1. Chapter 11 Decision making and Relevant Information
Linear Programming as a
decision facilitating tool

2. Introduction This chapter explores the decision-making process.
It focuses on specific decisions such as
accepting or rejecting a one-time-only special order,
insourcing or outsourcing products or services, and
replacing or keeping equipment.
Furthermore it introduces Linear Programming as a method to cope with multiple constraints
A decision model is a formal method for making a choice, often involving quantitative and qualitative analysis.

3. Five-Step Decision Process
Gathering information
Making predictions
Choosing an alternative
Implementing the decision
Evaluating performance

4. The Meaning of Relevance
Relevant costs and relevant revenues are expected future costs and revenues that differ among alternative courses of action.
Historical costs are irrelevant to a decision but are used as a basis for predicting future costs.
Sunk costs are past costs which are unavoidable.
Differential income (net relevant income) is the difference in total operating income when choosing between two alternatives.
Differential costs (net relevant costs) are the difference in total costs between two alternatives.

5. Quantitative and Qualitative Relevant Information
Quantitative factors are outcomes that are measured in numerical terms:
Financial
Nonfinancial
a one-dimensional objective is required to arrive at a preference order between alternatives
a common approach is to optimize a financial objective under restrictions on nonfinancial performance measures
Qualitative factors are outcomes that cannot be measured in numerical terms
Aspiration levels for qualitative factors restrict the feasible set of alternatives

6. One-Time-Only Special Order
Decision criterion:
Accept the order if the revenue differential is greater than the cost differential.
Accept the order if the contribution margin is positive
But: Beware of aftereffects.
Is it really an isolated one-time-only special order or does it change the situation for future business?
does it accustom sales people to accept prices below full cost?
once the order is accepted, better opportunities might arrive but capacity is now insufficient to deal with them: opportunity costs!

7. Short term production decisions
Income = revenue - cost
Contribution of a Product = (variable) revenue - variable costs
Contribution Margin = contribution  number of product units
Rule 1: Do not produce products with a negative
contribution margin.

8. Constraints
Mostly, a company is not free in its decision but faces constraints
procurement constraints
production constraints
sales constraints
Constraints might affect
only single products (e.g. sales constraints)
multiple products several products compete for scarce resources (e.g. procurement constraints)

9. The formal decision problem
Maximize the firm‘s profit
such that
sales constraints
production constraints
procurement constraints
are kept satisfied

10. Only sales constraints
Special case 1:
Only sales constraints
Rule 2
Identify all products with a positive contribution margin
For each selected product set the production level equal to the maximum quantity

11. Example

12. a single resource constraint
Special case 2:
a single resource constraint
Example:
Problem: production of an additional unit of product 1 makes production of a1/ a2 units of product 2 impossible a1
Resource A raw material
Resource 3:
Machine
(limited
capacity)
Product 1 a2
Resource B
raw material
Product 2

13. When should you expand production 1?
Expansion should increase total contribution
additional contribution (p1 - k1) ·1
loss of contribution (p2 - k2) · a1/a2
Rule: or
„Relative contribution margins“
(CM per machine hour)

14. Product-Mix Decisions Under Capacity Constraints
Which product(s) should be produced first?
The product(s) with the highest contribution margin per unit of the constraining resource.
Detailed rule (rule 3)
Step 1: go for the product with the highest contribution margin per hour of capacity usage
until sales constraint is binding
or until capacity constraint is binding
if there is capacity left after step 1...
delete product from candidate list
Step 2: repeat step 1 on the remaining list until there is no capacity left

15. Example
Contribution: 16,000
Profit: 12,000

16. Insourcing versus Outsourcing
Outsourcing is the process of purchasing goods and services from outside vendors rather than producing goods or providing services within the organization, which is called insourcing.

17. Opportunity Costs, Outsourcing, and Constraints
Opportunity cost is the contribution to income that is forgone or rejected by not using a limited resource in its next best alternative use.
The opportunity cost of holding inventory is the income forgone from tying up money in inventory and not investing it elsewhere.
Carrying costs of inventory can be a significant opportunity cost and should be incorporated into decisions regarding lot purchase sizes for materials.

18. Opportunity Costs, Outsourcing, and Constraints
Opportunity costs are not recorded in formal accounting records since they do not generate cash outlays.
These costs also are not ordinarily incorporated into formal reports: ad hoc analyses required to estimate them

19. Make-or-Buy Decisions
Decisions about whether to outsource or produce within the organization are often called make-or-buy decisions.
The most important factors in the make-or-buy decision are quality, dependability of supplies, and costs.
Should a firm manufacture the part or buy it from an outside supplier?
The answer depends on the difference in expected future costs between the alternatives.

20. Again: Beware of the long-run consequences of your decision
dependence on suppliers
technological know-how may be lost
information asymmetry may increase to the detriment of the buyer
strategic orientation of outsourcing decisions: intended core competencies will not be outsourced even if this would be profitable from a pure accounting standpoint

21. Equipment-Replacement Decisions
Assume
The new machine is more efficient than the old machine.
Revenues will be unaffected.
Approach:
Calculate the present value C of all expenditures for the new machine
if the machine will presumably replaced indefinitely: let C equal the present value of expenditures for the replacemnet chain
what is gained by postponing the replacement to the next period at which cost?
gain: C occurs one period later; gain: interest rate (r) on C
cost: the maintenance and operating cost c of the old machine for the current period
Rule: replace only if c becomes greater than rC.

22. Equipment-Replacement Decisions
Irrelevance of Past Costs:
The book value of existing equipment is irrelevant since it is neither a future cost nor does it differ among any alternatives (sunk costs never differ).
The disposal price of old equipment and the purchase cost of new equipment are relevant costs and revenues because...
they are future costs or revenues that differ between alternatives to be decided upon.

23. Decisions and Performance Evaluation
In the real world would the manager replace the machine?
An important factor in replacement decisions is the manager’s perceptions of whether the decision model is consistent with how the manager’s performance is judged.
Managers often behave consistent with their short-run interests and favor the alternative that yields best performance measures in the short run.
When conflicting decisions are generated, managers tend to favor the performance evaluation model.
Top management faces a challenge – that is, making sure that the performance-evaluation model of subordinate managers is consistent with the decision model.

24. Multiple Constraints Activities may be characterized by
output: e.g. products, services, (also for internal use)
restricted due to commitments or
for unrestricted sale, to be valued at sales prices
input:
of committed resources, restricted availability
current inputs (unrestricted availability at purchase prices)
activity level (determines both input and output quantities)
Special case: linear activities
output and input quantities vary linearly with the activity level

25. Linear Activity Analysis
Activities are characterized by column vectors*) a•j:
component aij
represents the net production of the ith resource per unit of activity j
= gross production – gross consumption of resource i (per unit of the activity level)
component a0j
represents contribution to gross profit per unit of the activity level; measurement in: [monetary units]
a0j = sales revenue – cost of current inputs
(per unit of the activity level)
*) the first index is the row index, the second one is the column index.
A dot • in place of an index means a running index. So a•j denotes a
column vector while ai• would denote a row vector.

26. Linear Activity Analysis, (cont’d)
Commitments and capacity limits are represented in a column vector a•0
Activity levels xj may be subject to an upper or lower bound: xj ³ xj ³ xj ³ 0
Types of restrictions
minimum output requirement: Sj aij xj ³ ai0
in matrix notation*) : ai• x ³ ai0
input restriction: ai• x ³ ai0
input-output balance: ai• x = 0
(xj must always be nonnegative)
Both sides
negative!
*) x denotes the column vector of activity levels with components xj

27. Modeling specific activities
Pure procurement activity for restricted resource i:
a0j < 0; aij > 0; alj = 0 (l ¹ i); xj ³ xj
input-output balance: ai• x = 0
Pure selling activity for a product i produced in several alternative production activities
a0j > 0; aij < 0; alj = 0 (l ¹ i); xj ³ xj
Storage activity:
aij = - 1 in line i for the respective good this period
ai+1,j = +1 in line i +1 for the same good next period

28. Example: Exercise 2-4, Kaplan/Atkinson: Advanced Management Accounting, 3rd ed. p. 51
SHC produces chemicals for the paint industry.
Chemical A is bought at $4/liter and processed in dept. 1 in batches of 150 liters. Each batch produces 100 liter of chemical B and 50 liters of C.
B is sold for $15 per liter.
C is used in dept. 2 in batches of 200 liters to produce 120 liters of D, 50 liters of E, and 30 liters of F.
D is sold for $18 per liter,
E is a waste product that can be given away at no cost,
F is hazardous waste that has to be disposed of at a cost of $8 per liter. It can also be processed in dept. 3 in batches of 40 liters to produce 20 liters of C.
No more than 1000 liters of C can be produced due to storage constraints.
Sales limits: B: liters, D: liters.
Labor requirements (hrs per batch): Dept. 1: 12, dept. 2: 18, dept. 3: 15.
8000 labor hrs. available, paid at $15 per hour.
Restrictions on the number of batches: Dept. 1: 700, dept. 2: 120, dept. 3: 70.
Other variable costs: Dept. 1: $300, dept. 2: $825, dept. 3: $ 120 per batch.

29. Activities: Restrictions:
production processes in departments j = 1,2,3; upper bounds on all production activity levels
selling products B, D and F (j = 4,5,6)
F at a negative price, upper bounds for B and D.
no procurement activities need be modeled explicitly, since procurement is not restricted.
Restrictions:
input-output balances for all products
upper bound for production of C (storage restriction)

30. Details of activities A $4 B 150 x1 100 x1 x4 B $15 50 x1 C 200 x2
xj := no. of batches in dept. j (j = 1,...,3)
:= no. of liters of resp. product to be sold (j = 4,...,6)

31. Sales restrictions: B: x4 £ 40,000 D: x5 £ 15,000
Input-output balances
B: (i = 1) : 100 x = x4
C: (i = 2) : 50 x x3 ³ 200 x2
D: (i = 3) : 120 x = x5
E: not relevant
F: (i = 4) : x3 + x = 30 x2
Sales restrictions: B: x4 £ 40,000
D: x5 £ 15,000
Capacity restrictions: vats: x1 £ 700
x2 £ 120
x3 £
labor hours: (i = 5): x x x3 £ 8000
storage restriction C: (i = 2): x x3 – 200 x2 £ 1000

32. Objective function Objective function:
for a spreadsheet solution see:
ProductMix.xls at the course
web site
Objective function:
x x x x x5 - 8 x6

33. System design decisions
Activities may be reengineered
add the new version of the activity to the model
the model will show then whether the new version is useful under given capacity restrictions
New capacity can be introduced
this will entail additional committed cost
it is profitable if the optimal objective function value enhances more than this additional cost
If reengineering or capacity enhancement requires investments then estimate the benefit for the future periods from the LP solution, calculate the present value and compare to the investment outlay

34. Bottlenecks The model shows the bottleneck(s)
There may be short-run adaptation opportunities that may widen the bottleneck at an additional cost
The Lagrange Multiplier (dual variable) for a bottleneck gives an estimate of the maximum allowable cost per unit of additional capacity

35. CCs for chapter 11 11-19 (5%) 11-21 (5%) same as in 11th ed.
11-29 (5%) new in 12th ed.
11-31 (5%) (= )
11-23 (3%) (same as in 11th ed.
11-33 (8%)(= )
11-25 (5%)
11-35 (8%)
11-27 (5%)
11-41 (similar in 11th ed.)
Excel solution, with calculation of opportunity cost values for the capacities (15%)
same as in 11th ed.
same as in 11th ed.