𝑋6 = 1 Se seleccionó la ubicación Ambalpadi

Por 0.51 ft2 no se alcanzó la meta de que el espacio de las

instalaciones fuera mayor o igual a 10.01 ft2.
𝑠−1= 0.51
𝑠+ = 0 Después de analizar la desviación estándar (0.5), se sigue
1
concluyendo que no se alcanzó la meta pues la variable de
desviación superó a la desviación estándar.
Por 2.20 ft2 no se alcanzó la meta de que el espacio del
estacionamiento fuera mayor o igual a 14.20 ft2. Además, la
𝑠−2= 2.20 variable de desviación superó la desviación estándar.
𝑠+ = 0
2 Después de analizar la desviación estándar (2.15), se sigue
concluyendo que no se alcanzó la meta pues la variable de
desviación superó a la desviación estándar.
Por 1 minuto no se alcanzó la meta de que el tiempo de entrega a
domicilio fuera menor o igual a 13.5 min. Además, la variable de
𝑠−3= 0 desviación superó la desviación estándar.
𝑠+ = 1.0
3 Después de analizar la desviación estándar (0.75), se sigue
concluyendo que no se alcanzó la meta pues la variable de
desviación superó a la desviación estándar.

𝑠− = 0 Por 1.25 puntos se superó la meta de que la disponibilidad de la

+4
𝑠 = 1.25 infraestructura fuera mayor o igual a 7.25 puntos.
4

𝑠−5= 0 Por 0.7 (miles) de personas se superó la meta de que el tamaño de la

𝑠+ = 0.7 población objetivo fuera mayor o igual a 12.3 (miles) de personas.
5

𝑠6− = 0 Se igualó la meta de que el puntaje de la disponibilidad de

𝑠+ = 0 carreteras fuera mayor o igual a 8.5 puntos.
6
 𝑠− = Por 2.2 competidores se superó la meta de que el promedio de
2.20
7+ competidores fuera menor o igual a 3.2 competidores.
𝑠 =0
7

𝑠8− = 3.0 Por 3 kilómetros se superó la meta de que la distancia al

𝑠+ = 0 mercado fuera menor o igual a 5.5 kilómetros.
8

Recomendaciones
De acuerdo con los resultados obtenidos por medio de la programación por metas y utilizando la
función @bin podemos concluir que la mejor ubicación para el nuevo local es 𝐴𝑚𝑏𝑎𝑙𝑝𝑎𝑑𝑖 ya
que cumple con la mayoría de los requerimientos establecidos por Roa como la infraestructura, la
cantidad de clientes ubicados en dicha localidad, la facilidad para llegar y el número de
competidores presentes y la distancia al mercado.
A pesar de que no se cumplieron los criterios del espacio de las instalaciones, el espacio del
estacionamiento y el tiempo de entrega, escoger 𝐴𝑚𝑏𝑎𝑙𝑝𝑎𝑑𝑖 como la ubicación óptima asegura
que se cumplan la mayor cantidad de criterios.

Referencias
Mina, M. (agosto 2016). Modelación matemática. Una teoría para la práctica. UNC.
Recuperado de: https://www.famaf.unc.edu.ar/~revm/Volumen23/digital2333
Méndez, G. (junio 2016). ¿Cuáles son las ventajas de optimizar? GESTIONES Y
TENDENCIAS. Recuperado de: https://gestion.pe/tendencias/son-ventajas-optimizar
Método Heurísticos. (2018). Universidad Politécnica Nacional. Recuperado de:
https://www.ipn.mx
Programación por metas ponderadas o prioridades. (2017). Visual Mind. Recuperado de:
https://visualmind.com.mx/blog/ejemplo-practico-del-metodo-de-ponderacion
Anexos