ECON 3300 LEC

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ECON 3300 LEC 8b

• 09/28/06

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0-1 Integer Example

• Capital Budgeting Example
• The University Bookstore at Tech is considering
  several expansion
• projects, including developing a store Web site
  for online retail and
• Catalog purchases, buying an off-campus warehouse
  and its
• subsequent expansion, developing a clothing and
  gift department
• specializing in university logo apparel, opening
  a computer
• department carrying both hardware and software
  products, and
• creating a banking pavilion of three automated
  teller machines
• outside the store. Some of the projects will be
  developed over a
• two-year and some over a three year period, as
  funds permit. The
• net present value costs per year and the
  projected net present
• value of returns for a five-year period for each
  of the projects are
• shown in the following table.

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0-1 Integer Example
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0-1 Integer Example

• In addition, the store does not have
• enough space available to create both a
• computer department and a clothing
• department. The bookstore store director
• wants to know which projects to select to
• maximize returns.

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0-1 Integer Example

• Decision variables
• x1selection of website project
• x2selection of warehouse project
• x3selection of clothing department
• x4selection of computer department project
• x5selection of ATM project
• Constraints
• 55x145x260x350x430x5lt150
• 40x135x225x335x430x5lt110
• 25x120x230x4lt60
• x3x4lt1
• xi0 or 1

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0-1 Integer Example

• Objective function
• maximize Z120x185x2105x3140x4 70x5

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Mixed Integer Example

• Frijo-Lane Food Products own farms in the
• Southwest and Midwest where it grows and harvests
• potatoes to three processing plants in Atlanta,
  Baton Rouge,
• And Chicago where different varieties of potato
  products,
• including chips, are produced. Recently, the
  company has
• experienced a growth in its product demand so it
  wants to
• buy one or more new farms to produce more potato
• products. The company is considering six new
  farms with
• the following annual fixed costs and projected
  harvest.

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Mixed Integer Example
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Mixed Integer Example

• The company currently has the following
  additional available production capacity (tons)
  at its three plants that it wants to utilize

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Mixed Integer Example

• The shipping costs () per ton from the farms
  being considered for purchase to the plants are
  as follows

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Mixed Integer Example

• The company wants to know which of the
• six farms it should purchase that will meet
• available production capacity at the
• minimum total cost, including annual fixed
• costs and shipping costs.

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Mixed Integer Example

• Decision variables
• yi0 if farm i is not selected and
• 1 if selected
• Where
• i1, 2, 3, 4, 5, 6
• xijpotatoes (tons, 1,000s) shipped from farm I
  to plant j
• Where
• i1, 2, 3, 4, 5, 6 and jA, B, C

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Mixed Integer Example

• Constraints
• x1Ax1Bx1C-11.2y1lt0
• x2Ax2Bx2C-10.5y2lt0
• x3Ax3Bx3C-12.8y3lt0
• x4Ax4Bx4C-9.3y4lt0
• x5Ax5Bx5C-10.8y5lt0
• x6Ax6Bx6C-9.6y6lt0
• x1Ax2Ax3Ax4Ax5Ax6A12
• x1Bx2Bx3Bx4Bx5Bx6B10
• x1Cx2Cx3Cx4Cx5Cx6C14

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Mixed Integer Example

• Objective function
• Minimize Z18x1A15x1B12x1C13x2A12x6C405y13
  90y2465y6

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Model Formulation

• The Skimmer Boat Company manufactures three kinds
  of
• molded fiber glass recreational boats a bass
  fighting boat,
• a ski boat, and a speedboat. The profit for a
  bass boat is
• 20,500, the profit for a ski boat is 12,000,
  and the profit for
• a speedboat is 22,300. The company believes it
  will sell
• more bass boats than the other two boats
  combined, but no
• more than twice as many. The ski boat is its
  standard
• production model, and bass boats and speedboats
  are
• modifications. The company has production
  capacity to
• manufacture 210 standard (ski-type) boats
  however, a bass boat
• requires 1.3 times the standard production
  capacity, and a
• speedboat requires 1.5 times the normal
  production capacity.

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Model Formulation

• In addition, only 160 of the high-powered
• engines that are installed in the bass
• boats, and two of which are installed in the
• speed boats, are available. The company
• wants to know how many boats of each
• type to produce to maximize profit.

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Model Formulation

• Corsouth Mortgage Associates is large home
• mortgage firm in the Southwest. It has a pool of
• permanent and temporary computer operators who
• process mortgage accounts, including posting
• payments and updating escrow accounts for
• insurance and taxes. A permanent operator can
• process 220 accounts per day and a temporary
• operator can process 140 accounts per day. On
• average, the firm must process and update at
  least
• 6,300 accounts daily. The company has 32 computer
  workstations available

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Model Formulation

• Permanent and temporary operators work 8 hours
  per day.
• A permanent operator will average about 0.4
  errors per day,
• whereas a temporary operator will average 0.9
  errors per
• day. The company wants to limit errors to 15 per
  day. A
• permanent operator is paid 120 per day, whereas
  a
• temporary operator is paid 75 per day. It is
  also considering
• hiring some hourly, part-time computer operators
  in addition
• to its permanent and temporary operators. A
  part-time operator is
• paid 4.50 per hour. A part-time operator can
  process 12 accounts
• per hour and averages 0.16 errors per hour.
  Corsouth wants to
• know the number of permanent, temporary and
  part-time hours it
• should arrange for.

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Model Formulation

• The Reliance Manufacturing Company produces an
  aircraft part. The company can produce the part
  entirely at a flexible work center with multiple
  computerized machines. The company has four work
  centers, all of which are different because they
  were purchased at different times. Each work
  center has a single operator however, the
  companys operators have different skill levels,
  resulting in different levels of daily output and
  product quality. The following tables show the
  average daily output and average number of
  defects per day for each of the companys five
  operators who are capable of producing the
  aircraft part.

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Model Formulation
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Model Formulation
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Model Formulation

• The company wants to determine which
• operator to assign to each machine to
• maximize daily output and keep the
• percentage of defects to less than 4.