USING LINEAR PROGRAMMING TO COMPARE DIRECT AND ABSORPTION COSTING

Main report submitted to
The Department of Industrial Engineering of Çankaya University
in partial fulfillment of the requirement for
IE 456 Mathematical Modeling and Applications course





IE 456 REPORT





USING LINEAR PROGRAMMING
TO COMPARE
DIRECT AND ABSORPTION COSTING






By

?LTER KARADA? 200112050
PEYKAN SAMLI 200312032
NESLIHAN GAMZE ÖZTÜRK 200412052

Group No: 06




Submitted to
Instructor Benhür SATIR



05.01.2009

---

TABLE OF CONTENTS


Table
of
Contents







i
List of Tables ii


1. CHAPTER 1

1.1 Introduction
1
1.2 Direct Costing
2

1.2.1. Direct Material
2

1.2.2. Direct Labor
2

1.2.3. Direct Expenses
2
1.3. Advantages of the Direct Costing
3
1.4. Absorption Costing
4
1.5. Advantages of the Direct Costing
4
1.6. Comparison Between Direct and Absorption Costing
5
2. CHAPTER 2

2.1 Formulating the Linear Programming Model
6

2.1.1. Decision Variables
6
2.1.2.
Constants
7
2.1.3.
Parameters
7

2.1.4. Linear Profit Equations
8
2.1.5.
Constraints
9
3. CHAPTER 3

3.1 An Illustration
10
4. CHAPTER 4

4.1 Calculation Method of Each Period




12
4.2 Sensitivity Analysis for Period Four in DC
17

i

---

LIST OF TABLES



Table 1: Comparison between Direct and Absorption Costing
5
Table 2: Production Capacity per Period
10
Table 3: Selling Price and Variable Cost Data
10
Table 4: Unit Fixed Manufacturing Costs
11
Table 5: Period 2 Modifications
13
Table 6: Period 3 Modifications
14
Table 7: Period 4 Modifications
15
Table 8: Period 5-6-7 Modifications
16

ii

---

CHAPTER 1


1.1. INTRODUCTION

This study gives information about Comparison of direct costing (DC) and absorption
costing (AC) over linear programming.
Linear programming and optimal product mix decisions directed toward maximizing
accounting income typically have assumed the use of direct costing. However, in this
article a linear programming model is utilized to establish optimal sales and
production levels, which maximize income measured in terms of absorption costing.
Since optimal sales and production levels may differ under the two systems, the use
of linear programming represents a valuable pedagogical approach to the
comparison of direct and absorption costing results in multiproduct situations.
Discussion involving comparison of the two methods in multiproduct situations can be
enhanced by a linear programming (LP) model. It is common knowledge, of course,
that for the class of LP problems involving the determination of an optimal product
mix to maximize profits, the linear objective function traditionally has assumed the
use of direct costing (DC). However, what is not readily apparent is that the linear
function also may be formulated in terms of absorption costing (AC) profit.
If management desires to maximize reported accounting income, the appropriate
production and sales volume decisions may differ depending on whether such
income is measured by a DC or AC system. The following discussion, based on the
use of LP, involves a comparison of these different production and sales volume
decisions under DC and AC in multiproduct situations. This LP approach serves as a
useful pedagogical device for making such comparisons.

1

---

1.2. DIRECT COSTING

Direct cost is a cost that can be directly traced to producing specific goods or
services. For example, the cost of meat in a hamburger can be attributed directly to
the cost of manufacturing that product.
Note that every cost that is not a direct cost is an indirect cost. The cost is not directly
attributable to the manufacturing of a product.
There are three types of direct cost:
• Direct
Material
• Direct
Labor
• Direct
Expenses

1.2.1. Direct Material:
Cost of material that can be specifically identified with the product, such as wood and
nails in furniture, but not gasoline that fueled the power saws used to fell the trees.
1.2.2. Direct Labor:
Cost of personnel that can be identified in the product, such as the salary of the
person who works at the production machine, but not the administrator’s salary.
1.2.3. Direct Expenses:
Direct expenses are those expenses that are levied during the production of goods.
For example wages. The expenses of the company that determine its gross profit,
expenses like salary, telephone bill, transportation and rent.


2

---

1.3. ADVANTAGES OF THE DIRECT COSTING

There are some advantages to using direct costing in internal reports and analysis.
• Income is not affected by changes in production volume: Under absorption
costing, reported net income is affected by changes in production since fixed
costs are spread across more or fewer units. This can distort income and may
even result in income moving in an opposite direction from sales. This does
not occur under direct costing.
• Fixed costs are more visible: The impact of fixed costs on profits is
emphasized because the total amount of such costs for the period appears
separately and is highlighted in the income statement rather than being buried
in cost of goods sold and ending inventory.
• Understandability: Managers should find it easier to understand direct costing
reports because data are organized by behavior and because direct costing is
much closer to cash flow.
• Control is facilitated: Direct costing ties in with cost control methods such as
flexible budgets.
• More useful for Cost Volume Profit (CVP) analysis: Direct costing statements
provide data that are immediately useful for CVP analysis since they
categorize costs based on their behavior. In contrast, it is often difficult to
rework absorption costing data so that they can be used in CVP analysis and
in decisions.





3

---

1.4. ABSORPTION COSTING

Absorption costing means that all of the manufacturing costs are absorbed by the
units produced. In other words, the cost of a finished unit in inventory will include
direct materials, direct labor, and both variable and fixed manufacturing overhead.
Absorption costing calculates the unit cost of an item taking into account all costs. As
a result, absorption costing is also referred to as full costing or the full absorption
method.
Two assumptions to insure Linear Objective Function (LOF):
• The unit fixed overhead cost for each product is normalized
• Any fixed overhead volume variances are treated as period costs
Absorption costing involves all overheads other costing.

1.5. ADVANTAGES OF THE ABSORPTION COSTING

• Fixed costs are recovered: Fixed costs are incurred in order to make output so
it is only fair to charge all output with a share of these costs.
• Identifies total cost: This is useful where pricing is on a cost plus basis.
• A useful method of pricing: A useful method of pricing is to add a profit equal
to a percentage to total production cost when fixing selling prices. Such a
method ensures that fixed overhead costs will be covered.
• Identifies the profitability of different products and services




4

---

1.6. COMPARISON BETWEEN DIRECT AND ABSORPTION
COSTING

A comparison between direct and absorption costing follows:

DIRECT COSTING
ABSORPTION COSTING
Not accepted for outside reporting
Required for outside reporting
Does not include fixed overhead as
Includes fixed overhead as an
an inventoriable cost1
inventoriable cost1
Stresses contribution margin
Stresses gross profit
Has a higher net income when sales
Has a higher net income when
exceed production
production exceeds sales
Table 1: Comparison between Direct and Absorption Costing







1 Cost of Inventory on Hand

5

---

CHAPTER 2


2.1. FORMULATING THE LINEAR PROGRAMMING MODEL

DC profit is solely a function of the sales level and AC profit is a function of both
sales and production levels.
In order to insure a linear objective function under AC, two assumptions are
necessary:
• the unit fixed overhead cost for each product is normalized,
• any fixed overhead volume variances resulting from the use of the normalized
system are treated as period costs.
The general form of the linear profit equations and constraints associated with DC
and AC may now be developed for a multiproduct manufacturing situation, each of
the products requiring processing in one or more operating departments.
In linear programming model, we use “decision variables”, “constants” and
“parameters” for writing an “objective function” and “constraints” of the model.

2.1.1. Decision Variables:

Decision variables of the model are these;

X = Total
sales
(in
units )
of
the
i th
product
i

Y = Total
production
(in
units )
of
the
i th
product
i

6

---

2.1.2. Constants:

The model has some constant values as;
a unit selling price of

the i th
=
product
i
b
of
cost

ing
manufactur

ble
unit varia
i

the th
=
product

i
K total
=
period

fixed

manufactur

ing cost

associated with the jth department


, j = 1,…, m
j
H

in the

available

hours
capacity

total
jth
=
period

for the

department

j
h
of

e
manufactur
for

required

hours

of
unit

one

i

the th
=

in the
product

jth department

ij
k = K

j

for the
hour
per
cost

ing
manufactur

fixed

ned
predetermi

jth
=
department

j
H j
c = k h
of
cost

ing
manufactur

fixed
unit

i

the th
=

in the
product

jth department

ij
j
ij

m
c =
c
i
? = unit

fixed manufactur

ing cost

of the i
th product,

for

department

all
s
ij

j 1
=
th
=
d
of
cost

turing
nonmanufac

ble
unit varia

i

the
product

i
D
cost

turing
nonmanufac

fixed

period

total
=

2.1.3. Parameters:

These are parameters for using the LP model:
P =
of

hours

available

total
production


department
in
capacity

period.

for the
j
j
Q =

a
at

period

for the

sales

maximum
i.
product
for

price

selling
given

i
R =

of

units

the
of

beginning

at the
inventory
in

i
product

period.

the
i
s =
the space

requiremen

one
for
t
unit

of product

i.
i
S=
of

beginning

at the

available

space

unoccupied

total
the
of

storage
for

period

the
products.

all


7

---

Document Outline

• CHAPTER 1
• 1.1. INTRODUCTION
• 1.2. DIRECT COSTING
• 1.3. ADVANTAGES OF THE DIRECT COSTING
• 1.4. ABSORPTION COSTING
• 1.5. ADVANTAGES OF THE ABSORPTION COSTING
• 1.6. COMPARISON BETWEEN DIRECT AND ABSORPTION COSTING
• CHAPTER 2
• 2.1. FORMULATING THE LINEAR PROGRAMMING MODEL
• CHAPTER 3
• 3.1. AN ILLUSTRATION
• CHAPTER 4
• 4.1. CALCULATION METHOD OF EACH PERIOD
• 4.2. SENSITIVITY ANALYSIS FOR PERIOD FOUR IN DC

---