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tÉlÉcharger merton truck company case solution pdf

Merton Trucks Case Note
Abstract
We discuss Merton Trucks [Dhe90a] as a case to introduce linear
programming in the MBA program. This case adapted from Sherman
Motor Company case, was used to introduce Linear Programming
formulations as well as duality. Refer to the teaching note [Dhe90b].
Our approach differs from the approach suggested by
Dhebar [Dhe90b]. First, our audience consists pre-dominantly of engineers with not too much work experience. As a result, handling
math and algebra is relatively easy. Explaining the algebraic formulation, graphical approach and using the Excel solver do not consume
that much time. Second, because this case is used during the first
week of the MBA program, students are still unfamiliar with the case
methodology and we spend significant time in understanding case
facts. The circular logic used in allocating fixed costs based on the
product mix that in turn is used in deciding the product mix takes
some time to understand. Third, because of the participant background, they have difficulty in translating the model to the specific
business situation and interpreting the trade-offs involved in various
what-if analyses that are prompted by the case questions.
We return to the case when we teach duality. After explaining
duality, we analyze the case to show how some of the questions and
what-if analyses can be simplified using duality.
This note is based on our experiences with teaching three large
batches of students in our MBA programs.
1
1 Without Duality: (2 × 70) minutes
We use the case to illustrate the following issues:
• Analyze case facts:
– What is the factual basis for some of the opinions expressed?
– Where did the overhead cost numbers shown in Table B come
from?
– Is it appropriate to allocate fixed costs as done in Table C?
• Decision making alternatives:
– Evaluate one product suggestions and current product-mix.
– Evaluate trade-offs and how to improve a solution manually
with its limitations.
– Algebraic formulation of the linear program.
– Graphical solution method and its limitations.
– Solution using Excel solver.
1.1 Objective: 5 minutes
We ask the students to articulate in plain English answers to the following
questions without going into the low level details:
• What is Merton deciding?
• On what should this decision be based?
• What constrains Merton?
1.2 Roles and Rationales: 5 minutes
We would like the students to understand the data that supports the opinions expressed in the case. This is a prelude to analyzing validity of the
data.
2
• Why do the company president and sales manager feel that 101’s
are making a loss and hence 101’s production should be stopped?
From Table B, it costs $40,205 to produce a 101-truck while it sells for
$39,000.
• Why do the president and the production manager feel outsourcing
engine assembly will help? No slack in engine assembly currently.
Show “Resource Usage” worksheet of merton facts.xls.
• Why does the controller feel that cutting back on 102s is an answer?
Overheads are the answer and they are dealt next.
1.3 Understanding the Exhibits: 15 minutes
The numbers in Table A are straight forward resource utilization numbers. The numbers in Table B show total costs including fixed overheads
allocated based on Table C. Allocation of fixed costs are done based on
the ratio of resource usage. The fallacy in allocating fixed costs based on
product mix to decide the product mix can be illustrated by using the “Exhibits” worksheet of merton facts.xls. The grayed out areas represent data
that does not change with product mix. Try the following combinations as
a basis for the controller’s comments:
• (1000, 1500) for negative contributions of 101s and to explain current
exhibit values in Table B,
• (2500, 500) for both positive contributions,
• (2500, 125) for negative contributions of 102s and
• (500, 125) for both negative contributions.
1.4 Relevance of Overheads: 5 minutes
Allocated fixed costs should not be included in deciding the contributions.
The actual costs for (101s, 102s) are:
• direct materials - ($24,000, $20,000) from Table B,
• direct labor - ($4,000, $4,500) from Table B and,
3
• variable overhead - ($8,000, $8,500) from Table C.
What are the contributions of 101s and 102s? ($3000, $5000).
1.5 Evaluate current plan: 15 minutes
We use the “Evaluate” worksheet of merton facts.xls to set up the model
close to the algebraic formulation discussed next.
Analyzing the president and sales manager’s decision to stop 101s is
easy. The constraints imply that the number of 102s produced should be
given by min[4000/2, 6000/2, 4500/3]. This gives $7.5 million, worse than
the current plan contributions of $10.5 million.
Current plan for productions is (101s, 102s) = (1000, 1500). Is this the
best?
Reduce one model 102 and see how many extra 101s can be produced.
Reducing one 102 frees (2, 2, -, 3) resources in (engine assembly, metals
stamping, 101-assembly, 102-assembly) that can be used to produce two
101s. Show that this increases contribution by $1000 (2 × $3000 − $5000).
How long can you do this? Net resource effect of the substitution of
each 102 is (-, +2, +4, -3) on remaining resources (-, 1000, 3000, -). This
implies that we can change up to a minimum of (-, 1000/2, 3000/4, -) and
non-negativity requirement on number of 102s produced. Explain that it
is tedious to do this kind of analysis, and more than two product-lines
implies many trade-offs.
1.6 Algebraic Model: 5 minutes
How do we describe the model algebraically? Decisions are coded using
variables called decision variables. How do we express the objective and
constraints using these variables?
Decisions variables: