LO2 5. Refer to Example 13-3. Suppose that the new union con- tract limits the number of temporary workers in any month to 28 (i.e., 20 percent of permanent workers). Recall from Example 13-2 that up to 400 units can be produced dur- ing overtime per month. Using trade-off analysis and trial-and-error, find the minimum cost plan in this case. (Hint: Hire 10 temps for three months and 15 temps for two months starting in month 3.) ( EXAMPLE 13-3 The third option is to use temporary workers during months of high demand. Suppose that tem- porary workers will be working during a second shift and enough of them are available. Develop an aggregate production plan in this case (Plan 3). SOLUTION Dividing the number of short units (1,200) by the output rate of 20 per temporary worker, you find that 60 temporary worker- months are needed (e.g., 60 temporary workers for one month each, or 30 temporary workers for two months each, or 20 tempo- rary workers for three months each, etc.). Therefore, the planner tried each of the alternatives: hiring 60 temporary workers in month 5 on a one-month contract, or hiring 30 temporary workers starting in month 4 on a two-month contract, or hiring 20 temporary workers starting in month 3 on a three- month contract, and so on. The plan with the lowest total cost, including inventory holding cost, hires temporary workers starting in month 4 on a two-month contract. The completed worksheet for this plan is given below. Note that the hiring cost applies to only the first month of employment Month 1 3 4 5 6 2 2,000 Total 18,000 2,000 3,000 4,000 5,000 2,000 2,800 2,800 2,800 2,800 2,800 2,800 600 16.800 1,200 600 800 800 -200 -600 -1.600 800 0 1,000 2,600 2.400 1,800 200 1,800 2,600 1,800 200 Forecast Output Regular permanent Temporary Overtime Output forecast Inventory Beginning Ending Average Back order Costs Labour Regular perm (at $100/unit) Temporary (at $100/unit) Overtime (at $150/unit) Hire temporary (at $25/unit) Inventory (at $10/unit/month) Back order (at $150/unit/month) Total cost 1,000 2,400 2,500 0 1,400 0 1,800 2,100 0 2,200 0 9,800 1,000 600 0 o 0 $280,000 $280,000 $1,680,000 $280,000 $280,000 60,000 $280,000 $280,000 60,000 120.000 0 15,000 14,000 98,000 0 o 15,000 0 0 22,000 25,000 21,000 10,000 6,000 0 0 0 0 0 $302,000 $305,000 $376,000 $350,000 $286,000 0 0 $294,000 $1.913,000 Overall, the total cost for this plan ($1,913,000) seems to be the lowest possible, so Plan 3 seems to be optimal. LO2 5. Refer to Example 13-3. Suppose that the new union con- tract limits the number of temporary workers in any month to 28 (i.e., 20 percent of permanent workers). Recall from Example 13-2 that up to 400 units can be produced dur- ing overtime per month. Using trade-off analysis and trial-and-error, find the minimum cost plan in this case. (Hint: Hire 10 temps for three months and 15 temps for two months starting in month 3.) ( EXAMPLE 13-3 The third option is to use temporary workers during months of high demand. Suppose that tem- porary workers will be working during a second shift and enough of them are available. Develop an aggregate production plan in this case (Plan 3). SOLUTION Dividing the number of short units (1,200) by the output rate of 20 per temporary worker, you find that 60 temporary worker- months are needed (e.g., 60 temporary workers for one month each, or 30 temporary workers for two months each, or 20 tempo- rary workers for three months each, etc.). Therefore, the planner tried each of the alternatives: hiring 60 temporary workers in month 5 on a one-month contract, or hiring 30 temporary workers starting in month 4 on a two-month contract, or hiring 20 temporary workers starting in month 3 on a three- month contract, and so on. The plan with the lowest total cost, including inventory holding cost, hires temporary workers starting in month 4 on a two-month contract. The completed worksheet for this plan is given below. Note that the hiring cost applies to only the first month of employment Month 1 3 4 5 6 2 2,000 Total 18,000 2,000 3,000 4,000 5,000 2,000 2,800 2,800 2,800 2,800 2,800 2,800 600 16.800 1,200 600 800 800 -200 -600 -1.600 800 0 1,000 2,600 2.400 1,800 200 1,800 2,600 1,800 200 Forecast Output Regular permanent Temporary Overtime Output forecast Inventory Beginning Ending Average Back order Costs Labour Regular perm (at $100/unit) Temporary (at $100/unit) Overtime (at $150/unit) Hire temporary (at $25/unit) Inventory (at $10/unit/month) Back order (at $150/unit/month) Total cost 1,000 2,400 2,500 0 1,400 0 1,800 2,100 0 2,200 0 9,800 1,000 600 0 o 0 $280,000 $280,000 $1,680,000 $280,000 $280,000 60,000 $280,000 $280,000 60,000 120.000 0 15,000 14,000 98,000 0 o 15,000 0 0 22,000 25,000 21,000 10,000 6,000 0 0 0 0 0 $302,000 $305,000 $376,000 $350,000 $286,000 0 0 $294,000 $1.913,000 Overall, the total cost for this plan ($1,913,000) seems to be the lowest possible, so Plan 3 seems to be optimal