Analysis assuming optimal fashion
Provide your detailed answers below every part of each question.
The annual demand for a product is 64,000 items and the holding cost is $0.50/ item/ year. The operates 300 days per year and lead time is 9 days. The ordering cost is $250 per order.
a) Find the following assuming that the company is operating in an optimal fashion:
Economic Order Quantity _________
Cycle Time __________
Cycle Inventory _________
Safety Inventory _______
ROP __________
Annual Holding Cost __________
Grand Total Cost ________
b) Now assume that the company keeps safety stock of 200 items to account for the standard deviation in demand of 50 items and the lead time standard deviation of 2 days. Find the following:
Cycle Inventory _________
Safety Inventory _______
ROP _______
CSL_________
E(#Short) ________
Fill rate _______
Average Inventory _________
Average Flow Time __________
Inventory Holding Cost ________
c) Now Suppose that the company decides that they operate at a service level of 0.95 What will Cycle Inventory _________
Safety Inventory _______
ROP _______
E(#Short) ________
Fill rate _______
Average Inventory _________
Average Flow Time __________
Inventory Holding Cost ________
a) Analysis assuming optimal fashion:
Given data:
Demand per year = 64,000 items
Holding cost = $0.50/item/year
Operating days per year = 300 days
Lead time = 9 days
Ordering cost = $250/order
To find the Economic Order Quantity (EOQ), we use the formula:
EOQ = √((2 * Demand per year * Ordering cost) / Holding cost)
EOQ = √((2 * 64,000 * $250) / $0.50) = √(32,000,000 / $0.50) = √64,000,000 = 8,000 items
To find the Cycle Time (CT):
CT = EOQ / Demand per day
Demand per day = Demand per year / Operating days per year
CT = 8,000 / (64,000 / 300) = 8,000 / 213.33 = 37.50 days
To find the Cycle Inventory (CI):
CI = EOQ / 2
CI = 8,000 / 2 = 4,000 items
To find the Safety Inventory (SI):
SI = Demand per day * Lead time
SI = (64,000 / 300) * 9 = 213.33 * 9 = 1,920 items
To find the Reorder Point (ROP):
ROP = Demand per day * Lead time + Safety Inventory
ROP = (64,000 / 300) * 9 + 1,920 = 213.33 * 9 + 1,920 = 3,920 items
To find the Annual Holding Cost:
Annual Holding Cost = CI * Holding cost
Annual Holding Cost = 4,000 * $0.50/item/year = $2,000
To find the Grand Total Cost:
Grand Total Cost = Ordering cost * (Demand per year / EOQ) + Annual Holding Cost
Grand Total Cost = $250 * (64,000 / 8,000) + $2,000 = $2,000 + $2,000 = $4,000
b) Analysis with safety stock:
Given data:
Safety stock = 200 items
Standard deviation in demand = 50 items
Standard deviation in lead time = 2 days
To find the Cycle Inventory (CI):
CI = EOQ / 2
CI = 8,000 / 2 = 4,000 items
To find the Safety Inventory (SI):
SI = Safety stock + (Standard deviation in demand * √Lead time)
SI = 200 + (50 * √9) = 200 + (50 * 3) = 200 + 150 = 350 items
To find the Reorder Point (ROP):
ROP = Demand per day * Lead time + Safety Inventory
ROP = (64,000 / 300) * 9 + 350 = 213.33 * 9 + 350 = 3,920 + 350 = 4,270 items
To find the Cycle Service Level (CSL):
CSL = (1 - Safety stock / ROP) * 100
CSL = (1 - 200/4,270) * 100 = (1 - 0.0468) * 100 = 95.32%
To find E(#Short):
E(#Short) = Demand per day * (1 - CSL/100)
E(#Short) = (64,000 / 300) * (1 - 95.32/100) = 213.33 * (1 - 0.9532) ≈ 10 items
To find Fill rate:
Fill rate = (1 - E(#Short) / Demand per day) * 100
Fill rate = (1 - 10/213.33) * 100 ≈ (1 - 0.0468) * 100 ≈ 95.32%
To find Average Inventory:
Average Inventory = CI + SI
Average Inventory = 4,000 + 350 ≈ 4,350 items
To find Average Flow Time:
Average Flow Time = CT + Lead time
Average Flow Time ≈ 37.50 + 9 ≈ 46.50 days
To find Inventory Holding Cost:
Inventory Holding Cost = Average Inventory * Holding cost
Inventory Holding Cost ≈ 4,350 * $0.50/item/year ≈ $2,175
c) Analysis with a service level of 0.95:
Given data:
Service level (CSL) = 0.95
To find the Cycle Inventory (CI):
CI remains unchanged from previous calculations.
CI ≈ 4,000 items
To find the Safety Inventory (SI):
SI remains unchanged from previous calculations.
SI ≈ 350 items
To find the Reorder Point (ROP):
ROP remains unchanged from previous calculations.
ROP ≈ 4,270 items
To find E(#Short):
E(#Short) remains unchanged from previous calculations.
E(#Short) ≈ 10 items
To find Fill rate:
Fill rate remains unchanged from previous calculations.
Fill rate ≈ 95.32%
To find Average Inventory:
Average Inventory remains unchanged from previous calculations.
Average Inventory ≈ 4,350 items
To find Average Flow Time:
Average Flow Time remains unchanged from previous calculations.
Average Flow Time ≈ 46.50 days
To find Inventory Holding Cost:
Inventory Holding Cost remains unchanged from previous calculations.
Inventory Holding Cost ≈ $2,175