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56 CHAPTER 2 AN INTRODUCTION TO LINEAR PROGRAMMING

MANAGEMENT SCIENCE IN ACTION

Optimizing production planning at Jan de Wit Company, Brazil
ou might be forgiven for thinking initially that two years before it is sufficiently mature to produce
Y mathematical linear programming and the gen- flowers. The company imports around 3.5 million
teel business of growing lily flowers in Brazil couldn’t bulbs a year in over 50 different varieties. The com-
be further apart from each other. And you couldn’t be pany also faces very seasonal demand with peaks
more wrong! Johannes de Wit is owner and general at specific dates, such as Mother’s Day, Easter, All
manager of the Jan de Wit company in Brazil. The Soul’s Day and Christmas and to complicate this
company is Brazil’s largest producer of Oriental and further the varieties and colours in demand vary for
Asian lily flowers in a domestic market with an annual each peak period. Depending on the variety, the
value of over US$1 billion. Johannes credits the bulb size, and the time of planting the production
introduction of linear programming into the business cycle can vary from six to 16 weeks. To succeed,
with helping: Jan de Wit Company must plant the right bulbs
during the right week. An LP optimization model
• increase company revenue by 26 per cent;
was developed to maximize total contribution mar-
• reduce costs as a percentage of sales by around gin. Considerable effort was taken to involve the
3 percentage points; company’s top management in the modelling proc-
• increase the return on owner’s equity by over 7 ess and to ensure that the computer model used
percentage points; was as user-friendly as possible for the non-MS
• increase the quality of lily production. staff in the company.
Try telling him that LP and lilies don’t mix.
Based on J. V. Caixeta-Filho, J. M. van Swaay-Neto and A. de
Production planning in such a business is not a
Pa’dua Wagemaker, ‘Optimization of the Production Planning and
trivial task. The bulbs from which the flowers grow Trade of Lily Flowers at Jan de Wit Company’, Interfaces 32
are imported from Holland, although a bulb will take (Jan–Feb, 2002): 35–46.

First we note in Row 18 Maximize Total Profit at 7668, which is the value of the
objectivefunction at theoptimal solution.Justabove,Row 16,weseeBags
Produced with 539.99842 for Standard bags and 252.00110 for Deluxe bags. After
rounding, this confirms our graphical solution of 540 and 252 bags respectively.
The last section, Constraints, shows the left-hand side (LHS) value for each con-
straint at the optimal solution against the RHS value in the initial problem for-
mulation. So, for the cutting and dyeing constraint, we see that initially we have
630 hours available (RHS) and at the optimal solution calculated we are using 630
hours (LHS). We know, therefore that this constraint is binding.
It is worth noting that Excel Solver produces additional output in the form of optional
reports. We shall see later how to use the information that these reports contain.

NOTES AND COMMENTS

inear programming solvers are now a standard these spreadsheet packages was developed by
L feature of most spreadsheet packages. Excel, Frontline Systems and provides a similar user inter-
Lotus 1– 2–3 and Quattro Pro all come with built-in face. In Appendix 2.1 we show how spreadsheets
solvers capable of solving optimization problems, can be used to solve linear programmes by using
including linear programmes. The solver in each of Excel to solve the GulfGolf problem.

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