Play Time Toy faces a highly seasonal pattern of sales. In the past, Play Time has used a seasonal production schedule, where the amount produced each month matches the sales for that month. Under this production plan, inventory is maintained at a constant level. The production manager, Thomas Lindop, is proposing a switch to a level, or constant, production schedule. This schedule would result in significant savings in production costs but would have higher storage and handling costs, fluctuating levels of inventories, and implications for financing. Jonathan King, president of Play Time Toy, has been reviewing pro forma income statements, cash budgets, and balance sheets for the coming year under the two production scenarios. Table 9.9 shows the pro forma analysis under seasonal production, and Table 9.10 shows the pro forma analysis under level production.
Greg Cole, chief financial officer of Play Time, prepared the two tables. He explained that the pro forma analyses in Tables 9.9 and 9.10 take fully into account the 11% interest payments on the unsecured loan from Bay Trust Company and the 3% interest received from its cash account. An interest charge of 11%/12 on the balance of the loan at the end of a month must be paid the next month. Similarly, an interest payment of 3%/12 on the cash balance at the end of a month is received in the next month..
The inventory available at the end of December 2006 is $530,000 (measured in terms of cost to produce). Mr. Cole assumed that this inventory represents a sales value of $530,000/0.651667 = $813,300.
Mr. Lindop felt that a minimum of $813,300 of inventory (measured in terms of sales value, or $530,000 measured in terms of cost to produce) must be kept on hand at the end of each month. This inventory level represents a reasonable safety stock, which is required because orders do not occur uniformly during a month.
Mr. King was impressed at the possible increase in profit from $237,000 under the seasonal production plan to $373,000 under level production. While studying the pro forma projections, Mr. King realized that some combination of the two production plans might be even better. He asked Mr. Lindop to try to find a production plan with a higher profit than the seasonal and level plans.
Mr. Lindop proceeded to develop a spreadsheet based LP model to maximize annual net profit.
Question
Note: Mr. Lindop’s model is contained in the file. Play Time.xlsx.The spreadsheet is ready to be optimized, but it has not been optimized yet.
1. Run the optimization model in this file. What is the optimal production plan? What is the optimal annual net profit? How does this optimal production plan compare to the seasonal and level production plans?
2. Suppose that Play Time’s bankers will not extend any credit over $1.9 million—in other words, the loan balance in any month cannot exceed $1.9 million. Modify the spreadsheet model to take into account this restriction. What is the optimal production plan in this case? What is the optimal annual net profit?
3. Annual profit is a measure of reward for Play Time Toy. The maximum loan balance is a measure of risk for the bank. Construct a tradeoff curve between optimal annual profit and the maximum loan balance.