Part I)  The crabtree olive distribution company The crabtree olive distribution company distributes olives Grown in florida to markets in california.  The olives are Stored in distribution centers, at which they are kept in Special, temperature controlled facilities.  When needed, The olives are shipped to retail stores, usually large super Markets around the state of california.  The crabtree company Currently maintains five distribution and storage centers in California, which ship to six retail outlets in the state. Thor heyardahl, the operations manager for the company wishes to determine a shipping pattern of olives from distribution centers to retail outlets in an appropriate manner.  The table below indicates the costs per bushel of olives for shipping from distribution centers to retail outlets.  Also shown in the table are the monthly supplies (in bushels) of olives available at each distribution center and the monthly demand for olives (also in bushels) at each retail outlet.   

You are to advise thor (the operations manager) on an appropriate shipping pattern using:

a) the northwest corner rule

b) the least-cost method

In your results make sure to show the shipping patterns for each method.  Also, calculate the total shipping cost for each method.  Compare these costs and summarize your recommendations. Note that all costs in the table are in dollars ($), and represent the cost of shipping one bushel of olives from the corresponding distribution center to the appropriate destination (retail outlet).

DISTRIB-          DESTINATION (RETAIL OUTLET)

UTION

CENTER A      B      C       D       E       F       SUPPLY  

                                                   (BUSHELS)

 1 $ 28.43  27.25  26.54   29.27   26.37   29.04      500

 2   37.62  29.55  38.87   37.64   29.37   46.78      600

 3   29.88  38.99  39.52   35.98   37.23   36.97      400

 4   28.01  37.66  29.70   36.45   38.27   39.33      300

 5   26.42  27.87  25.22   36.71   22.88   36.33      700

DEM-

AND   380    450    530     480     370     290

(BUSH-

 ELS)

Part II: Scheduling bart train operators the operations management dept. For bart wishes to schedule train operators on a daily basis.  All operators are scheduled to work a six hour shift (no "swing shifts" allowed). The operators are scheduled to work during the bart operating Hours of 4 a.m. to 12 a.m.  the operators are paid $30.00 per hour, with the exception of operators working before 10 a.m. And after 8 p.m. being paid $40.00 per hour (for those hours only).  The required staffing levels for each two hour period during the day are as shown below:

                             OPERATORS

  TIME PERIOD                 REQUIRED

  4 AM  -  6 AM                 12

  6 AM  -  8 AM                 16

  8 AM  - 10 AM                 28

 10 AM  - 12 PM                 22

 12 PM  -  2 PM                 18

  2 PM  -  4 PM                 20

  4 PM  -  6 PM                 30

  6 PM  -  8 PM                 26

  8 PM  - 10 PM                 18

 10 PM  - 12 AM                 13 

The bart management has appointed wiley post as operations manager responsible for developing a schedule for bart operators.

I) Develop a schedule using a simple tabular procedure of your choosing.  Make sure to show your work for this!! Determine:

A) the number of bart train operators to be assigned to each 6-hour shift you consider.

B) the total number of bart train operators you will need for your assignment.

C) the total cost for your assignment.  Make sure to show how you calculated these and the results above.

Note that you will not need the computer to calculate the results for the above!

II) formulate this problem as an integer programming problem. (you do not have to solve!!!!)  Make sure to define your variables, and write your objective function and constraints.  Note That your objective is to minimize the daily cost of train operator scheduling!

Why do you think it would be better to address this as an integer and not a linear problem?