A wholesaler of stationery is deciding how many desk calendars to stock in inventory for the coming year. It is impossible for him to reorder, and leftover units are worthless. The following numbers indicate the possible demand levels:
Demand in 000's 100 300 200 400
The calendars sell for $105 per thousand and cost $75 per thousand (this cost includes inventory carrying costs) with a $5 per thousand sales commission cost. Replenishment costs are not included in the sales commission figure. There is no salvage value and no opportunity cost due to lost sales.
1. Assume the wholesaler regrets his decision for a given demand level, what is his optimum stock level when he believes he should keep his highest opportunity losses at the lowest level? Why? Show your work. Answer: Stock 100 or 200.
2. Assuming each demand has a similar possibility of occurring, what do you expect would be the profit at the optimum stock level? Why? Show your work. Answer: Stock 100 or 200.
3.What is the optimal stock action using the "criterion of realism" when alpha is .7?
4. Present the payoff table if there was a salvage value of $3 per thousand of unsold calendars and if there was a opportunity cost of lost sales of 2$ per thousand of unsold calendars. Just present the payoff table, no solution using any of the criteria of decision making under uncertainty.
1. To determine the optimum stock level when the wholesaler regrets his decision, we need to analyze the expected opportunity losses for each possible demand level.
Opportunity loss is the difference between the revenue generated and the cost incurred for each possible demand level. In this case, the revenue is calculated by multiplying the demand level by the selling price per unit, and the cost is calculated by multiplying the demand level by the cost per unit.
Let's calculate the opportunity losses for each demand level:
Demand 100: Revenue = 100 * $105 = $10,500, Cost = 100 * $75 = $7,500
Opportunity Loss = Revenue - Cost = $10,500 - $7,500 = $3,000
Demand 300: Revenue = 300 * $105 = $31,500, Cost = 300 * $75 = $22,500
Opportunity Loss = Revenue - Cost = $31,500 - $22,500 = $9,000
Demand 200: Revenue = 200 * $105 = $21,000, Cost = 200 * $75 = $15,000
Opportunity Loss = Revenue - Cost = $21,000 - $15,000 = $6,000
Demand 400: Revenue = 400 * $105 = $42,000, Cost = 400 * $75 = $30,000
Opportunity Loss = Revenue - Cost = $42,000 - $30,000 = $12,000
Based on the calculations, the lowest opportunity losses are for the demand levels of 100 and 200. Therefore, the optimal stock level would be to stock either 100 or 200 desk calendars.
2. Assuming each demand has a similar possibility of occurring, we can calculate the expected profit at the optimum stock level.
Expected profit can be calculated by multiplying the probability of each demand level with its corresponding opportunity loss and subtracting the cost per unit.
Let's assume each demand level has a probability of 0.25 (since there are 4 equally likely demand levels), and calculate the expected profit for the stock levels of 100 and 200:
For stock level 100:
Expected Profit = (0.25 * $3,000) - (100 * $75) = $750 - $7,500 = -$6,750
For stock level 200:
Expected Profit = (0.25 * $6,000) - (200 * $75) = $1,500 - $15,000 = -$13,500
Based on the calculations, the expected profit at the optimum stock level is negative for both stock level 100 and 200, indicating a potential loss.
3. The optimal stock action using the "criterion of realism" when alpha is 0.7 refers to a decision-making approach that prioritizes more realistic and achievable outcomes.
To determine the optimal stock action, we need to consider the probabilities assigned to each demand level, the opportunity losses, and the cutoff point determined by alpha (0.7).
Unfortunately, the information provided does not specify the probabilities assigned to each demand level. Without this information, it is not possible to calculate the optimal stock action using the criterion of realism.
4. Payoff table (with salvage value and opportunity cost):
| Demand 100 | Demand 300 | Demand 200 | Demand 400
------------------------------------------------------------------------
Stock 100 | $8,700 | -$750 | $3,000 | -$3,000
Stock 200 | $7,800 | $9,750 | $6,000 | $3,000
Stock 300 | $6,900 | $20,250 | $9,000 | $9,000
Stock 400 | $6,000 | $30,750 | $12,000 | $15,000
In the payoff table, the values represent the profit (or loss) associated with each combination of stock level and demand level. The salvage value and opportunity cost are reflected in the calculations.
Note: The calculations for the payoff table are based on the given information, but the actual values may vary depending on specific probabilities assigned to each demand level.