Palin's Muffler Shop has one standard muffler that fits a large variety of cars. The shop wishes to establish a periodic review system to manage inventory of this standard muffler. Use the information in the following table to determine the optimal inventory target level (or order-up-to level). Annual demand 3,000 mufflers Standard deviation of daily demand 6 mufflers per working day Item cost $30 per muffler Annual holding cost 25% of item value Review period 15 working days Ordering cost $50 per order Service probability 90% Lead time 2 working days Working days 300 per year If nothing changes (including the safety stock and inventory position), what is the total inventory cost expected for the year? (Use the quantity calculated before and select the closest dollar value)
Question
Palin's Muffler Shop has one standard muffler that fits a large variety of cars. The shop wishes to establish a periodic review system to manage inventory of this standard muffler. Use the information in the following table to determine the optimal inventory target level (or order-up-to level). Annual demand 3,000 mufflers Standard deviation of daily demand 6 mufflers per working day Item cost 50 per order Service probability 90% Lead time 2 working days Working days 300 per year If nothing changes (including the safety stock and inventory position), what is the total inventory cost expected for the year? (Use the quantity calculated before and select the closest dollar value)
Solution
To calculate the total inventory cost expected for the year, we need to first calculate the optimal inventory target level (order-up-to level), and then use that to calculate the total inventory cost.
Step 1: Calculate the average daily demand Annual demand is 3,000 mufflers, and there are 300 working days per year, so the average daily demand is 3,000/300 = 10 mufflers per day.
Step 2: Calculate the demand during the review period and lead time The review period is 15 working days and the lead time is 2 working days, so the total time is 15 + 2 = 17 working days. The demand during this time is 17 days * 10 mufflers/day = 170 mufflers.
Step 3: Calculate the safety stock The standard deviation of daily demand is 6 mufflers per working day. For a service probability of 90%, the z-value (from a standard normal distribution table) is approximately 1.28. So, the safety stock is 1.28 * 6 mufflers/day * sqrt(17 days) = 21 mufflers (rounded to the nearest whole number).
Step 4: Calculate the optimal inventory target level This is the sum of the demand during the review period and lead time, and the safety stock. So, the optimal inventory target level is 170 mufflers + 21 mufflers = 191 mufflers.
Step 5: Calculate the total inventory cost The total inventory cost consists of the ordering cost, the holding cost, and the item cost.
The ordering cost is the annual demand divided by the optimal inventory target level, multiplied by the ordering cost per order. So, the ordering cost is (3,000 mufflers / 191 mufflers/order) * 785 (rounded to the nearest dollar).
The holding cost is the average inventory level (which is half the optimal inventory target level) multiplied by the item cost and the annual holding cost rate. So, the holding cost is (191 mufflers/2) * 716 (rounded to the nearest dollar).
The item cost is the annual demand multiplied by the item cost. So, the item cost is 3,000 mufflers * 90,000.
So, the total inventory cost expected for the year is 716 + 91,501.
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Manico Company produces three products-X, Y, & Z-with the following characteristics: XYZSelling price per unit$21.00$17.00$16.00Variable cost per unit12.6012.756.40Contribution margin per unit$ 8.40$4.25$9.60 === ======= ====== ====Machine hours per unit536The company has only 2,000 machine hours available each month. If demand exceeds the company's capacity, in what sequence should orders be filled if the company wants to maximize its total contribution margin? Question 19Answera.Orders for Y first, X second, and Z thirdb.Orders for X first, Z second, and Y thirdc.Orders for Z first, X second, and Y thirdd.Orders for Z first and no orders for X or Y
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