Optimal Production Planning for Sodium Bisulfate Manufacturing
a) How many bags per run is optimal?
a) 500 bags per run
b) What would the average inventory be, in bags, for this lot size?
b) 50,000 bags
c) Determine the approximate length of a production run, in days.
c) 500 days
d) About how many runs per year would there be?
d) 3 runs per year
e) How much could the company save annually if the setup cost could be reduced to $25 per run?
e) $225 annually
a) - e) Solutions and Detailed Explanation
a) To determine the optimal number of bags per run, we need to consider the demand and the production capacity. Demand for sodium bisulfate is 20 tonnes per day, and the production capacity is 50 tonnes per day. Since 1 tonne is equal to 1,000 kg, the demand is 20,000 kg per day and the production capacity is 50,000 kg per day. Each bag of sodium bisulfate weighs 100 kg, so we can calculate the optimal number of bags per run by dividing the production capacity by the weight of each bag: 50,000 kg / 100 kg = 500 bags per run. Therefore, the optimal number of bags per run is 500.
b) To calculate the average inventory in bags for this lot size, we consider the total production capacity and the even distribution of production throughout the year. The total production capacity per year is 10,000 tonnes, which is equal to 100,000 bags. The average inventory is half of the total production capacity, so the average inventory in bags for this lot size would be 100,000 bags / 2 = 50,000 bags.
c) The approximate length of a production run can be determined by dividing the total production capacity by the daily demand. With a total production capacity of 10,000 tonnes and a demand of 20 tonnes per day, the approximate length of a production run is 10,000 tonnes / 20 tonnes/day = 500 days.
d) The number of runs per year is estimated by dividing the total production capacity by the annual demand. With a total production capacity of 10,000 tonnes and an annual demand of 4,000 tonnes, the number of runs per year would be 10,000 tonnes / 4,000 tonnes = 2.5 runs. Rounded to the nearest whole number, there would be approximately 3 runs per year.
e) If the setup cost could be reduced to $25 per run, the company would save $225 annually. The current annual setup cost is $300 based on a setup cost of $100 and 3 runs per year. By reducing the setup cost to $25 per run, the new annual setup cost would be $75. Therefore, the company could save $300 - $75 = $225 annually if the setup cost could be reduced to $25 per run.