ANNUAL TRANSPORTATION AND IN-TRANSIT INVENTORY COSTS

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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

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
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

Calculating the Annual In-transit Inventory Cost
• 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)

Two new variables:
• I = opportunity cost of capital = cost of carrying in-transit inventory (%)
• T = average transit time (in days)
Annual in-transit inventory level =

(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

Average value of inventory per unit = V
• Cost of carrying in-transit inventory = I
• Thus, annual in-transit inventory cost = DTVI/365
New and improved annual T.L.C.:

.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.

Total cost

Annual cost

(dollars)

L

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E

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Q

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Inventory

carrying

cost

Ordering cost

Size of order

Transport cost

In-transit inv. cost

QT

EOQ