BBA/B.Com Operations Research April 2024

Description

Operations Research

April 2024 Examination

 

 

Q1. A retail company operates several distribution centers (D1, D2, D3, and D4) and serves multiple retail stores (S1, S2, and S3). The shipping costs (in Rs.) per unit from each distribution center to each retail store are presented in the following table

 

	D1	D2	D3	D4	Supply
S1	19	30	50	10	7
S2	70	30	40	60	9
S3	40	8	70	20	18
Demand	5	8	7	14

 

Find the initial basic feasible solution using Vogel’s Approximation Method (VAM) for the given transportation problem. Post that, implement the stepping-stone method to find the optimal solution for the transportation problem. Calculate the total shipping cost for the optimal solution.   (10 marks)

 

Ans 1.

To find the initial basic feasible solution using Vogel’s Approximation Method (VAM), we start by calculating the penalty for each row and column. The penalty for each row is the difference between the two lowest costs in that row, and the penalty for each column is the difference between the two lowest costs in that column. We will use these penalties to determine which cells to allocate first.

Step 1: Calculate It is only half solved

 

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Q2.  A manufacturing company has several plants (P1, P2, and P3) and several warehouses

(WH1, WH2, WH3, and WH4) for distribution. The shipping costs (in Rs.) per unit from each plant to each warehouse are presented in the following table:

 

Source	WH1	WH2	WH3	WH4	Supply
P1	19	30	50	12	7
P2	70	30	40	60	10
P3	40	10	60	20	18
Requirement	5	8	7	15

 

 

Find  an  initial  feasible  solution  using  the  Northwest  Corner  Method  and  Least  Cost Method, and also determine the optimal solution using Modified Distribution (MODI) method.  (10 marks)

(Note- For each method, show the step-by-step calculations, allocations, and the total transportation cost for the final optimal solution)

Ans 2.

 

To solve this transportation problem, we will use three methods as you requested: the Northwest Corner Method, the Least Cost Method, and the Modified Distribution (MODI) Method. We’ll calculate the total transportation cost for each method. Let’s begin:

1. Northwest Corner Method

The Northwest Corner

 

 

Q3. A small project consisting of eight activities has the following characteristics: Time- Estimates (in weeks)

Activity	Preceding   activity	Most optimistic   time (a)	Most likely   time (m)	Most pessimistic   time (b)
A	None	2	4	12
B	None	10	12	26
C	A	8	9	10
D	A	10	15	20
E	A	7	7.5	11
F	B,C	9	9	9
G	D	3	3.5	7
H	E,F,G	5	5	5

 

PART a)  Prepare the activity schedule for the project and determine the critical path. (5 marks)

 

Ans 3a.

Introduction

In project management, creating an activity schedule and determining the critical path are essential steps in planning and executing a project efficiently. The given project, consisting of eight activities with varying time estimates, requires careful analysis to establish the sequence and duration of each activity. By applying the Critical Path Method (CPM), we can identify the longest stretch of dependent activities and forecast the shortest time possible to complete the project. This

 

 

PART b) Suppose a 30-week deadline is imposed, what is the probability that the project will be finished within the time limit?  Also, if the project manager wants to be

99% sure that the project is completed on the scheduled date, how many weeks before that date should he start the project work?  (5 marks)

Ans 3b.

To determine the probability that the project will be finished within the time limit, we can use the completion probability of the critical path activities. The completion probability of an activity is the probability that the activity will be completed on time, given its estimated duration and the time limit.

The completion probability of an activity is calculated as follows:

Completion