Chapter 6, Problem 6P

A furniture factory makes two types of wooden tables, large and small. See the flowchart below.

	Setup Time, Minutes	Run Time per Piece, Minutes	Capacity, Pieces per Hour
Wood cutting	30	5	15
Male four legs	60	10	10
Male tops	60	12	8
Finish the wood	20	8	12
Assemble and ship	20	17	14

Small tables are made in batches of 100, and large tables are made in batches of 50. A batch includes a fixed setup time for the entire batch at each process step and a run time for each piece in the batch. Both large and small tables have the same processing times. The capacities of each process step are given, and apply to production of either type of table, as shown in the flowchart.

1. a. What is the capacity of the system, and what is the bottleneck?
2. b. What are the throughput times for batches of large and small tables?
3. c. When producing at a rate of six small tables per hour on average, how many tables will be in the system?

Summary Introduction

To determine: The capacity of the process.

Introduction:

Flow rate is the number of flow units through a business procedure per unit time. Flow rate refers to the number of customers who will be served per hour or the parts produced per minute.

Explanation of Solution

Given information:

A furniture factory makes large and small wooden tables. The given information is tabulated below:

	Setup time (Minutes)	Run time per piece (Minutes)	Capacity (Pieces per hour)
Wood cutting	30	5	15
Make four legs	60	10	10
Make tops	60	12	8
Finish the wood	20	8	12
Assemble and ship	20	17	14

Small wooden tables are finished in batches of 100 and large wooden tables are finished in the batches of 50. A batch includes fixed setup time and run time. Both small tables and large tables have the same processing time.

Determine the capacity:

As both large wooden table and small wooden table have same capacities, the capacity of the system is minimum of the capacity of the resources. The minimum capacity resource is 8 tables per hour and the process is making tops.

	Setup time (Minutes)	Run time per piece (Minutes)	Capacity (Pieces per hour)
Wood cutting	30	5	15
Make four legs	60	10	10
Make tops	60	12	8
Finish the wood	20	8	12
Assemble and ship	20	17	14

Summary Introduction

To determine: The average throughput time.

Introduction:

Flow rate is the number of flow units through a business procedure per unit time. Flow rate refers to the number of customers who will be served per hour or the parts produced per minute.

Explanation of Solution

Given information:

A furniture factory makes large and small wooden tables. The given information is tabulated below:

	Setup time (Minutes)	Run time per piece (Minutes)	Capacity (Pieces per hour)
Wood cutting	30	5	15
Make four legs	60	10	10
Make tops	60	12	8
Finish the wood	20	8	12
Assemble and ship	20	17	14

Small wooden tables are finished in the batches of 100 and large wooden tables are finished in the batches of 50. A batch includes fixed setup time and run time. Both small tables and large tables have the same processing time.

Determine the average throughput time:

	Small tables	Large tables
Batch size	100	50
Wood cutting	530	280
Make four legs	1,060	560
Make tops	1,260	660
Finish the wood	820	420
Assemble and ship	1,720	870
Total time	4,330	2,230

Hence, the average throughput time for small tables is 4,330 minutes and the average throughput time for large tables is 2,230 minutes.

Working note:

Wood cutting for small tables:

It is calculated by adding the setup time to the multiplied value of run time and batch size.

$\begin{array}{c}\text{Wood cutting for small tables}=\text{Setup time}+\left(\text{Run time}\times \text{Batch size}\right)\\ =30+\left(5\times 100\right)\\ =30+500\\ =530\end{array}$

Wood cutting for large tables:

It is calculated by adding the setup time to the multiplied value of run time and batch size.

$\begin{array}{c}\text{Wood cutting for small tables}=\text{Setup time}+\left(\text{Run time}\times \text{Batch size}\right)\\ =30+\left(5\times 50\right)\\ =30+250\\ =280\end{array}$

Note: The calculation is carried out for all the processes.

Compute the throughput time for small tables:

While adding the time taken, the maximum amount should be chosen from the process of making four legs and tops, as they can be done in parallel.

$\begin{array}{c}\text{Throughput time}=530+1,260+820+1,720\\ =4,330\end{array}$

Compute the throughput time for large tables:

While adding the time taken, the maximum amount should be chosen from the process of making four legs and tops, as they can be done in parallel.

$\begin{array}{c}\text{Throughput time}=280+660+420+870\\ =2,230\end{array}$

Summary Introduction

To determine: The number of tables in the system.

Introduction:

Flow rate is the number of flow units through a business procedure per unit time. Flow rate refers to the number of customers who will be served per hour or the parts produced per minute.

Explanation of Solution

Given information:

A furniture factory makes large and small wooden tables. The given information is tabulated below:

	Setup time (Minutes)	Run time per piece (Minutes)	Capacity (Pieces per hour)
Wood cutting	30	5	15
Make four legs	60	10	10
Make tops	60	12	8
Finish the wood	20	8	12
Assemble and ship	20	17	14

Small wooden tables are finished in the batches of 100 and large wooden tables are finished in the batches of 50. A batch includes fixed setup time and run time. Both small tables and large tables have the same processing time. The factory is producing at the rate of six small tables per hour.

Formula to determine the average number of tables in the system:

$\text{I}=\text{T}\times \text{R}$

Here

I refers to the number of orders in the systems.

T refers to the average throughout time.

R refers to the average flow rate in the process.

Determine the average number of tables in the system:

It calculated by multiplying the average throughput time with the average flow rate in the process.

$\begin{array}{c}\text{I}=\text{T}\times \text{R}\\ =\left(\frac{4,330}{60}\right)\times 6\\ =72.167\times 6\\ =433\text{ tables}\end{array}$

Hence, the average number of tables in the system is 433 tables.