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ENGR Fundamentals of Logistics Engineering

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									ENGR 3210 Fundamentals of
  Logistics Engineering

            Class 33
        November 11, 2002
How do you size a warehouse?
What are the important variables?
   Throughput or demand for goods moving through
   Inventory turnover (defines how much inventory
    is stored in the warehouse)
   Storage size requirements for the units to be stored
   The fraction of the total warehouse that is actually
    used for storage (vs. aisle and other space)
      Material handling equipment and storage
        systems used helps to define this fraction

                                                       2
A simple example
   The warehouse will handle 2,400,000 lbs of
    widgets per month
   Monthly turnover of inventory is 3 turns per
    month (turnover is monthly sales divided by
    average inventory)
   The storage system to be used requires that 50%
    of the floor space would be devoted to aisles
   Only 70% of the warehouse is really used for
    storage. The rest will be used for office facilities
   One pound of widgets is packaged in boxes that
    are 0.5 cubic feet in size
   The boxes of widgets can be stacked 16 feet high
    on pallets                                             3
How many square feet do we
need in the warehouse?
   How many pounds of widgets are going to be stored in the
    warehouse?
      2,400,000 lbs / 3 turns per month =800,000 lbs

   How many cubic feet do the widgets take up?
      800,000 lbs (0.5 cu. ft. per lb.) = 400,000 cu. ft.

   How many square feet do the widgets occupy?
      400,000 cu. Ft. / 16 ft. = 25,000 sq ft.

   How much aisle space do we need?
      An equal amount to the widget space = 25,000 sq. ft.

   What about office space ?
      50,000 sq. ft. / 70% = 71,428 sq, ft in the entire
       warehouse
                                                               4
The real question here is not size but cost
(If we are to minimize Total Logistics
Costs)
   Construction of the warehouse is assumed to cost
    $30 / sq. ft.
   The construction cost is amortized over 20 years
    with an interest rate that breaks the construction
    cost down to $1.50 per sq. ft. each year.
   The annual fixed cost to operate a warehouse of
    this type is $3.00 per sq. ft.
   The materials handling charge for this material is
    $0.05 per lb. of throughput.

                                                         5
What is the annual cost of
operating the warehouse?
   What is needed to pay off the construction loan?
      71,428 sq. ft. ($1.50 per sq. ft.) = $107,142

   What is needed to operate the warehouse for a
    year?
      71,428 sq. ft. ($3.00 per sq. ft.) = $214,284

   What is needed to handle the material for a year?
      2,400,000 lbs. (12months) ($0.05) =
       $1,440,000
   Total cost = $1,761,426 per year
                                                        6
A simplified computation for the
example
 Space (sq. ft.)=Monthly demand(lbs.) x
  (1/3)(0.5/16)(1/0.5)(1/.7)
  = Monthly demand x .03
 Annual Cost = Space (sq. ft.) ($4.50) +
  Monthly demand ($0.60)




                                            7
Exploring some design tradeoffs
   What is the cost of the warehouse if the aisle
    requirements are:
      35% of the total space?

      40% of the total space?

      45% of the total space?

   What is the cost of the warehouse if the stacking
    height is:
      17 feet?

      18 feet?

      19 feet?

   What could you afford to spend on equipment to
    achieve each of these improvements?               8
 A spreadsheet solution
Throughput    2,400,000 lbs/mo                                     Construction Cost/sf/yr                  $1.50
Turns                 3 turns/mo                                   Operation Cost/sf/yr                     $3.00
                                                                   Handling Cost/lb                         $0.05
                                                                   Cubic feet/lb                             0.50

SQUARE FEET REQUIRED

                          Stack height
Aisle %             14             15           16           17             18           19          20
    35.00%      62,794         58,608       54,945       51,713         48,840       46,270      43,956
    40.00%      68,027         63,492       59,524       56,022         52,910       50,125      47,619
    45.00%      74,212         69,264       64,935       61,115         57,720       54,682      51,948
    50.00%      81,633         76,190       71,429       67,227         63,492       60,150      57,143
    55.00%      90,703         84,656       79,365       74,697         70,547       66,834      63,492
    60.00%     102,041         95,238       89,286       84,034         79,365       75,188      71,429


ANNUAL COST

                          Stack height
Aisle %              14            15            16           17            18           19           20 AVG $/ft
    35.00%   $1,722,575    $1,703,736    $1,687,253   $1,672,708    $1,659,780   $1,648,213   $1,637,802  $14,129
    40.00%   $1,746,122    $1,725,714    $1,707,857   $1,692,101    $1,678,095   $1,665,564   $1,654,286  $15,306
    45.00%   $1,773,952    $1,751,688    $1,732,208   $1,715,019    $1,699,740   $1,686,070   $1,673,766  $16,698
    50.00%   $1,807,347    $1,782,857    $1,761,429   $1,742,521    $1,725,714   $1,710,677   $1,697,143  $18,367
    55.00%   $1,848,163    $1,820,952    $1,797,143   $1,776,134    $1,757,460   $1,740,752   $1,725,714  $20,408
    60.00%   $1,899,184    $1,868,571    $1,841,786   $1,818,151    $1,797,143   $1,778,346   $1,761,429  $22,959
Avg $/5%        $35,322       $32,967       $30,907      $29,089       $27,473      $26,027      $24,725        9
The results graphed

$1,900,000

 $1,850,000

 $1,800,000

 $1,750,000                                                     35%
                                                                40%
 $1,700,000                                                     45%
                                                                50%
 $1,650,000
                                                                55%
  $1,600,000                                                    60%
                                                          60%
  $1,550,000                                            55%
                                                       50%
  $1,500,000                                          45%
               14                                   40%
                    15   16   17                  35%
                                   18
                                        19   20


                                                                      10
 Which variable promises the biggest
 bang for your dollar?
Throughput    2,400,000 lbs/mo                                     Construction Cost/sf/yr                  $1.50
Turns                 3 turns/mo                                   Operation Cost/sf/yr                     $3.00
                                                                   Handling Cost/lb                         $0.05
                                                                   Cubic feet/lb                             0.50

SQUARE FEET REQUIRED

                          Stack height
Aisle %             14             15           16           17             18           19          20
    35.00%      62,794         58,608       54,945       51,713         48,840       46,270      43,956
    40.00%      68,027         63,492       59,524       56,022         52,910       50,125      47,619
    45.00%      74,212         69,264       64,935       61,115         57,720       54,682      51,948
    50.00%      81,633         76,190       71,429       67,227         63,492       60,150      57,143
    55.00%      90,703         84,656       79,365       74,697         70,547       66,834      63,492
    60.00%     102,041         95,238       89,286       84,034         79,365       75,188      71,429


ANNUAL COST

                          Stack height
Aisle %              14            15            16           17            18           19           20 AVG $/ft
    35.00%   $1,722,575    $1,703,736    $1,687,253   $1,672,708    $1,659,780   $1,648,213   $1,637,802  $14,129
    40.00%   $1,746,122    $1,725,714    $1,707,857   $1,692,101    $1,678,095   $1,665,564   $1,654,286  $15,306
    45.00%   $1,773,952    $1,751,688    $1,732,208   $1,715,019    $1,699,740   $1,686,070   $1,673,766  $16,698
    50.00%   $1,807,347    $1,782,857    $1,761,429   $1,742,521    $1,725,714   $1,710,677   $1,697,143  $18,367
    55.00%   $1,848,163    $1,820,952    $1,797,143   $1,776,134    $1,757,460   $1,740,752   $1,725,714  $20,408
    60.00%   $1,899,184    $1,868,571    $1,841,786   $1,818,151    $1,797,143   $1,778,346   $1,761,429  $22,959
Avg $/5%        $35,322       $32,967       $30,907      $29,089       $27,473      $26,027      $24,725      11
Which has a steeper slope?

$1,900,000

 $1,850,000

 $1,800,000

 $1,750,000                                                     35%
                                                                40%
 $1,700,000                                                     45%
                                                                50%
 $1,650,000
                                                                55%
  $1,600,000                                                    60%
                                                          60%
  $1,550,000                                            55%
                                                       50%
  $1,500,000                                          45%
               14                                   40%
                    15   16   17                  35%
                                   18
                                        19   20


                                                                      12
Implications for design
   For these economic assumptions the total costs are
    more sensitive to reducing aisle width than
    increasing stacking height
   Therefore we would favor materials handling and
    storage systems which minimized aisle width
    (over increasing stacking height)
   Reducing aisle width by 5% will save about
    $30,000 annually
   How much could I spend on equipment to achieve
    this?
                                                     13
Engineering Economics greatly
simplified
   A dollar in your pocket today is worth more than
    the promise of a dollar one year from now
   If you had a dollar today you could put it into a
    savings account earning interest and at the end of
    one year you could extract the dollar plus the
    interest
   There is a “time value of money”
   Comparing equipment investment strategies that
    have different initial costs and varying annual
    costs and benefits require comparing the costs at a
    single point in time                               14
Engineering Economics generally refers
to the process of making economic
comparisons of Engineering investments
like the Equipment in the warehouse
 Forecast or estimate the “streams” of costs
  (or cost savings over time)
 Convert those streams to a common point in
  time using interest rate concepts
 Compare the alternative designs at a
  common point in time in order to make the
  most economical choice
                                            15
A very simple example of the
time value of money
   Would you prefer $3000 now or $3100 a year
    from now?
      If I had $3000 now and could invest it in a bank
       earning 3% interest, the bank would give me
       $3090 at the end of the year. Take the $3100
       next year.
      If I could invest it in another bank which
       offered 5% interest, that bank would give me
       $3150 at the end of the year. Take the $3000
       now.
                                                     16
Translating present worth to
future sums using interest
i = annual rate of interest
n = number of interest periods (usually years)
P = the principal or present value of money
F= the future amount of money




                                             17
Relating F to P is what it is all
about
F=P(1+i) at the end of the first year
F= (P(1+i))(1+i)=P(1+i)2 at the end of the
  second year

F=P(1+i)n at the end of the nth year

Or P=F/(1+i)n to bring a future value back to
 a present value
                                                18
This enables comparison of
alternatives with different cash
flows
Alternative A:
  Costs $10,000 now but returns $4,000 each
    of the next 3 years
Alternative B:
  Costs $8,000 now but returns $3,000 each
    of the next 3 years

                                          19
Graphic Cash Flow Diagrams
 Interest periods on horizontal axis
 Upward arrows represent receipts (positive
  cash flow)
 Downward arrows represent costs (negative
  cash flows)
 Flows assumed to be at end of period



                                           20
The two alternatives depicted
graphically:

                     $4,000 $4,000 $4,000
 Alternative A
                 0      1      2      3

              $10,000
                     $3,000 $3,000 $3,000
  Alternative B
                   0     1      2    3
             $8,000

                                            21
How do you compare them using
Net Present Worth?
 Assume some time value of money or
  interest rate
 Convert the cash flows to a common point
  in time
 Select the alternative with the largest net
  present worth


                                                22
To convert to the present use the
formula: P=F/(1+i)n

                     $4,000 $4,000 $4,000
 Alternative A
                 0      1      2      3

              $10,000
                     $3,000 $3,000 $3,000
  Alternative B
                   0     1      2    3
             $8,000

                                            23
Choosing an appropriate interest
rate
   One way is to think about what it will cost to
    borrow the money from a bank
   Another way to acquire capital is to sell shares of
    stock
   A third method is to think about what could be
    earned if the money were invested in some other
    “project”
   Often a blending of the three
   Seek guidance from your accounting or finance
    department
                                                          24
To convert to the present use the
formula: P=F/(1+i)n (Choose 8% for i)

                     $4,000 $4,000 $4,000 Each future
                                             value must
  Alternative A
                  0      1                   be converted
                                2      3
                                             back to the
              $10,000                        present time, 0
                     $3,000 $3,000 $3,000
  Alternative B
                   0     1       2     3 PA,2=4000/(1+.08)2
              $8,000                     PA,2= 3429

                                                         25
To convert to the present use the
formula: P=F/(1+i)n

             $3429 $4,000        $4,000 Each future
                                           value must
 Alternative A
                 0      1                  be converted
                              2      3
                                           back to the
             $10,000                       present time, 0
                    $3,000 $3,000 $3,000
 Alternative B
                  0     1      2     3 PA,2=4000/(1+.08)2
             $8,000                     PA,2= 3429

                                                       26
Convert all the future values to
present values using P=F/(1+i)n
                      $3704        Net Present Worth
                                   = $10,308 - $10,000
                      $3429
Alternative A         $3175        = $308
                    0     1    2   3
          $10,000
                     $2778         Net Present Worth
                     $2572         = $7,731 - $8,000
                      $2381        = - $269
Alternative B       0      1   2    3
                $8,000

                                                       27
Lets go back to the equipment
expense question
 How much can I afford to spend on
  equipment to reduce the aisle percentage by
  5%?
 Reducing the aisle percentage by 5% saves
  us $30,000 annually
     $30k $30k              $30k


     ??
                                            28
Some key questions needed to
find the appropriate investment in
the equipment
 What is the useful life of the equipment?
 Are there operating charges that should be
  estimated for each year?
 Is there a salvage value at the end of the
  useful life?
 What is an appropriate interest rate?


                                               29
Including $5k operating costs and a
salvage value of $5k at the end of 8 years


       $30k $30k          $30k     $5k


  ??    $5k                      $5k




                                         30
We could invest 146,000 dollars
   Interest=       0.08   Future        Present
                          Value         Value
               1                   25    23.14815
               2                   25    21.43347
               3                   25    19.84581
               4                   25    18.37575
               5                   25    17.01458
               6                   25    15.75424
               7                   25    14.58726
               8                   30    16.20807
                          Total          146.3673

                                                    31

								
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