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152 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

MANAGEMENT SCIENCE IN ACTION

Scheduling the Orange Harvest in Brazil
razil is the world’s largest exporter of orange project developed a linear programming model to
B juice and the product is critically important both investigate the effect of the orange harvesting sched-
to the economy at the macroeconomic level and to ule. The model took into account factors such as the
the individual farmers at the microeconomic level. To productivity characteristics of orange orchards, the
remain competitive, the quality of the final product fruit characteristics and transportation distances from
must be both consistent and high. However, this is the orchards to the processing plant. The model
not necessarily as easy as it might seem. Typically, used two alternative objective functions to allow dif-
the orange producers are small, independent farm- ferent scenarios to be examined. The first maximized
ers, over 20 000 in one area of Brazil alone, who sell the total soluble solids achieved through processing;
their produce to the processing companies who then the second maximized the total quantity of oranges
transform the oranges into orange juice. The quality harvested. The project found that, using the model,
and quantity of the finished product will depend on profit contribution could be increased by around
several factors: the variety of oranges grown; their US$2.5 million in a season.
juice yield; the ratio of juice to solids; their acidity.
Based on J. V. Caixeta-Filho, ‘Orange harvesting scheduling manage-
These factors in turn are heavily affected by the
ment’, Journal of the Operational Research Society 57 (2006): 37–42.
decision of when to harvest the orange crop. This

available in each department is fixed, we can formulate McCormick’s problem as a
standard product-mix linear program with the following decision variables:
P 1 ¼ units of product 1
P 2 ¼ units of product 2

Table 4.6 Minimum Cost Production Schedule Information for the Bollinger Electronics Problem
Activity April May June
Production
Component 322A 500 3 200 5 200
Component 802B 2 500 2 000 0
Totals 3 000 5 200 5 200
Ending inventory
Component 322A 0 200 400
Component 802B 1 700 3 200 200
Machine usage
Scheduled hours 250 480 520
Slack capacity hours 150 20 80
Labour usage
Scheduled hours 200 300 260
Slack capacity hours 100 0 40
Storage usage
Scheduled storage 5 100 10 000 1 400
Slack capacity 4 900 0 8 600
Total production, inventory and production-smoothing cost ¼ E225 295

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