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THE TAIWAN ELECTRONIC COMMUNICATIONS (TEC) PROBLEM 121

Summary
l This chapter has introduced and developed sensitivity analysis as a standard part of the LP solution
and analysis. Sensitivity analysis, or post-optimality analysis, is concerned with showing how changes
in the formulation parameters will affect the optimal solution.
l Sensitivity analysis can be undertaken on the objective function coefficients and on the right-hand side
values of the constraints.
l Computer output from LP solutions provides the sensitivity information that we can use.
l Sensitivity analysis provides useful information to management allowing them to undertake what-if
analysis without the need for re-formulation and re-solution of the original problem.

WORKED EXAMPLE

ollmer Manufacturing in Germany produces a Solution
V variety of components used in refrigerators. The
Well, let us start by formulating the LP problem.
components are produced for a variety of refrigera-
We have effectively got three decision variables –
tion companies such as Neff, Bosch, Hotpoint. The
how many of each of the three components
company is in the process of planning its next batch
should we make. We only have information about
of production. Three particular components are
profit, so it will be a profit maximization problem.
being planned: BFX1, AHS15 and CTY45. Each of
We obviously have constraints relating to the two
the three components goes through a two-part pro-
production processes and there are also con-
duction process using automated machinery and
straints about sales of the three components. If
systems: a shaping process and a grinding proc-
we rename the components as B, A and C for
ess. Each component requires a differing amount of
simplicity we would then have a formulation of:
time on the two processes, shown below in minutes
per component:
Max 8B þ 6A þ 9C
s:t 6B þ 4A þ 4C 7200 ðShaping constraint
Component Shaping Grinding
converted to minutesÞ
BFX1 6 4 4B þ 5A þ 2C 6600 ðGrinding constraint
AHS15 4 5 converted to minutesÞ
CTY45 4 2
C 200 ðmaximum sales of
For the next production period, there will be an CTY45Þ
anticipated 120 hours available for the shaping B 1000 ðmaximum sales of
process and an anticipated 11 hours for the grind-
BFX1Þ
ing. The three components have profit contribu-
A 1000 ðmaximum sales of
tion, respectively, of E8, E6and E9. Based on
AHS15Þ
previous production and sales, the company
B 600 ðexisting order for
expects to sell no more than 200 units of CTY45,
although expected sales for the other two compo- BFX1Þ
nents could reach 1000 units each. In addition, A, B, C 0
the company already has an order for 600 units
of BFX1. The Excel output for the problem is shown below.
What advice can you give the company? From the first part of the output we can advise

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