National planning problem
The original problem refers to national rice production and distribution planning in a
country of South East Asia. The full situation is as follows:
“A country has some twenty five provinces. There is a national agency that regulates
the availability of some staple food and controls prices. Some provinces create
surpluses; i.e., they produce more than they consume. Other provinces have deficits;
they consume more than they produce. Food production is seasonal but spread over
several months. This is due to the type of crop itself and to the different weather
conditions in the various provinces. There is extensive experience of food planning and
food production. Forecasts exist on a monthly basis a year in advance. These forecasts
are regularly revised. Natural disasters or political events may affect food availability
and it is desirable to keep strategic stocks. There are silos that can store the product,
capacity is limited in the short run but can be increased at a cost in the future. The
country does not exist in isolation, it is possible to buy food from abroad and sell in the
international markets, although a prime policy objective is to support the home producer
and price in the international markets is only of secondary interest. The National
Planning Agency requires a model to be used for planning and negotiating purposes. It
must not be too detailed but must incorporate the fundamental aspects of the situation.
The model must be able to run on a portable computer.”
We will simplify the situation in order to develop a prototype for the model.
Estimated production and consumption figures are given for five production areas (1, 2, 3,
4, 5) and three time periods (A, B, C). The data is contained in the table below:
Produc
tion
Produc
tion
Produc
tion
Consump
tion
Consump
tion
Consump
tion
A B C A B C
Area 1 100 200 300 150 100 200
Area 2 300 350 200 200 200 100
Area 3 50 30 40 75 50 70
Area 4 40 25 30 60 50 75
Area 5 25 30 40 50 60 80
We see that areas 1 and 2 generate surpluses, while the other three have deficits. It is
necessary to transport rice from province to province in order to satisfy the demand.
Transportation cost per unit of product are as follows.
From 1 From 2
To 3 10 11
To 4 9 12
To 5 8 13
Initial stock, desired final stocks, and storage capacity are:
