Cost Management

Accounting

Theory Of Constraints
(TOC)

Prepared by: Moataz Elbanna, MBA, CTP, FMVA@

moatazelbanna@gmail.com
https://www.linkedin.com/in/moatazelbanna/
Theory of constraints (TOC) page 463 ,15th Edition

The theory of constraints (TOC) describes methods to maximize operating income when faced with some
bottleneck and some non-bottleneck operations. The TOC defines these three measures:
1. Throughput margin equals revenues minus the direct material costs of the goods sold.
2. Investments equal the sum of (a) material costs in direct materials, work-in-process,
and finished goods inventories; (b) R&D costs; and (c) capital costs of equipment and buildings.
3. Operating costs equal all costs of operations (other than direct materials) incurred to earn throughput
margin. Operating costs include costs such as salaries and wages, rent, utilities, and depreciation.

Inpu Output
t

Throughput “Value
added”
‫)‪Theory of constraints (TOC‬‬ ‫‪page 463 ,15th Edition‬‬

‫نظرية القيود‪:‬‬
‫الغ)رض من تل)ك النظري)ة ه)و الحص)ول على أعلى ه)امش ربح تش)غيلى عن)د وج)ود (نقط)ة عن)ق الزجاج)ة) فى العملي)ة‬
‫اإلنتاجية و هى عدم وجود إمكانية النتاج كامل االنتاج المطلوب‪.‬‬
‫على س))بيل المث))ال هن))اك ع))دد من المنتج))ات يتم إنتاجه))ا على ع))دد معين من خط))وط االنت))اج و لكن طاق))ة أح))د تل))ك‬
‫الخط)وط لن يس)تطيع الوف)اء باجم)الى كمي)ة االنت)اج المف)ترض إنتاجه)ا ‪ ،‬هن)ا يتم االس)تفادة من ه)ذة النظري)ة فى تحدي)د اى‬
‫تل)ك المنتج)ات أك)ثر ربحي)ة و بالت)الى يتم اعط)اء االولوي)ة فى االنت)اج على ه)ذا الخ)ط ثم الطاق)ة المتبق)ة من)ه توج)ه للمنتج‬
‫التالى فى الربحية ‪ ....‬و هكذا‪.‬‬
‫مث)ال أخ)ر‪ :‬ع)دد من‬
‫المنتج)ات و اى منه)ا‬
‫الب)د من م)روره على‬
‫مرحل))ة تالي))ة و لكن‬
‫طاق)ة تل)ك المرحل)ة‬
‫ال تس)))))طيع ان تنتج‬
‫جمي)ع المنتج)ات هن)ا‬
‫يك))ون علين))ا تحدي))د‬
‫االولوي)ة للمنتج االك)ثر‬
‫ربحية لمروره اوال‪.‬‬
Exercise

A company manufacture two types of products: G1 & G2 , selling price 24, 36 per unit.
Three machines are used: M1, M2 & M3.
Capacity of each machine 35 hours per week.
Production plan 250 units of G1 & 150 units of G2.
Required minutes per unit:
M1 M2 M3
G1 3 6 4.5
G2 7 7.5 2.3
Direct materials: 10 & 21
Solution

Machine G1 G2 Total
capacity Hours
M1 (3 minutes /60) hour X 250 units = 12.5 Hours (7 minutes /60) hour X 150 units = 17.5 Hours 30
More than available hours per week”35”

M2 (6 minutes /60) hour X 250 units = 25 Hours (7.5 minutes /60) hour X 150 units = 18.75 43.75
Hours
M3 (4.5 minutes /60) hour X 250 units = 18.75 Hours (2.3 minutes /60) hour X 150 units = 5.75 Hours 24.5

We have a bottleneck at machine M2 as the available hours not enough to produce both product, so we have to
know which product has more throughput margin to produce it and the rest of capacity produce the another
product.
Throughput = Selling price - Direct materials
Throughput = 24 – 10 = $14 36 – 21 = $15
Minutes required to produce one unit at M2 6 minutes 7.5 minutes
Throughput per $14 ÷ 6 minutes = $2.33 $15 ÷ 7.5 minutes = $2
minute
Because G1 has more throughput per unit, the production priority will be for G1 then G2
Solution
M2
The total available hours for M2 is 35 hours , we will produce 250 unit on 25 hours from G1,

The remain hours is 35-25 = 10 hours to produce G2 .

G1 G2
25 hours 10 hours
Number of unit from G2 = 10 hours / (7.5 minutes / 60) = 80 units 250 units 80 units

 The problem of M1 & M3 is excess capacity.

 We need to make improvement for M2 to increase it’s capacity

 We need to use the excess capacity of M1 & M3.

Exercise
Solution
Objective Function = Maximum contribution margin
Contribution margin = Selling price – cost “given”
Objective Function = 14 Y + 16 Z

Subject to: Where T = Idle Capacity

Labour 6Y+8Z 6 Y + 8 Z + T1 = 2880

Material 8Y+4Z 8Y + 4 Z + T2 = 3440

Capacity 4Y+6Z 4Y + 6 Z + T3 = 2760

Sales Y Y + T4 = 420

Solve using Simplex

method
Exercise page 719,14th Edition
Solution 19 -25

Throughput = Selling price - Direct materials = $72 – $32 = $40

1) Should Mayfield acquire these tools? 4) Should Mayfield accept the
Hunt’s offer?
Increase output by 1000 unit : 1000 unit x $40 throughput = $40,000
No, Mayfield shouldn’t
Additional cost by $30,000
accept the Hunt’s offer due to
Net increase in throughput = $10,000
no need for more capacity.
Yes, Mayfield should acquire these tools.
2) Should Mayfield implement the change?
No, Mayfield shouldn’t implement the change due to no need for more capacity.
3) Should Mayfield accept the subcontractor’s offer?
Increase output by 12,000 unit : 12,000 unit x $40 throughput = $480,000
Additional cost by 12,000 unit x $10 per unit = $120,000
Net increase in throughput = $360,000
Yes, Mayfield should accept the subcontractor’s offer.
Solution
19 - 26

1) In the machining operation, what is the cost to Mayfield of the defective items produced?
In the machining operation the cost will be only direct materials
2000 units x $32 direct material in machining operation = $64,000

2) In the finishing operation, what is the cost to Mayfield of the defective items produced?
In the finishing operation the total costs are direct materials cost plus the opportunity cost “Profit foregone”
2000 units x $32 direct material in finishing operation = $64,000
2,000 units x $40 throughput = $80,000
Total cost to Mayfield of the defective items produced = $144,000
Exercise page 722,14th Edition
Solution

1) Should Nevada implement the new method?

No, Nevada shouldn’t implement the new method, there is excess capacity. Nevada will loss $60 per unit.

2) Should Nevada use the new design?

Due to new design the direct material will be $35,000 + $3,000 = $38,000
Current design New design
Throughput = $60,000-$35,000 = $25,000 $60,000-$38,000 = $22,000
Sales Unit = 250 280
Total sales = 6,250,000 6,160,000

Variance Loss $90,000

No, Nevada shouldn’t use the new design. Nevada will loss $90,000.
Solution

3) Should Nevada implement the new technique?

The new technique will increase the installed equipment by 7.
Throughput = $60,000-$35,000 = $25,000 x 7 additional equipment = $175,000
Additional cost per year = $45,000
Net increase in throughput = $130,000
Yes, Nevada should implement the new technique.

4) Do you think the new proposal is a good idea?

Nevada need to apply the new proposal only for workers at installation department to motivate them to improve their
productivity.
while no need to apply the new proposal for workers at manufacturing department due to there are excess capacity.
Exercise page 723 14th Edition
Solution

1) Which doll would FTT produce? How many of these dolls would it make and sell?
We need to determine which factor is a more critical (bottleneck)
Materials (30,000 pounds) Hours (8,500 hours)
Chatty Chelsey 30,000 ÷ 1.5 = 20,000 8,500 ÷ 0.33 = 25,500
Talking Tanya 30,000 ÷ 2 = 15,000 8,500 ÷ 0.5 = 17,000
So, the critical factor is materials (the hours can produce more dolls but material not enough).
Chatty Chelsey Talking Tanya
Selling price $39 $51
Variable cost:
Direct material 1.5 x $12 = $18 2 x $12 = $24
Direct labor 0.33 x $18 = $6 0.5 x $18 = $9
Total variable cost $24 $33
Throughput $15 $18
Sales units 20,000 15,000
Profit according to available DM $300,000 $270,000

Chatty Chelsey would be produce & sell by 20,000 units to achieve more profit.
Solution

2) How many dolls of each? What would be the total contribution margin?

Chatty Chelsey Talking Tanya

Sales dolls 2 1
Direct materials 1.5 2
= 3 2
3X + 2X = 30,000 (total materials)
5X = 30,000
X = 6,000
6,000 x 2 = 12,000 dolls 6,000 X 1 = 6,000 dolls
Throughput = 12,000 X $15 = $180,000 6,000 X $18 = $108,000

Total margin = $180,000+$108,000 = $288,000

Solution

3) How much would production & contribution margin when add 15 pound?

Chatty Chelsey Talking Tanya

Sales dolls 2 1
Direct materials 1.5 2
= 3 2
3X + 2X = 15 (added materials)
5X = 15
X= 3
3 x 2 = 6 dolls 3 X 1 = 3 dolls
Throughput = 6 X $15 = $90 3 X $18 = $54

Total margin = $90+$54 = $144

4) FTT has an excess capacity in hour, so no nee for new capacity with additional cost