The reorder point r = dm is defined as the lead-time demand for an item. in cases of long lead times, the lead-time demand and thus the reorder point may exceed the economic order quantity q*. in such cases, the inventory position will not equal the inventory on hand when an order is placed, and the reorder point may be expressed in terms of either the inventory position or the inventory on hand. consider the economic order quantity model with d = 5,000, co = $32, ch = $2, and 250 working days per year. identify the reorder point in terms of the inventory position and in terms of the inventory on hand for each of the following lead times:
a. 5 days
b. 15 days
c. 25 days
d. 45 days

Please find the detailed answer as follows:

Explanation:

Daily Demand

Daily Demand = Annual Demand / Working days per year

= 5,000 units / 250 days

= 20 units per day

Economic Order Quantity [EOQ]

Economic Order Quantity [EOQ] is calculated by using the following formula

Economic Order Quantity = [(2 × Annual Demand x Ordering Cost) / Carrying Cost Per Order]½

Economic Order Quantity = [(2 × Annual Demand x Ordering Cost) / Carrying Cost Per Order] ½

= [(2 × 5,000 x 32) / 2]½

= [320,000 / 2] ½

= [160,000]½

= 400 Units

Reorder point and inventory on hand if the lead time is 5 Days

Re-order Point = 100 Units [5 Days x 20 units per day]

Inventory position and inventory on hand = 100 units [Since, the Re-order Point is less than the EOQ]

Reorder point and inventory on hand if the lead time is 15 Days

Re-order Point = 300 Units [15 Days x 20 units per day]

Inventory position and inventory on hand = 300 units [Since, the Re-order Point is less than the EOQ]

Reorder point and inventory on hand if the lead time is 25 Days

Re-order Point = 500 Units [25 Days x 20 units per day]

Inventory position and inventory on hand = 400 units [Since, the Re-order Point is greater than the EOQ]

Reorder point and inventory on hand if the lead time is 45 Days

Re-order Point = 900 Units [45 Days x 20 units per day]

Inventory position and inventory on hand = 400 units [Since, the Re-order Point is greater than the EOQ]

b

explanation: