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THE TAIWAN ELECTRONIC COMMUNICATIONS (TEC) PROBLEM 119

second constraint, that relating to salesforce availability is non-binding (and has a
shadow price of zero). Increasing the salesforce availability beyond its current
maximum of 1800 hours will add nothing to profit, given that we are not using all
the 1800 hours anyway. In fact, we can advise management that they can reduce
availability by 25 hours without affecting current maximum profit. The third con-
straint was the production constraint imposed by management. Given that this was a
strict equality constraint then it is no surprise to see it as a binding constraint
(without this constraint being met the problem would not have a solution at all). It
has a shadow price of $60 implying that a relaxation of this constraint by 1 (i.e., to
601) would increase profit by $60. However, we also see from the allowable increase
that only a small increase would be permissible in any event (of 3.57 units). Finally,
we have the retail stores constraint, requiring us to provide at least 150 units to retail
stores. This constraint is also binding, and as we noted earlier, the surplus associated
with this variable (since it takes the form ) is also zero. In other words, the 150 unit
requirement is being met in the current optimal solution but only just. This implies
that this requirement, whilst being met, is actually having an adverse effect on
potential profit. This is confirmed if we look at the constraint’s shadow price. Here
it is $17, a negative value. Recollect the meaning of a shadow price. It shows the
change in the objective function if we allow a marginal increase in the right-hand
side. In other words if we set this constraint equal to 151 then the shadow price

MANAGEMENT SCIENCE IN ACTION

Tea Production and Distribution in India
n India, one of the largest tea producers in the agers would determine the amounts of loose tea of
I world, approximately $1 billion of tea packets and each blend to ship to each packing unit, the quantity
loose tea are sold. Duncan Industries Limited (DIL), of each line of tea to be packed at each packing unit,
the third largest producer of tea in the Indian tea and the amounts of packed tea of each line to be
market, sells about $37.5 million of tea, almost all transported from each packing unit to the various
of which is sold in packets. depots. This process requires two to three days
DIL has 16 tea gardens, three blending units, six each month and often results in stockouts of lines
packing units and 22 depots. Tea from the gardens in demand at specific depots.
is sent to blending units, which then mix various Consequently, a linear programming model involv-
grades of tea to produce blends such as Sargam, ing approximately 7000 decision variables and 1500
Double Diamond and Runglee Rungliot. The constraints was developed to minimize the com-
blended tea is transported to packing units, where pany’s freight cost while satisfying demand, supply
it is placed in packets of different sizes and shapes and all operational constraints. The model was tested
to produce about 120 different product lines. For on past data and showed that stockouts could be
example, one line is Sargam tea packed in 500-gram prevented at little or no additional cost. Moreover, the
cartons, another line is Double Diamond packed in model was able to provide management with the
100-gram pouches and so on. The tea is then ability to perform various what-if types of exercises,
shipped to the depots that supply 11 500 distributors convincing them of the potential benefits of using
through whom the needs of approximately 325 000 management science techniques to support the deci-
retailers are satisfied. sion-making process.
For the coming month, sales managers provide
estimates of the demand for each line of tea at each Based on Nilotpal Chakravarti, ‘Tea Company Steeped in OR’, OR/MS
depot. Using these estimates, a team of senior man- Today (April 2000).

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