- A company is trying to decide between using TL (Truck Load) versus LTL (Less than truck load) for ordering a certain item. The item cost is $50 for each unit, the ordering cost is $100/order paid to the supplier, and the holding cost is 20% per year. The trucking cost is $400 for TL with a capacity of 750 units of a truck and $1 per unit for LTL. Should the company use TL or LTL if the annual demand for this item is:
a) 2000 items? (Specify the most economical Q for both options and total cost)
b) 4000 items? (Specify the most economical Q for both options and total cost)
c) At what demand level both options will cost the same.
Full Answer Section
3. Less-Than-Truckload (LTL):
- Trucking Cost (T_LTL): $1 per unit
a) Annual Demand (D) = 2000 items:
TL:
-
Calculate EOQ for TL assuming all 2000 units are shipped in one go (since TL capacity is 750, we won't reach the reorder point):
- EOQ_TL is not applicable here as the entire demand is shipped at once.
-
Calculate Total Cost for TL (assuming one order per year):
- Total Cost_TL = Annual Demand (D) * Item Cost (C) + Ordering Cost (S) + Trucking Cost (T_TL)
- Total Cost_TL = 2000 * $50 + $100 + $400 = $105,000
LTL:
-
Calculate EOQ for LTL:
- EOQ_LTL = √( (2 * D * S) / H)
- EOQ_LTL = √( (2 * 2000 * $100) / $10) = √40000 = 200 units
-
Calculate the number of orders per year (assuming even distribution of demand):
- Number of Orders_LTL = D / EOQ_LTL = 2000 / 200 = 10 orders per year
-
Calculate Total Cost for LTL:
- Total Cost_LTL = (D * C) + (Number of Orders_LTL * S) + (D * T_LTL)
- Total Cost_LTL = (2000 * $50) + (10 * $100) + (2000 * $1) = $102,000
In this case (D = 2000 items), LTL (Less-Than-Truckload) with an annual cost of $102,000 is more economical than TL with a cost of $105,000.
b) Annual Demand (D) = 4000 items:
TL:
-
Calculate EOQ for TL (assuming we still need two orders because the demand is higher than TL capacity):
- EOQ_TL = √( (2 * D * S) / H) for the first order to fill the truck (750 units)
- EOQ_TL = √( (2 * 750 * $100) / $10) = √15000 = 122 units (rounded down to nearest whole unit)
-
Calculate the number of orders per year:
- Number of Orders_TL = D / Q_TL = 4000 / 750 = 5.33 orders (rounded up to 6 orders since we can't place partial orders for a truck)
-
Calculate Total Cost for TL:
- Total Cost_TL = (D * C) + (Number of Orders_TL * S) + (Number of Orders_TL * T_TL)
- Total Cost_TL = (4000 * $50) + (6 * $100) + (6 * $400) = $210,000
LTL:
-
Calculate EOQ for LTL remains the same:
-
Calculate the number of orders per year:
- Number of Orders_LTL = D / EOQ_LTL = 4000 / 200 = 20 orders per year
-
Calculate Total Cost for LTL: