Speciality Toys.
The Synopsis of the problem:
Specialty Toys, a retailer of Children’s toys is planning to launch a new toy called “Weather Teddy”. Sales Managers at the stores are working relentlessly to forecast the most appropriate demand order quantity in such a way that profit could be maximized. The analysis of the problem calls for an ideal demand order quantity situation with lower probability of stock-out option.
Following is the statistical information given:
The cost of goods sold per unit = $ 16
The cost of Sales price Per Unit = $ 24
Surplus inventory sales price per unit = $ 5
Cost of excess inventory per unit = $ 16- $ 5 = $ 11
Expected Demand predicted by Sales Forecaster= 20,000 units
Probability of demand between 10,000 units and 30,000 units = 0.95
Solution of the problem:
In order to make the most appropriate recommendation to Management, a Managerial report has been prepared that addresses following issues:
1. Normal Probability Distribution sketch used to approximate the demand distribution with the its mean and Standard Deviation
0.4750
0.4750
0.95
10,000 20,000 30,000 10,000 20,000 30,000
Figure 1: Normal Probability Distribution Curve for Expected demand Expected Demand = 20,000 Hence, Mean () = 20,000 The probability of demand units to be in between 10,000 and 20,000 is 0.95 as also given in the Figure 1. In order to compute Standard Deviation, we will use following statistical formula: Z = (x - )/ …………………………………………………………..(1.1) Where, Z = mean of normal distribution X = The demand units = The mean of demand order quantity = Standard deviation of mean order quantity In order to calculate z value from the probability given, we need to calculate the exact probability @ 30,000 units order quantity. Since the 0.95 probability of demand being in between 10,000 units and 20,000 units represent the orange shaded region in Figure 1, the probability at 30,000 units has been calculated as below:
Specialty Toys, a retailer of Children’s toys is planning to launch a new toy called “Weather Teddy”. Sales Managers at the stores are working relentlessly to forecast the most appropriate demand order quantity in such a way that profit could be maximized. The analysis of the problem calls for an ideal demand order quantity situation with lower probability of stock-out option.
Following is the statistical information given:
The cost of goods sold per unit = $ 16
The cost of Sales price Per Unit = $ 24
Surplus inventory sales price per unit = $ 5
Cost of excess inventory per unit = $ 16- $ 5 = $ 11
Expected Demand predicted by Sales Forecaster= 20,000 units
Probability of demand between 10,000 units and 30,000 units = 0.95
Solution of the problem:
In order to make the most appropriate recommendation to Management, a Managerial report has been prepared that addresses following issues:
1. Normal Probability Distribution sketch used to approximate the demand distribution with the its mean and Standard Deviation
0.4750
0.4750
0.95
10,000 20,000 30,000 10,000 20,000 30,000
Figure 1: Normal Probability Distribution Curve for Expected demand Expected Demand = 20,000 Hence, Mean () = 20,000 The probability of demand units to be in between 10,000 and 20,000 is 0.95 as also given in the Figure 1. In order to compute Standard Deviation, we will use following statistical formula: Z = (x - )/ …………………………………………………………..(1.1) Where, Z = mean of normal distribution X = The demand units = The mean of demand order quantity = Standard deviation of mean order quantity In order to calculate z value from the probability given, we need to calculate the exact probability @ 30,000 units order quantity. Since the 0.95 probability of demand being in between 10,000 units and 20,000 units represent the orange shaded region in Figure 1, the probability at 30,000 units has been calculated as below: