Provide your detailed answers below every part of each question.
The demand for a product is 4000 boxes per month. The holding cost is 20 %/year and the fixed ordering cost is $600 per order. The company is currently using EOQ policy. The supplier regularly charges $4 per box.  The supplier is offering a short-term trade promotion to lower price to $3.60 per box.
Current situation using EOQUsing Trade promotion
EOQÂ Â Optimal Q
Q we end up using
Annual Holding Cost
Annual Ordering Cost
Total Inventory Cost
# of orders/year
Annual Item cost
Grand Total Cost
Cycle Time
Avg. Flow Time
Cycle Inventory
How much is the forward buying? _______________
Annual Savings by accepting the promotion? ___________
To calculate the forward buying, we need to determine the difference in price per box between the current situation and the trade promotion.
Price per box in the current situation = $4
Price per box in the trade promotion = $3.60
Forward buying = (Price per box in the current situation - Price per box in the trade promotion) * Demand per month
Forward buying = ($4 - $3.60) * 4000
Forward buying = $0.40 * 4000
Forward buying = $1600
Therefore, the forward buying amount is $1600.
To calculate the annual savings by accepting the promotion, we need to compare the total inventory costs between the current situation and using the trade promotion.
Calculating total inventory costs for the current situation:
EOQ (Optimal Q) = √((2DS) / H)
EOQ = √((2 * 4000 * $600) / 0.20)
EOQ ≈ √(4,800,000 / 0.20)
EOQ ≈ √24,000,000
EOQ ≈ 4,898 boxes
Annual holding cost = EOQ / 2 * H * Price per box
Annual holding cost = (4,898 / 2) * 0.20 * $4
Annual holding cost ≈ 2,449 * 0.20 * $4
Annual holding cost ≈ $1,959.20
Annual ordering cost = (Demand per year / EOQ) * Ordering cost per order
Annual ordering cost = (4000 * 12 / 4,898) * $600
Annual ordering cost ≈ (48,000 / 4,898) * $600
Annual ordering cost ≈ 9.82 * $600
Annual ordering cost ≈ $5,892
Total inventory cost = Annual holding cost + Annual ordering cost
Total inventory cost = $1,959.20 + $5,892
Total inventory cost ≈ $7,851.20
Calculating total inventory costs using the trade promotion:
Q we end up using = Demand per month = 4000 boxes
Annual holding cost = Q / 2 * H * Price per box
Annual holding cost = (4000 / 2) * 0.20 * $3.60
Annual holding cost ≈ 2000 * 0.20 * $3.60
Annual holding cost ≈ $1,440
Annual ordering cost = (Demand per year / Q) * Ordering cost per order
Annual ordering cost = (4000 * 12 / 4000) * $600
Annual ordering cost ≈ (48,000 / 4000) * $600
Annual ordering cost ≈ 12 * $600
Annual ordering cost ≈ $7,200
Total inventory cost = Annual holding cost + Annual ordering cost
Total inventory cost = $1,440 + $7,200
Total inventory cost ≈ $8,640
Annual savings by accepting the promotion = Total inventory cost in the current situation - Total inventory cost using the trade promotion
Annual savings by accepting the promotion = $7,851.20 - $8,640
Annual savings by accepting the promotion ≈ -$788.80
Therefore, there would be a negative annual savings of approximately -$788.80 if the company accepts the trade promotion.