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                                  Semester III, AY 2011-12

                        MGMT 3060 – Assignment Problem Sheet
                 This problem Sheet has THREE (3) Questions and THREE (3) pages.

                                 Instructions: Attempt all Questions

Question 1 : LP Assignment model

The Akron Police Department has five detective squads available for assignment to five open
crime cases. The chief of detectives, Paul Kuzdrall, wishes to assign the squads so that the total
time to conclude the cases is minimized. The average number of days, based on past
performance, for each squad to complete each case is as follows:

           SQUAD            A             B           C         D          E
              1             14             7           3         7         27
              2             20             7          12         6         30
              3             10             3           4         5         21
              4              8            12           7        12         21
              5             13            25          24        26          8

       a) Using the Hungarian (manual) method, determine the optimal assignment of squads
          to cases in order to minimize the time for completion of cases. Indicate this overall
                                                                       ( 15 marks )

       b) Write an LP formulation for this problem with an objective function and constraints
          for the squads and cases
                                                                       ( 15 marks )
Question 2     MRP

The demand for subassembly S is 100 units in week 7. Each unit of S requires 1 unit of T and 2 units
of U. Each unit of T requires 1 unit of V, 2 units of W and 1 unit of X. Finally, each unit of U requires
2 units of Y and 3 units of Z. One firm manufactures all items. It takes 2 weeks to make S, 1 week to
make T, 2 weeks to make U, 2 weeks to make V, 3 weeks to make W, 1 week to make X, 2 weeks to
make Y, and 1 week to make Z.
The following is the on-hand inventory for the various items.

        ITEM          ON-HAND INVENTORY            ITEM         ON-HAND INVENTORY

        S                       20                 W                      30

        T                       20                 X                      25

        U                       40                 Y                      240

        V                       30                 Z                      40

                a)   Construct a product structure. Identify all levels, parents, and components.
                                                                           ( 10 marks )

                b) Prepare a time-phased product structure.
                                                                         ( 10 marks )

                c) Use the pre-ruled schedules attached at back of the question sheet to determine
                   complete schedules for items S, T, W, U, Z and Y
                                                                     ( 15 marks )

Question 3

    a) Marilyn Charles is the purchasing agent for Central Valve Company, which sells
       industrial valves and fluid-control devices. One of Central’s most popular valves is the
       Western, which has an annual demand of 4,000 units. The cost of each valve is $90, and
       the inventory carrying cost is $9. Marilyn has made a study of the costs involved in
       placing an order for any of the valves that Central stocks, and she has concluded that the
       average ordering cost is $25 per order. Furthermore it takes about 5 working days for an
       order to arrive from the supplier. During this time the demand per week for valves is
       approximately 80.
    Determine :

          i.   The economic order quantity                                     ( 5 marks )
         ii.   The average inventory if the EOQ is used ?                      ( 2 marks )
        iii.   The optimal number of orders per year ?                         ( 3 marks )
        iv.    The optimal number of days between any two orders, assuming 250 working days
               per year ?                                                      ( 4 marks )
         v.    The total annual inventory cost (carrying cost plus order cost) ( 3 marks )
        vi.    The reorder point.                                              ( 3 marks )

b) Wang Distributors has an annual demand for an airport metal detector of 1,400 units. The
   cost of a typical detector to Wang is $400. Carrying cost is estimated to be 20% of the
   unit cost and the ordering cost is $25 per order.

    If Ping Wang, the owner, orders in quantities of 300 - 600, he can get a 5% discount on
    the cost of the detectors.

   i.      Should Wang take the quantity discount ?                            ( 10 marks )
  ii.      Would his decision change if the discount was 10% for orders above 600 ?
                                                                               ( 5 marks )

                                    End of Question Sheet

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