MBA 650: Quantitative Analysis

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MBA 650 Quantitative Analysis
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Bay Area Bakery

• Assumptions
• A linear relationship between time and demand
• Prices and costs remain constant over time
• Options
• Do nothing (capacity 6500 Cwt.)
• Build San Jose (capacity 6500 1200 Cwt.)
• Lease San Jose (capacity 6500 700 Cwt.)
• Expand Richmond (capacity 6500 500 to 1000
  Cwt. in increments of 100 Cwt.)

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Bay Area Bakery Suggested Financial Analysis
(Ignore Depreciation)
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Transportation Problem

• Special structure all aij are 1 or 0
• Artificial variables none
• Input
• Si supply at source i
• Dj demand at destination j
• Cij unit transportation cost between source i
  and destination j
• Output
• xij amount shipped from source i to destination
  j
• z total cost

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Transportation ProblemLP Formulation

• Min z Smi1Snj1 cij xij
• m represents rows n represents columns
• No. of decision variables m n
• St Smi1 xij gt Dj, j 1, 2, . ,n
• Snj1 xij lt Si, i 1, 2, . ,m
• No. of constraints m n
• xij gt 0
• aij 1 or 0
• This gives the model a computational advantage
  over the simplex method

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Transportation Problem3-Step Solution Procedure

• 1. Determine initial, feasible solution
• Use NW corner rule or Vogels approximation
  method
• 2. Determine entering variable
• 3. Determine leaving variable

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TP Solution Procedure Step 2

• 2. Determine entering variable
• i. For BASIC vars ui vj cij
• ii. For NONBASIC vars c-barij ui vj cij
• MIN problem most positive c-barij enters
• MAX problem most negative c-barij enters
• iii. If all c-barij lt 0 (MIN problem) or gt 0 (MAX
  problem), STOP!
• Iv. If not, go to STEP 3!

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TP Solution Procedure Step 3

• 3. Determine leaving variable
• i. Construct closed loop
• Start and end with entering var
• Use only BASIC vars to turn corners
• ii. Add units to entering var until a BASIC var
  is driven to zero
• iii. The leaving var is the BASIC var driven to
  zero first
• iv. Calculate new Z
• v. Return to STEP 2!