Unit5 Inventory Independent Demand by 547U6b

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									           OPER2110 Advanced Operations Management Unit 5 Inventory Systems for Independent Demand


5.0 Inventory Systems for Independent Demand
     1.1 Introduce different inventory types and reasons for carrying inventory.
     1.2 Describe costs and benefits of carrying inventory.
     1.3 Discuss classical inventory models.
     1.4 Introduce several current methods of inventory management.

Inventory
 inventory is the stock of items owned by the company which will be resold as is, or be resold after
   value is added, to the company’s end-use customer.
 inventory management focuses on minimizing cost and maximizing customer satisfaction:
       o how much to hold in inventory
       o when to reorder
       o how much to order

Types of Inventory
 raw material:
      o purchased items to which no labour has been added by the company.
 finished goods:
      o goods which have been fully manufactured, ready for shipment.
 work in progress (wip):
      o materials which are partially through the manufacturing system, but processing is not
          complete.

Reasons for Having Inventory
 to buffer the company from uncertainty:
      o uncertainty due to raw material supply (lead times, quantities).
      o uncertainty due to manufacturing process.
               wip inventory can improve efficiency and decouple separate processes.
      o uncertainty of demand requires finished goods inventory.
 for support for a strategic plan:
      o if a company has a level production strategy (constant workforce, constant production rate)
          then inventory creates a buffer against variation in demand.
 to achieve economies of scale:
      o reduces setup cost per unit by running more units.
      o allows purchasing and transporting at lower prices.




Andrew Campbell                                                                     Page 1 of 9
           OPER2110 Advanced Operations Management Unit 5 Inventory Systems for Independent Demand


Inventory Costs

Holding/Carrying Costs
 3 types:
      o storage costs: cost of storage facility: rent, insurance, personnel etc.
      o capital costs: opportunity cost of owning inventory (money could be invested in projects etc.
          which would be earning a return).
      o Obsolescence/shrinkage costs:
               Obsolescence: inventory that loses value through depreciation, end of life cycle etc.
               Shrinkage: theft, breakage, loss, taxes etc.
 holding costs rise the longer an item is held in stock.
 can be expressed as a cost per unit or as a percentage of the item value.
 carrying costs can range from 10-40% of the items value (manufactured items).

Setup/Ordering Costs
 setup costs occur at the beginning of production and are the cost of adjusting production equipment
   so part is produced to specification.
 ordering costs are incurred through the time and other costs (telephone etc.) associated with
   ordering.
 cost given as a setup or ordering cost per order.
 ordering costs go down as the order quantity increases (fewer orders per year placed).

Stockout Costs
 occurs when a customer orders an item that is out of stock.
 cost is measured in customer ill will and loss of profit.
 cost decreases as inventory rises (fewer shortages).
 difficult to estimate so is often an educated guess.

Purchase Costs
 purchase price of material.

   a goal of inventory management is finding ordering quantities which minimize the sum of these
    costs.

Independent/Dependent Demand

Dependent Demand
 demand for individual components is determined by the number of finished units required.
      o ie. to produce a car requires 4 rims, 4 tires, 1 engine, etc.

Independent Demand
 pertains to the requirements for end products
 demand for components are not related.
 quantities required must be determined independently.
 to determine what needs to be ordered/produced, rely on forecasts, customer surveys, trends etc.


Andrew Campbell                                                                     Page 2 of 9
           OPER2110 Advanced Operations Management Unit 5 Inventory Systems for Independent Demand


Types of Inventory Systems

   an inventory system provides infrastructure/policies for carrying/controlling material to be stocked.
   system responsible for:
        o ordering/receiving goods.
        o timing orders and recording order details.
        o tracking orders and ship dates.
        o establishing procedure for reordering.
   two types:
        o fixed time period (reorder at the end of a time period).
        o fixed order quantity (reorder when a certain minimum stock level is reached).
                fixed order quantity more popular, with bar coded products and computerized
                   inventory control, reduce the work required this method.

Some Differences Between the Two Types
o fixed order quantity
      o requires perpetual inventory (always knowing stock level).
      o average inventory size lower due to certainty of stock levels.
              preferred for expensive items,
      o better system for critical items or items that have long lead times.
      o requires more time to manage.
o fixed time period
      o preferred if buying different products from one supplier
      o take advantage of volume discounts and lower transport costs.
      o orders are placed at the end of the review period only.

Economic Order Quantity (EOQ)
 order quantity of an inventory item which minimizes its total inventory cost.
 use inventory models to determine EOQ.

Basic Fixed-Order Quantity Model
o determines specific quantity in stock R at which product is reordered and Q size of order.
o model assumes:
       o demand known and constant for period.
       o lead time (time from order to receipt) constant.
       o unit price constant (no volume discounts).
       o ordering and setup costs constant.
       o since demand known, no back orders or stockouts.
       o no relation between products (wrt quantities/inventory levels).




Andrew Campbell                                                                     Page 3 of 9
           OPER2110 Advanced Operations Management Unit 5 Inventory Systems for Independent Demand




                                                                         When inventory levels reach R product is
                                                                         reordered. Order received at end of lead
                                                                         time L.



Cost Model

Total Annual Cost = Annual Purchase Cost + Annual Ordering Cost + Annual Holding Cost

                                   D   Q
                       TC  DC      S H
                                   Q   2
                       Where
                       TC  Total annual cost
                       D  Annual unit demand
                       C  Unit cost
                       Q  Quantity to be ordered
                           (optimum amount is economic order quantity or EOQ)
                       S  Setup or ordering cost per setup or order
                       H  Annual unit holding cost

Holding cost usually expressed as a fraction of unit cost (so H=iC where i is annual % holding cost).




Andrew Campbell                                                                     Page 4 of 9
           OPER2110 Advanced Operations Management Unit 5 Inventory Systems for Independent Demand


Find Q which minimizes cost. Take partial derivative of total cost wrt quantity and set equal to 0:
                              (TC )   DS H
                                      2  0
                               Q      Q   2
                                       2 DS
                             EOQ 
                                        H


To determine reorder quantity R:


                                 R  dL
                                 Where
                                 R  reorder point.
                                 d  Average demand per time period.
                                 L  lead time in periods.

      this is a robust model since EOQ is equal to the square root of a quantity:
           o effect of errors in quantities with square root are reduced.

Example for Text (Davis)




Andrew Campbell                                                                     Page 5 of 9
           OPER2110 Advanced Operations Management Unit 5 Inventory Systems for Independent Demand




Fixed-Order Quantity Inventory Model with Usage

   with previous model the quantity ordered is received in one lot.
   doesn’t allow for inventory being drawn before the order is complete.
   this situation arises when the company is manufacturing to inventory, but inventory is used during
    the manufacturing process.
   can also arise when a supplier doesn’t ship an order completely and inventory is drawn before the
    order is complete.
   this changes the last model total cost in its last term, which calculates holding cost.
        o since inventory is drawn, the inventory level never reaches Q.




The total cost equation for this model:




Andrew Campbell                                                                     Page 6 of 9
           OPER2110 Advanced Operations Management Unit 5 Inventory Systems for Independent Demand



                                  D     1       Q
                       TC  DC     S  (p - d) H
                                  Q     2       p
                       All terms weredefined previously except :
                       p  production rate of item
                       d  continual usage rate

The last term represents the annual holding cost:
        the ½ is present to take the average inventory level
        p-d represents the net production per time period
        Q/p represents number of time periods which pass before production stops (when order is
            filled).
        all together (p-d)Q/p = Imax, which is the peak instock level (less than Q).

To find Q (order quantity) to minimize the total cost, differentiate TC wrt Q and equate to 0.
Results in:
                                                     Note as p (production rate)
                        2DS p                        increases p/(p-d) approaches 1
                EOQ 
                         H pd                       and EOQ approaches EOQ
                                                     without usage.
Example from Davis Text




      result of example is place order for 1826 units when there are 280 units left.



Andrew Campbell                                                                       Page 7 of 9
          OPER2110 Advanced Operations Management Unit 5 Inventory Systems for Independent Demand


ABC Classification System
 tracking, counting, ordering inventory is expensive.
 ABC system classifies inventory so the focus is on items with highest inventory value.
   15% of items in inventory make up 80% of inventory value.
         o items which fall into this range are classified as “A” items.
   35% of items account for about 15% of inventory value.
         o items which fall into this range are classified as “B” items.
   50% of items account for 5% of inventory value.
         o items which fall into this range are classified as “C” items.
 once classified:
      o “A” items are controlled strictly:
               in-stock levels kept as low as possible
               means accurate demand forecasts and inventory record keeping
      o “B”, “C” items require less control and quantities can be higher.
 a major disadvantage of this system:
      o doesn’t take into account length of lead times, customer dissatisfaction with stockout.
      o items which have importance for other reasons than cost can be classified as “A” items.




Andrew Campbell                                                                    Page 8 of 9
          OPER2110 Advanced Operations Management Unit 5 Inventory Systems for Independent Demand


Example (From Russel and Taylor)

  Item                   Annual
   No.      Unit Cost    Usage      Total Value    %Total Value         %Total Quantity
     1       $    60       90        $    5,400      6.32%                  9.00%
     2       $ 350         40        $ 14,000        16.39%                 4.00%
     3       $    30      130        $    3,900      4.57%                 13.00%
     4       $    80       60        $    4,800      5.62%                  6.00%
     5       $    30      100        $    3,000      3.51%                 10.00%
     6       $    20      180        $    3,600      4.22%                 18.00%
     7       $    10      170        $    1,700      1.99%                 17.00%
     8       $ 320         50        $ 16,000        18.74%                 5.00%
     9       $ 510         60        $ 30,600        35.83%                 6.00%
    10       $    20      120        $    2,400      2.81%                 12.00%
TOTAL                     1000       $   85,400

Sort in Descending Order by Total Value
Classify into A,B,C groups based on % total value by
inspection.



                                                                    %Value        % Total
 Item      Unit     Annual                     %Total   %Total      Cumlativ      Quantity       Classificat
  No.     Cost      Usage        Total Value    Value   Quantity       e         Cumulative         ion
    9    $ 510        60          $ 30,600     35.83%    6.00%       35.83%           6.00%          A
    8    $ 320        50          $ 16,000     18.74%    5.00%       54.57%          11.00%          A
    2    $ 350        40          $ 14,000     16.39%    4.00%       70.96%          15.00%          A
    1    $     60     90          $    5,400   6.32%     9.00%       77.28%          24.00%          B
    4    $     80     60          $    4,800   5.62%     6.00%       82.90%          30.00%          B
    3    $     30    130          $    3,900   4.57%    13.00%       87.47%          43.00%          B
    6    $     20    180          $    3,600   4.22%    18.00%       91.69%          61.00%          C
    5    $     30    100          $    3,000   3.51%    10.00%       95.20%          71.00%          C
   10    $     20    120          $    2,400   2.81%    12.00%       98.01%          83.00%          C
    7    $     10    170          $    1,700   1.99%    17.00%      100.00%         100.00%          C




Andrew Campbell                                                                    Page 9 of 9

								
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