Companies commonly use simple cut-and-try charting and graphing methods to develop aggregate plans. This approach involves costing out various production planning alternatives and selecting the lowest cost plan. Spreadsheets are often used to facilitate the calculations. Suppose we wish to set up a production plan for XYZ Company for the next six months. We are given the following information shown in Tables 1, 2, and 3.

TABLE 1: Forecasted demand and working days

	January	February	March	April	May	June	Totals
Demand forecast Number of working days	1,800 22	1,500 19	1,100 21	900 21	1,100 22	1,600 20	8,000 125

TABLE 2: Costs

Inventory holding cost Cost of stockout Cost of subcontracting Hiring and training cost Layoff/firing cost Labor hours required Straight-line cost (first 8 hours each day) Overtime cost (time and half)

$1.50/unit/month $5/unit/month $20/unit $200/worker $250/worker 5 hours/unit $4/hour $6/hour

TABLE 3: Initial inventory and safety stock requirements

Beginning inventory Safety stock

400 units 25% of month demand

NOTE: Straight-line production cost = regular-time (8 hours each day) production cost.

1. Calculating Aggregate Production Planning Requirements. Before investigating alternative production plans, it is often useful to convert demand forecasts into production requirements, which take into account the safety stock estimates. A safety stock is an extra stock often added to production requirements in aggregate plans to allow for uneven or uncertain future demand. In this example, the safety stock is equal to 25% of the monthly demand forecast (i.e. safety stock = 0.25 demand forecast for the month). Production requirement and ending inventory in each month are calculated as follows.

• Production requirement in month = Demand forecast in month + safety stock in month beginning inventory in month
• Ending inventory in month = Beginning inventory in month + Production requirement in month Demand forecast in month .
• If ending inventory in a month is positive, this means we have on-hand inventory at the end of the month.
• If ending inventory in a month is negative, this means we have a shortage. This shortage can be satisfied by using any of these strategies: backordering, overtime, undertime, subcontacting, etc.

Use the information given in Tables 1 and 3 to fill in appropriate values for the quantities listed in the first column of the following table (Table 4) for each month (January to June) of the planning period. In the column labelled Total, calculate the totals only for the rows indicated by a question mark (?).

2. Now XYZ wants to formulate and evaluate alternative production plans. XYZ wants to investigate four different plans with the objective of finding the one with the lowest total cost. These plans are:

PLAN 1: Chase demand strategy. Produce to exact monthly production requirements using a regular eight-hour day (i.e. regular time) by varying workforce size. Assume XYZ has 53 workers at the start of January. Use the information given in Tables 1, 2, 3, and 4 to fill in appropriate values for the quantities listed in the first column of the following table (Table 5) for each month (January to June) of the planning period. What is the total cost of production plan 1?

NOTE 1: In solving this aggregate plan, please be sure to give explicit equations/calculations you have used to obtain the quantities in the first column of TABLE 5 below for the months of January, February and March.

TABLE 5: Production Plan 1: EXACT PRODUCTION (i.e. CHASE STRATEGY); VARY WORKFORCE

PLAN 2: Level Strategy with constant workforce level. Produce to meet forecasted demand over the next six months by maintaining a constant workforce. What is the minimum number of workers needed in this case? For this plan, assume that the available workforce at the start of January is equal to the minimum number of workers needed for this plan (to be determined). In other words, there will be no hiring and firing for this plan.

NOTE 2: In this plan, inventory is allowed to accumulate, with shortages (stockouts) filled from next months production by back ordering. Since XYZ carries a safety stock in each month (refer to Table 4), the inventory costs in each month are calculated based on the units excess (Ending inventory Safety stock) of each month only if this amount is positive.

Use the information given in Tables 1, 2, 3, and 4 to fill in appropriate values for the quantities listed in the first column of the following table (Table 6) for each month (January to June) of the planning period. What is the total cost of production plan 2?

NOTE 3: In solving this aggregate plan, please be sure to give explicit equations/calculations you have used to obtain the number of workers required and the quantities in the first column of TABLE 6 below for the months of January, February and March.

TABLE 6: XYZ Production Plan 2: CONSTANT WORKFORCE; VARY INVENTORY AND USE STOCKOUT (IF NECESSARY). Actual production = actual number of units produced in each month.

PLAN 3: Produce to meet the minimum forecasted demand (Aprils demand) using a constant workforce on regular time. Subcontract to meet additional output requirements. The number of workers is calculated by locating the minimum monthly production requirement and determining how many workers would be needed for that month and subcontracting any monthly difference between requirements and production. What is the number of workers needed in this case?Again, for this plan, assume that the available workforce at the start of January is equal to the number of workers needed for this plan (to be determined). In other words, there will be no hiring and firing for this plan.

Use the information given in Tables 1, 2, 3, and 4 to fill in appropriate values for the quantities listed in the first column of the following table (Table 7) for each month (January to June) of the planning period. What is the total cost of production plan 3?

NOTE 4: In solving this aggregate plan, please be sure to give explicit equations/calculations you have used to obtain the number of workers required and the quantities in the first column of TABLE 7 below for the months of January, February and March.

TABLE 7: XYZ Company Production Plan 3: CONSTANT LOW WORKFORCE; USE SUBCONTRACTING ONLY (IF NECESSARY).

PLAN 4: Produce to meet forecasted demand for all but the first two months using a constant workforce on regular time. Use overtime to meet additional output requirements. The required number of workers is more difficult to compute for this plan, but the goal is to finish June with an ending inventory as close as possible to the June safety stock. By trial and error it can be shown that a constant workforce of 38 workers is the closest approximation. Again, for this plan, assume that the available workforce at the start of January is equal to 38 workers. In other words, there will be no hiring and firing for this plan.

Use the information given in Tables 1, 2, 3, and 4 to fill in appropriate values for the quantities listed in the first column of the following table (Table 8) for each month (January to June) of the planning period. What is the total cost of production plan 4? (5.5 marks)

NOTE 5: In solving this aggregate plan, please be sure to give explicit equations/calculations you have used to obtain the quantities in the first column of TABLE 8 below for the months of January, February and March.

TABLE 8: XYZ Company Production Plan 4: CONSTANT WORKFORCE; USE OVERTIME ONLY (IF NECESSARY).

The next step is to calculate the cost of each plan to determine the least-cost plan. This requires a series of simple calculations for each plan. Note that the required calculations and the order in which they must be done are different for each plan because each plan is a different problem requiring its own data and calculations. What is the least-cost plan? (1 mark). Summarize your calculations in the following table (TABLE 6).

TABLE 6: Determining the least-cost plan.