Intro to operations management (final exam today)

Chapter 9: Process Layout Design (From-To-Matrix)

Formula

Minimize Cost =  "#$%  "&$% Xij Cij

n = total number of work centers or departments

i, j = individual departments


Xij = number of loads moved from department i to department j

Cij = cost to move a load between department i and department j (distance * cost)

Chapter 9: Process Layout Design (From-To-Matrix)

Question 1.   Suppose we have 5 hospital departments. Assume that workers can’t move diagonally (through walls).

Assuming it costs $3/unit moved each unit distance

Departments

A: Receptionist

B: Waiting room

C: X-Ray

D: Exam room

E: Nurse station

The current layout looks like this

Patient and staff moved (load) per hour between work areas are shown below:

A B C D E

A - 5 2 4 1

B - 3 0 2

C - 0 0

D - 5

E -

Note: Loads could be the average number of patients that move between

the departments each hour.

a.   What is the hourly cost for this layout? b.   If the new layout looks like the chart below, what would be the hourly cost for the

new layout?

D

E

A

B C

A

B

D

E C

Chapter 9: Process Layout Design (From-To-Matrix)

Solution

Part a

Pair Load (X) Distance’s Cost (C) Cost (XC)

A-B 5 1x$3=$3 $15

A-C 2 3x$3=$9 $18

A-D 4 1x$3=$3 $12

A-E 1 2x$3=$6 $6

B-C 3 2x$3=$6 $18

B-D 0 2x$3=$6 $0

B-E 2 1x$3=$3 $6

C-D 0 2x$3=$6 $0

C-E 0 1x$3=$3 $0

D-E 5 1x$3=$3 $15

Hourly cost = 15+18+12+6+18+0+6+0+0+15 = $90

Part b:

Pair Load (X) Distance’s Cost (C) Cost (XC)

A-B 5 1x$3=$3 $15

A-C 2 2x$3=$6 $12

A-D 4 1x$3=$3 $12

A-E 1 2x$3=$6 $6

B-C 3 1x$3=$3 $9

B-D 0 2x$3=$6 0

B-E 2 1x$3=$3 $6

C-D 0 3x$3=$9 0

C-E 0 2x$3=$6 0

D-E 5 1x$3=$3 $15

Hourly cost = 15+12+12+6+9+0+6+0+0+15 = $75

Chapter 9: Process Layout Design (From-To-Matrix)

Question 2.   A job shop has four departments, A, B, C, and D. Assume it costs $1 to move 1 work piece 1 foot. Distances in feet between centers of the work

areas are show in the chart below:

A B C D

A - 5 10 7

B - - 6 8

C - - - 9

D - - - -

Workpieces (loads) moved per week between departments are shown below:

A B C D

A - 900 900 500

B - - 500 400

C - - - 700

D - - - -

What is the weekly total material handling cost of the layout?

Solution:

Pair Load (X) Distance’s Cost (C) Cost (XC)

A-B 900 5x$1=$5 $4500

A-C 900 10x$1=$10 $9000

A-D 500 7x$1=$7 $3500

B-C 500 6x$1=$6 $3000

B-D 400 8x$1=$8 $3200

C-D 700 9x$1=$9 $6300

The weekly total material handling cost of the layout:

Cost = 4500+9000+3500+3000+3200+6300 = $29,500

Chapter 9: Process Layout Design (From-To-Matrix)

Question 3.   An insurance claims processing center has 4 work centers, any of which can be placed into any of 4 physical departmental locations. Call the centers

1, 2, 3, and 4 the departments A, B, C, and D. The current set of assignments is

A-3, B-1, C-4, D-2

The (symmetric) matrix of departmental distances, in meters is shown below.

1 2 3 4 1 -- 5 30 20 2 -- 40 15 3 -- 50 4 --

The matrix of work flow (estimated trips per day) among centers is shown below.

A B C D A -- 35 20 30 B -- 100 60 C -- 50 D --

The firm estimates that each meter costs approximately $4. What is the cost of the current assignment?

Solution

1 2 3 4 B D A C

Matrix of departmental distances

1 (B) 2 (D) 3 (A) 4 (C)

1 (B) -- 5 30 20

2 (D) -- 40 15

3 (A) -- 50

4 (C) --

Pair X C XC

A-B 35 30x4= 120 4200

A-C 20 50x4= 200 4000

A-D 30 40x4= 160 4800

B-C 100 20x4=80 8000

B-D 60 5x4=20 1200

C-D 50 15x4= 60 3000

$25,200