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1.  Production Mix
2.  Diet
3.  Transportation
      a.  Pure form
      b.  Excess demand, Excess supply
      c.  Intermediate nodes: Warehouses
4.  Assignment
5.  Personnel Scheduling

1.  Production Mix

The decision variables are the amounts of different products to be produced from a fixed set of resources.
The objective function gives the organization's profit.
Constraints may involve minimum production levels or resource capacity limits.
Example in the text: 3.5 (p. 104)

2.  Diet

The decision variables are the amounts of different components (foods) to be included in a mix (a diet or meal plan or animal feed).
The objective function gives the cost of providing the mix.
Constraints may involve meeting specific nutritional requirements or having certain maxima or minima of some of the components.
Examples in the text: 3.10  and 3.11(p. 106)

3.  Transportation

Decission variables: Transportation problems find the quantities to be shipped from various sources to various destinations.  Each decision variable represents an amount to be shipped from source i to destination j.
The objective function gives the total cost of shipping the goods from the sources to the destinations.  The cost to ship one unit of the goods is constant and depends only on the route.  The object is to minimize the overall cost of shipping the goods.
Constraints typically include that the amounts shipped from a given source do not exceed the amount available at that source.  Similarly, the total amount shipped to a destination should not exceed the demand for the good at that destination.

Transportation problems are a special case of a broader class called network problems.
It is convenient to set up the decision variables in the form of a table where the rows indicate the sources and the columns indicate the destinations (or vice versa).
Transportation problems can be quickly solved by programs which take advantage of special features of the problem.  For small and moderately sized problems, modern computer spreadsheets can solve the problems well.

a.  Pure form

In the pure form of the problem, the total demands at all destinations equal the total supplies at all sources.
Example: 5.12 (p. 194)

b.  Excess demand, Excess supply

Excess demand can be accomodated in the standard transportation model by assuming that there is one dummy source that will provide the missing supply.  The costs of shipping from this source must be set equal to zero since no such goods will actually be shipped.  The problem then becomes a matter of deciding which demands can be met most economically.

Excess supply can be accommodated in a similar way by assuming that there is one dummy destination that will receive the excess goods.  The cost of shipping goods to this destination will be set to zero.  The problem becomes a matter of how to reduce each supplier's production so as to minimize the overall shipping costs.
Example: 5.8, 5.13 (p. 194)

c.  Intermediate nodes: Warehouses

A warehouse is both a source and a destination.  A constraint must be added to assure that the total amount to be shipped from the warehouse does not exceed the total amount received by the warehouse.
Realistically, if the costs of shipment are constant per unit per mile, warehouses will not be advantageous.  However, if some routes have higher per-mile costs than other routes have, warehouses may reduce costs.

4.  Assignment

The decision variables are the amounts of different resources to be assigned to various tasks, such as producing different kinds of products.
The objective function gives the total cost of accomplishing the tasks.
The constraints typically include minimum or maximum production amounts and limits on the amounts of the availability of the resources.
The constraints may also include restrictions that certain resources cannot perform certain tasks.  In such a case, the corresponding decision variable would be set to zero.
Example: 5.6 (p. 193)

5.  Personnel scheduling

The decision variables are the amounts of resources (workers), possibly of different types (full-time, part-time, overtime, skilled, unskilled) to hire for different shifts.  Shifts may start at various times, but the number of workers required may vary by the hour through a shift.
The objective function gives the total cost of hirig workers for all shifts.
The constraints would specify that there must be some minimal number of workers at various times through the day.  There may also be constraints that there must be at least one full-time worker on duty at all times, for example.
Example: 3.14 (p. 107)