The problem is to determine the optimal production level of the Egress new designed jacket given the uncertainty in the forecasted demand. As oppose to determining a single profit value in the deterministic approach, the probabilistic method will incorporate the uncertainty in estimated demand and provide insights of the range of profit outcomes and its associated risk (deviation from mean). The key issue is to understand impact of demand uncertainty and production level to the profit range and its distribution. In this case, we will determine the optimal decision variables (jacket production quantity) that will maximize our objective (average profit).
The given information from management is the variable production cost, the selling price, and the salvage value per unit. There is also the fixed production cost regardless of production level. Production can all be sold if it is not greater than the demand level. However, if the production quantity is greater than the demand, it will be sold to discounters at the salvage value price.
When dealing with uncertainty, the simulation model is useful to explicitly incorporate uncertainty into the input variables. This random input variable and the resulting output variables of interest are keep recorded. Hence, we are able to analyze how the outputs vary as of function of the varying inputs. In this case, the demand distribution was assumed normally distributed with the mean and standard deviation from 12 discrete forecasts from Egress employees. The optimal production level of Egress’ new designed is around 10,174 jackets with the average profit of $61,849 and standard deviation of $94,136.
* Decision:Production quantity of ski jacket
* Objective:Maximize the profit
* The decision variable (production quantity)) are non-negative * Variable production cost = $80/jacket
* Selling price = $100/jacket
* Salvage value = $50/jacket
* Fixed production cost = $100,000
* Demand is non-negative and normally distributed.
* Excel’s Add-in: Data Analysis (histogram and descriptive statistics) are used to obtain and analyze statistical data and uncertainty. * RAND function is used to randomly determine the probability of the demand distribution. RAND will generate values between 0 – 1. Number of samples is set at 1,000 to well represent the random range. * NORMINV function is used to convert the random probability to the normal cumulative distribution for the specified mean and standard deviation.
Demand is the normal inverse of the random probability given the mean and standard deviation Normal sales quantity = minimum btween demand and production quantity Salvage sales quantity = extra quantity when demand > production Revenue from normal sales = Selling Price/unit * Normal sales quantity Revenue from salvage value = Salvage Price/unit * Salvage sales quantity Variable costs = Variable Cost/unit * Production quantity
Profit = Revenue from normal sales + Revenue from salvage - Variable costs – Fixed cost Average profit = Average profit from the demand distribution at each production level
* Inputs are all numerical data in the problem
* The changing cells (decision variables) in blue box are the jacket production level. * The target cell (objective) in green box is average profit to be maximized * No constraint
Answer (1): If the normal distribution is a reasonable model for the demand of their ski jacket design in the upcoming season, based on the estimated demand forecast from 12 Egress employees, the mean of the demand distribution would be 12,000 jackets and standard deviation of 3,497. Figure 1 shows the Demand Distribution and Statistical Summary. This demand distribution will be used in calculating the profit at each production level. Figure 1: Demand Distribution and...