Chapter 9, Problem 24P

a.

Summary Introduction

Interpretation:

The company that has the lowest bid and the total cost of that bid.

Concept Introduction:

Under linear averaging method score of each tender will be result of sum of individual score in each category multiplied by corresponding category weight.

Explanation of Solution

Given information:

A tender invitation for a consulting project was sent and four companies have done the bidding as below-

	Junior consultant hourly rate ($)	Hours provided by junior consultants (hr)	Senior consultant hourly rate ($)	Hours provided by senior consultants (hr)
Company A	$30$	$10$	150	10
Company B	$35$	$15$	250	6
Company C	$40$	$20$	300	2
Company D	$40$	$20$	200	4

Based on the bid provided four companies, total cost for all consulting hours is calculated as below-

	Junior consultant hourly rate ($)	Hours provided by junior consultants (hr)	Senior consultant hourly rate ($)	Hours provided by senior consultants (hr)	Total bid cost($)
Company A	$30$	$10$	150	10	$\left(30\times 10+150\times 10\right)=1800$
Company B	$35$	$15$	250	6	$\left(35\times 15+250\times 6\right)=2025$
Company C	$40$	$20$	300	2	$\left(40\times 20+300\times 2\right)=1400$
Company D	$40$	$20$	200	4	$\left(40\times 20+200\times 4\right)=1600$

Thus it is clear that the lowest bid is from company C and the bid amount is $\$1400$ .

b.

Summary Introduction

Interpretation:

The company that will take the fewest hours to complete the work and the hours is may take.

Concept Introduction:

Under linear averaging method score of each tender will be result of sum of individual score in each category multiplied by corresponding category weight.

Explanation of Solution

Given information:

A tender invitation for a consulting project was sent and four companies have done the bidding as below-

	Junior consultant hourly rate ($)	Hours provided by junior consultants (hr)	Senior consultant hourly rate ($)	Hours provided by senior consultants (hr)
Company A	$30$	$10$	150	10
Company B	$35$	$15$	250	6
Company C	$40$	$20$	300	2
Company D	$40$	$20$	200	4

Based on the bid provided four companies, total consulting hours is calculated as below-

	Junior consultant hourly rate ($)	Hours provided by junior consultants (hr)	Senior consultant hourly rate ($)	Hours provided by senior consultants (hr)	Total consulting hours
Company A	$30$	$10$	150	10	$10+10=20$
Company B	$35$	$15$	250	6	$15+6=21$
Company C	$40$	$20$	300	2	$20+2=22$
Company D	$40$	$20$	200	4	$20+4=24$

Thus it is clear that the company A will take least time of $20$ hours to complete the work.

c.

Summary Introduction

Interpretation:

Price score and quality score of the bid based on stated specification.

Concept Introduction:

Under linear averaging method score of each tender will be result of sum of individual score in each category multiplied by corresponding category weight.

Explanation of Solution

Given information:

A tender invitation for a consulting project was sent and four companies have done the bidding as below-

	Junior consultant hourly rate ($)	Hours provided by junior consultants (hr)	Senior consultant hourly rate ($)	Hours provided by senior consultants (hr)
Company A	$30$	$10$	150	10
Company B	$35$	$15$	250	6
Company C	$40$	$20$	300	2
Company D	$40$	$20$	200	4

For calculation of price score, each company is awarded $100$ points initially and then penalized $1$ point for every $\$25$ their price exceeds the lowest bid.

For calculation of quality score, the proportion of hours provided by senior consultant is multiplied by $100$ (rounded to the nearest integer).

Based on the bid provided four companies, total cost for all consulting hours is calculated as below-

	Junior consultant hourly rate ($)	Hours provided by junior consultants (hr)	Senior consultant hourly rate ($)	Hours provided by senior consultants (hr)	Total bid cost($)
Company A	$30$	$10$	150	10	$\left(30\times 10+150\times 10\right)=1800$
Company B	$35$	$15$	250	6	$\left(35\times 15+250\times 6\right)=2025$
Company C	$40$	$20$	300	2	$\left(40\times 20+300\times 2\right)=1400$
Company D	$40$	$20$	200	4	$\left(40\times 20+200\times 4\right)=1600$

Thus it is clear that the lowest bid is from company C and the bid amount is $\$1400$ .

For calculation of price score, each company is awarded $100$ points initially and then penalized $1$ point for every $\$25$ their price exceeds the lowest bid. The price score is calculated as below-

	Total bid cost($)	Difference with lowest bid($)	Penalty for price score	Price score
Company A	$1800$	$400$	$\frac{400}{25}=16$	$\left(100-16\right)=84$
Company B	$2025$	$625$	$\frac{625}{25}=25$	$\left(100-25\right)=75$
Company C	$1400$	$0$	$0$	$100$
Company D	$1600$	$200$	$\frac{200}{25}=8$	$\left(100-8\right)=92$

For calculation of quality score, the proportion of hours provided by senior consultant is multiplied by $100$ (rounded to the nearest integer).

	Hours provided by junior consultants (hr)	Hours provided by senior consultants (hr)	Proportion of hours provided by senior consultant	Quality score
Company A	$10$	10	$\frac{10}{10}=1$	$1\times 100=100$
Company B	$15$	6	$\frac{6}{15}=0.4$	$0.4\times 100=40$
Company C	$20$	2	$\frac{2}{20}=0.1$	$0.1\times 100=10$
Company D	$20$	4	$\frac{4}{20}=0.2$	$0.2\times 100=20$

Hence company B has worst price score of $75$ and company C has worst quality score of $10$ .

d.

Summary Introduction

Interpretation:

The company that would win the bid based $70\%$ weightage of price and $30\%$ weightage of quality.

Concept Introduction:

Under linear averaging method score of each tender will be result of sum of individual score in each category multiplied by corresponding category weight.

Explanation of Solution

Given information:

A tender invitation for a consulting project was sent and four companies have done the bidding as below-

	Junior consultant hourly rate ($)	Hours provided by junior consultants (hr)	Senior consultant hourly rate ($)	Hours provided by senior consultants (hr)
Company A	$30$	$10$	150	10
Company B	$35$	$15$	250	6
Company C	$40$	$20$	300	2
Company D	$40$	$20$	200	4

For calculation of price score, each company is awarded $100$ points initially and then penalized $1$ point for every $\$25$ their price exceeds the lowest bid.

For calculation of quality score, the proportion of hours provided by senior consultant is multiplied by $100$ (rounded to the nearest integer).

For finalizing the contract $70\%$ weightage is given to price score and $30\%$ weightage is given to quality score. Based on the bid provided four companies and method used for calculation of price score and quality, below table is calculated:

	Price score	Quality score	Weighted average score
Company A	$84$	$100$	$\left(84\times 0.70+100\times 0.30\right)=88.8$
Company B	$75$	$40$	$\left(75\times 0.70+40\times 0.30\right)=64.5$
Company C	$100$	$10$	$\left(100\times 0.70+10\times 0.30\right)=73$
Company D	$92$	$20$	$\left(92\times 0.70+20\times 0.30\right)=70.4$

Hence, company A has highest weighted average score and should be awarded with the contract.