Questions
Syllabus
Qns. By Syllabus

Semester

Subject

Year

Credit:Eli TamangEli Tamang

Tribhuwan University

Institute of Science and Technology

2082

Bachelor Level / Second Year / Fourth Semester / Science

Bachelors in Information Technology (ORS255)

(Operations Research)

Full Marks: 60

Pass Marks: 24

Time: 3 Hours

Candidates are required to give their answers in their own words as for as practicable.

The figures in the margin indicate full marks.

Section A

Long Answers Questions

Attempt any TWO questions.
[2*10=20]
1.
A small cafe sells freshly made vegetable sandwiches each day. Unsold sandwiches cannot be stored overnight and thus become worthless at the end of the day. Following is the distribution of the daily demand for sandwiches observed over 100 days.
Daily  demand220230240250260No.  of  days520303510\begin{array}{|c|ccccc|}\hline Daily\;demand & 220 & 230 & 240 & 250 & 260 \\ \hline No.\;of\;days & 5 & 20 & 30 & 35 & 10 \\ \hline \end{array}
(a)  Find  the  optimal  quantity  that  will  maximize  the  expected  profit.(a)\;Find\;the\;optimal\;quantity\;that\;will\;maximize\;the\;expected\;profit.
(b)  Find  the  expected  profit  with  perfect  information  (EPPI).(b)\;Find\;the\;expected\;profit\;with\;perfect\;information\;(EPPI).
(c)  Find  the  expected  value  of  perfect  information  (EVPL).(c)\;Find\;the\;expected\;value\;of\;perfect\;information\;(EVPL).
[10]
2.
A software company is working on two new IT projects – Project A (Mobile App) and Project B (Web Portal). Each project generates profit contributions of Rs. 20,000 per unit for Project A and Rs. 30,000 per unit for Project B. Both projects require resources from three specialized departments: Design (D1), Programming (D2), and Testing (D3). Project A requires 3 hours of design department, 5 hours of programming department and 2 hours of testing department while Project B requires 3 hours of design department, 2 hours of programming department and 6 hours of testing department. The available time in hours per week are 36, 50 and 60 for the department of design, programming and testing respectively. Formulate this problem as a L.P.P. How should the company schedule his production in order to maximize contribution? Use simplex method. [10]
3.
The table below represent the profit of a company earned from different plants to different market. Develop a transportation schedule that maximizes the profit of the company.
Plants/MarketM1M2M3Supply  (units)P1222524170P2152018130P3302120100Demand  (units)200130120400/450\begin{array}{|c|ccc|c|}\hline Plants/Market & M1 & M2 & M3 & Supply\;(units) \\ \hline P1 & 22 & 25 & 24 & 170 \\ \hline P2 & 15 & 20 & 18 & 130 \\ \hline P3 & 30 & 21 & 20 & 100 \\ \hline Demand\;(units) & 200 & 130 & 120 & 400/450 \\ \hline \end{array}
[10]
Section B

Short Answers Questions

Attempt any Eight questions.
[8*5=40]
4.
A publication employs typist on hourly basis. There are five typists for service and their charges are different. According to earlier understanding, only one job is given to one typist. Find the least cost allocation for the following data.
Typists/JobsPQRSTA85756512575B90786613278C75665711469D80726012072E76645611268\begin{array}{|c|ccccc|}\hline Typists/Jobs & P & Q & R & S & T \\ \hline A & 85 & 75 & 65 & 125 & 75 \\ \hline B & 90 & 78 & 66 & 132 & 78 \\ \hline C & 75 & 66 & 57 & 114 & 69 \\ \hline D & 80 & 72 & 60 & 120 & 72 \\ \hline E & 76 & 64 & 56 & 112 & 68 \\ \hline \end{array}
[5]
5.
In a certain bank, customers arrive in a Poisson fashion with an average time of 20 minutes between arrivals of the customers. The service time of the bank cashier follows the exponential distribution with mean time 15 minutes. Under the assumptions of single channel queuing model, find
(a)  The  average  time  spent  by  a  customer  in  the  queue.(a)\;The\;average\;time\;spent\;by\;a\;customer\;in\;the\;queue.
(b)  The  probability  that  there  are  3  customers  in  the  bank.(b)\;The\;probability\;that\;there\;are\;3\;customers\;in\;the\;bank.
[5]
6.
Considering this information, answers the question given below.
Player  A′s  strategy/Player  B′s  strategyB1B2B3B4B5A120202012080A280−20−406060A3−60−402020140A412080−6060140\begin{array}{|c|ccccc|}\hline Player\;A's\;strategy/Player\;B's\;strategy & B_1 & B_2 & B_3 & B_4 & B_5 \\ \hline A_1 & 20 & 20 & 20 & 120 & 80 \\ \hline A_2 & 80 & -20 & -40 & 60 & 60 \\ \hline A_3 & -60 & -40 & 20 & 20 & 140 \\ \hline A_4 & 120 & 80 & -60 & 60 & 140 \\ \hline \end{array}
(a)  What  would  be  the  optimal  strategy  for  each  player?(a)\;What\;would\;be\;the\;optimal\;strategy\;for\;each\;player?
(b)  What  is  value  of  the  game?(b)\;What\;is\;value\;of\;the\;game?
[5]
7.
The table given below gives the information about the activities, their predecessors and time duration required to complete the activities of the project. Find the shortest time duration of the project within which the project can be completed.
ActivityABCDEFGPredecessor−−BBBEA,D,CTime  (in  days)1881414161020\begin{array}{|c|ccccccc|}\hline Activity & A & B & C & D & E & F & G \\ \hline Predecessor & - & - & B & B & B & E & A,D,C \\ \hline Time\;(in\;days) & 18 & 8 & 14 & 14 & 16 & 10 & 20 \\ \hline \end{array}
[5]
8.
The TechZone Software Company combines two key resources - Front-End Developers (A) and Back-End Developers (B) - to complete a software system that must involve exactly 150 person-hours of total work. Each Front-End Developer hour costs Rs. 2,000, and each Back-End Developer hour costs Rs. 8,000. The company must use at least 14 hours of Back-End work and no more than 20 hours of Front-End work in a project. Formulate objective function and constraints of this LPP. [5]
9.
Describe modified distribution (MODI) method of obtaining the optimal solution of transportation problem. [5]
10.
Describe different operation characteristics of single channel queuing model. [5]
11.
Describe the dominance rule of solving game theory problem. [5]
12.
Write short notes on: (a) Vogel's Approximation Method (VAM) (b) Objectives of operations research [0+2.5+2.5]