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ANNUAL TRANSPORTATION AND IN-TRANSIT INVENTORY COSTS. Calculating Annual Transportation Cost. Volume transportation rates: reduced rate applies to the entire shipment Annual transportation cost = (freight rate per unit) x (annual demand in units) F = freight rate per unit

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ANNUAL TRANSPORTATIONAND IN-TRANSIT INVENTORY COSTS


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Calculating Annual Transportation Cost

  • Volume transportation rates: reduced rate applies to the entire shipment

  • Annual transportation cost = (freight rate per unit) x (annual demand in units)

    • F = freight rate per unit

    • FD = annual transportation cost


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  • Many carriers (notably LTL motor carriers and railroads) quote transportation rates in $ per hundred pounds, or $ per cwt

    • Convert units to cwts or freight rate per cwt to freight rate per unit; we will convert the freight rate

    • Divide the freight rate per cwt by the number of units in a cwt; number of units in a cwt is 100/unit weight in pounds

      Example: freight rate per cwt = $30; weight per unit = 15 pounds; freight rate per unit = $30/(100/15) = $4.50 per cwt


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Calculating the Annual In-transit Inventory Cost quote transportation rates in $ per hundred pounds, or $ per cwt

  • Annual in-transit inventory cost =

    (annual in-transit inventory level in units)

    x

    (average value per unit of inventory)

    x

    (the cost of carrying in-transit inventory expressed as a percentage of investment in in-transit inventory)


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  • Two new variables: quote transportation rates in $ per hundred pounds, or $ per cwt

    • I = opportunity cost of capital = cost of carrying in-transit inventory (%)

    • T = average transit time (in days)


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Annual in-transit inventory level = quote transportation rates in $ per hundred pounds, or $ per cwt

(Q units in in-transit inventory each shipment)

x

(number of days in transit as percentage of a year, or T/365)

x

(number of shipments per year, or D/Q) =

(Q) x (T/365) x (D/Q) = DT/365


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  • Average value of inventory per unit = quote transportation rates in $ per hundred pounds, or $ per cwtV

  • Cost of carrying in-transit inventory = I

  • Thus, annual in-transit inventory cost = DTVI/365


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  • New and improved annual T.L.C.: quote transportation rates in $ per hundred pounds, or $ per cwt

    .5QVC + PD/Q + FD +DTVI/365

    Note: taking derivative, setting equal to zero, and solving for Q results in EOQ equation (because ‘Q’ does not show up in annual transportation cost and annual in-transit inventory cost expressions)

  • Thus, we need to compare T.L.C. at EOQ volume and at Q values greater than EOQ volume where transportation freight rate discounts are offered.


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Total cost quote transportation rates in $ per hundred pounds, or $ per cwt

Annual cost

(dollars)

L

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s

t

t

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t

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(

E

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Q

)

Inventory

carrying

cost

Ordering cost

Size of order

Transport cost

In-transit inv. cost

QT

EOQ