Chapter 13 Aggregate Sales and Operations Planning
Chapter 12 - Sales and Operations Planning
CHAPTER 12 SALES AND OPERATIONS PLANNING Review and Discussion Questions 1. What is the major difference between aggregate planning in manufacturing and aggregate planning in services? Variable affecting services operations can increase the need for overtime, a costly alternative. Also, services operations often have unique rules concerning the hours an employee may work (e.g., airlines, and trucking). Also intangibility of the product can make the use of MRP difficult. 2. What are the basic controllable variables of a production planning problem? What are the four major costs? Basic controllable variables: production rate, work force levels, and inventories. Major costs: production costs (fixed and variable), production rate change costs, inventory holding costs, and backlog costs. 3. Distinguish between pure and mixed strategies in production planning. Pure strategies use only one variable to absorb demand fluctuations. Mixed strategies involve two or more pure strategies. 4. Define level scheduling. How does it differ from the pure strategies in production planning. A Japanese approach, level scheduling focuses on holding production constant over a period of time. It is more like a combination of strategies in that for the period it keeps work force constant, inventory low and depends on a demand backlog to pull products through. 5. How does forecast accuracy relate, in general, to the practical application of the aggregate planning models discussed in the Chapter? A highly accurate forecast encourages the use of deterministic techniques such as linear programming which in turn permits the development of near optimal plans. Clearly, though, any reduction in uncertainty enhances the likely accuracy of any production planning method. 6. In which way does the time horizon chosen for an aggregate plan determine whether it is the best plan for the firm? Many factors affect the selection of an appropriate time horizon. Perhaps, the most important is what the firm intends to plan during that time period. An aggregate plan implies a period of up to 18 months wherein the firm takes its forecast and plans production using inventory, work force size, overtime and under time, subcontracting, and backlogging orders to achieve a reasonable schedule at reasonable costs. A very stable firm in a very stable environment with a very stable demand really doesn’t need to go out very far with its aggregate plan. However, when there is variation, especially when this variation is considerable, then a longer aggregate
12-1
Chapter 12 - Sales and Operations Planning
plan will show the need to find subcontractors, new workforce availability, etc. Planning for these can start early. 7. Review the opening vignette, how does sales and operations planning help resolve product shortage problems? Sales and Operations planning helps reduce shortages by getting all the key players (sales, finance, operations and product development) to work tog ether to help balance supply and demand. When a firm does a good job of sales and operations planning it is less likely to have demand and supply so far out of balance that there is product shortages. The opening vignette shows that better communication between the executives my have averted the problem they are discussing. 8. How would you apply yield management concepts to a barbershop? A soft drink vending machine? The first step would be to determine when peak and off-peak times existed. For the barbershop, lower prices could be given during off-peak times. For example, price discounts could be given during days of the week, or times of the day when demand is low. Another approach would be to offer a discount and an appointment to people that walk-in during peak times, thus transferring them to an off-peak time. Hopefully, lack of capacity would not be a problem for a vending machine, so reallocating peak demand should not be an issue. But, trying to increase usage during non-peak times is difficult because most vending machine can charge only one price. However, new technology could allow the prices to be changed based on time of day, or even the day of the week. Therefore, during off-peak times, a lower price could be charged to stimulate sales.
12-2
Chapter 12 - Sales and Operations Planning
Problems
1. Answers will vary, but Production Plan 2 is very difficult to beat in terms of total cost. 2. Forecast Fall Winter Spring Summer
10000 8000 7000 12000
Beginnin Productio Productio Productio Overtime Actual Ending Workers g n required n hours n hours hours productio inventor hired inventory required available n y
Back order
500 -2300 0 200
Fall Winter
9500 10300 7000 11800
Overtime Hiring
19000 20600 14000 23600 Lay off
$23,000 $49,600
Spring Summer
$2,000
$4,000
Total
14400 14400 14400 14400
7200 10300 7200 11800
6200
Inventory Straight time
-2300 0 200 0
Workers laid off
20*
20
Total
$72,000 $95,000 $72,000 $121,60 0 $1,000 $72,000 $73,000 $118,000 $124,00 0 $413,60 0
*Workers hired = (23,600-14400)/(8*60) = 19.17 workers
3. Forecast February March April May
80000 64000 100000 40000 Back order
February March April
Beginnin Productio Productio Productio Overtime g n n hours n hours hours Inventory required required available
0 80000 0 64000 0 100000 -16000 56000 Overtime Hiring
20000 16000 25000 14000 Lay off
16000 16000 16000 16000
$201,250 $161,750 $555,000
$80000 $160,000
$240,000 $1,158,000
$320,00 $75,000 0
May Total
Total
$200,000 $160,000 $160,000
$1,750
*(20,000-16,000)/(8*20) = 25 workers
12-3
Ending Workers Workers inventor hired laid off y
80000 0 64000 0 84000 -16000 64000 8000
5000
Inventory Straight time
$1,250
Actual production
25* 25
Chapter 12 - Sales and Operations Planning
12-4
Chapter 12 - Sales and Operations Planning
4. Forecast Spring Summer Fall Winter
Beginning Productio Productio Productio Overtime Inventory n n hours n hours hours required required available
20000 10000 15000 18000 Back order
Spring Summer Fall Winter Total
1000 0 0 0 Overtime
19000 10000 15000 18000 Hiring
38000 20000 30000 36000 Lay off
28000 28000 20000 30000
10000
Inventory Straight time
$150,000 $2,500 $24,000
Ending Workers Workers inventor hired laid off y
19000 0 10000 0 15000 0 15000 -3000
20 25
Total
$280,000 $200,000 $300,000 $300,000
$4,000
Actual production
$430,000 $204,000 $302,500 $324,000 $1,260,500
5. Jan. Forecast Beginning inventory Production requirements Ending inventory
Feb.
March April
May
June
July
August Sept.
Oct.
Nov.
Dec.
Ave.
2500
3000
4000
3500
3500
3000
3000
4000
4000
4000
3000
3000
500
1250
1500
2000
1750
1750
1500
1500
2000
2000
2000
1500
3250
3250
4500
3250
3500
2750
3000
4500
4000
4000
2500
3000 3458.3
1250
1500
2000
1750
1750
1500
1500
2000
2000
2000
1500
1500
2500
3000
4000
3500
3500
3000
3000
4000
4000
4000
3000
3000 40500
500
1360
1720
1080
940
800
1160
1520
880
240
-400
3360
3360
3360
3360
3360
3360
3360
3360
3360
3360
3360
1360
1720
1080
940
800
1160
1520
880
240
-400
-40
320
1250
1500
2000
1750
1750
1500
1500
2000
2000
2000
1500
1500
110
220
Total Forecast Beginning inventory Production plan Ending inventory Safety stock Excess inventory Back order
20 400
40
Cost
-40 3360 40320
$403,200
350
$1,750
440
$8,800
Total
$413,750
Next, try increasing or decreasing the number of workers by one, and recalculate the total cost. A better solution may be found.
12-5
Chapter 12 - Sales and Operations Planning
6. There is more then one solution. January 30.00
January RT
3800
January OT
1200
45.00
February
April
May
40.00
45.00
50.00
55.00
50.00
55.00
60.00
65.00
70.00
30.00
35.00
40.00
45.00
50.00
55.00
60.00
65.00
50.00
40.00
45.00
50.00
55.00
60.00
30.00
35.00
40.00
50.00
55.00
30.00
35.00
35.00
March
June
200
February RT
40.00
February OT
55.00
March RT
50.00
March OT
65.00
April RT
60.00
April OT
75.00
May RT
70.00
May OT
85.00
June RT
80.00
June OT
95.00
85.00
75.00
65.00
55.00
45.00
0
0
0
0
0
0
5000
4000
6000
6000
5000
4000
Unfilled Demand Total Demand
3800 45.00
200 50.00 600
40.00
600
30.00 4000
55.00
45.00 1200
50.00
40.00
4000 65.00
55.00
45.00 1200
60.00
50.00
40.00 200
75.00
65.00
55.00
3800 45.00
50.00
1200 70.00
60.00
50.00
40.00
30.00 4000
Total Cost = $1,003,000
12-6
Unused Capacity
Total Capacity
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
0
4000
1200
1200
Chapter 12 - Sales and Operations Planning
January January RT
30.00
February
March
April
May
June
35.00
40.00
45.00
50.00
55.00
4000
January OT
45.00
50.00
55.00
60.00
65.00
70.00
February RT
40.00
30.00
35.00
40.00
45.00
50.00
50.00
55.00
60.00
65.00
1000
February OT
55.00
March RT
50.00
March OT
65.00
April RT
60.00
April OT
75.00
May RT
70.00
May OT
85.00
June RT
80.00
June OT
95.00
Unfilled Demand Total Demand
3000 45.00
1200 40.00 1000 55.00
30.00
50.00
40.00
50.00
55.00
45.00
3000 45.00
60.00 1200
50.00
40.00
30.00
3000 65.00
35.00
40.00
50.00
55.00
1000
55.00
45.00 1000
60.00
50.00
40.00
200 30.00
35.00
45.00
50.00
4000 75.00
65.00
55.00
1000 70.00
60.00
50.00
40.00
200 30.00
4000 85.00
75.00
65.00
55.00
45.00 1200
0
0
0
0
0
0
5000
4000
6000
6000
5000
4000
Total Cost = $1,165,000
12-7
Unused Capacity
Total Capacity
0
4000
1200
1200
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
Chapter 12 - Sales and Operations Planning
7.
April RT April OT
April A
April B
April C
May A
May B
May C
June A
June B
June C
July A
July B
July C
4
5
6
7
9
11
10
13
16
13
17
21 1500
200
600 6
7.50
700 9
600 +1M
9
11.5 0
14
5
6
12
15.5
19
15
19.5
24 700
100 +1M
+1M
4
7
9
11
10
13
16
May RT
1300 100
May OT
+1M
+1M
+1M
6
700 7.50
500 9
400 +1M
+1M
+1M
+1M
9
11.5 0
14
5
6
12
15.5
19 650
250 +1M
+1M
4
7
9
11
June RT
1800 200
June OT
+1M
+1M
+1M
+1M
+1M
+1M
6
900 7.50
700 9
350 +1M
+1M
+1M
+1M
+1M
+1M
+1M
9
11.5 0
14
5
6
900
550 +1M
+1M
4
July RT
1700 900 +1M
+1M
+1M
+1M
+1M
+1M
+1M
+1M
+1M
6
800
7.50
9
July OT
850 650
200
Unfilled Demand Demand
Supply
50 50 800
600
700
600
700
500
800
900
700
Objective value = 55,300. There are alternative optimal solutions, such as:
12-8
120 0
1100
850
Chapter 12 - Sales and Operations Planning
April RT April OT
April A
April B
April C
May A
May B
May C
June A
June B
June C
July A
July B
July C
4
5
6
7
9
11
10
13
16
13
17
21 1500
100
600 6
7.50
700
100 9
9
11.5 0
14
5
6
12
15.5
19
15
19.5
24 700
700 +1M
+1M
+1M
4
7
9
11
10
13
16
May RT
1300 700
May OT
+1M
+1M
+1M
6
7.50
500 9
100 9
11.5 0
14
+1M
+1M
+1M
15.5
19 650
600 +1M
12 50
+1M
+1M
4
5
6
7
9
11
June RT
1800 900
June OT
+1M
+1M
+1M
+1M
+1M
+1M
6
7.50
700 9
800 +1M
+1M
+1M
+1M
+1M
+1M
+1M
200 9
11.5 0
14
5
6
900
100 +1M
+1M
4
July RT
1700 900 +1M
+1M
+1M
+1M
+1M
+1M
+1M
+1M
+1M
6
800
7.50
9
July OT
850 650
200
Unfilled Demand Demand
Supply
50 50 800
600
700
600
700
500
Objective value = 55,300
12-9
800
900
700
120 0
1100
850
Chapter 12 - Sales and Operations Planning
8. Number of workers = (6700-200)10/(249*8) = 32.6 or 33 workers Monthly production (except July) = 22(8)33/10 = 580 units/month Forecast Beginning inventory Available Production Ending inventory
Jan. Feb. March April May June July August Sept. Oct. Nov. Dec. Total 600 800 900 600 400 300 200 200 300 700 800 900 6700 200 180 0 0 0 180 460 444 824 1104 984 764 580
580
580
580
580
580
184
580
580
580
580
580
180
-40
-320
-20
180
460
444
824
1104
984
764
444
Total
Costs Lost Sales Inventory Total
6564
800 900 900
800
6400 6400
400 400
900 900
2300 2300
2220 2220
4120 4120
5520 5520
4920 4920
3820 3820
7600 2220 26920 2220 34520
Since there appears to be excessive inventory costs, another plan should be attempted with 32 workers for comparison purposes.
9.
January February March
Forecast Beginnin Safety Producti Productio Working Workers Beginning Worker Product Ending g stock on n hours days needed workers hired ion inventor Inventor required required y y 1000 500 500 1000 10000 22 57 50 7 1003 503 1500 1200
503 751
750 600
1747 1049
17470 10490
19 21
115 63
57 115
58 -52
1748 1058
751 609
Cost Hiring Layoffs Total $13,000 $15,600 $28,600
Note, inventory cost are at the minimum because the inventory levels are at the safety stock levels. Therefore, only the cost of hiring and laying off workers has been included.
12-10
Chapter 12 - Sales and Operations Planning
10. Current capacity per Month 12 full-time employees = 2460 per month for a four month total of 9840 units 3 Part-time employees = 495 per month for a four month total of 1980 units Giving Total capacity for 11,820 units Capacity needed: Total demand is 12,100 – Current Inventory is 403 = Needed product is 11,697 Current Capacity meets demand and a reduction in part-time labor is not feasible May Demand is 3200 – 403 = 2797 This production minimizes carrying cost and only inventory cost is included in the table. Carrying cost would be $40*(.24/12) = $.80 per month May
June 0
May Fulltime
2460
May Temps
337
0
July
.80
1.60
2.40
.80
1.60
2.40
.80
1.60
.80
1.60
35 0
June Fulltime
2460 0
June Temps
305
190 0
July Fulltime
2460
July Temps
450
0
.80 .80 45 0
August Fulltime
2460 0
August Temps Unfilled Demand Total Demand
August
495 0
0
0
0
2797
2800
3100
3000
Total Cost = $216.00
12-11
Unused Capacity
Total Capacity
0
2460
123
495
0
2460
0
495
0
2460
0
495
0
2460
0
495
CHAPTER 12 SALES AND OPERATIONS PLANNING Review and Discussion Questions 1. What is the major difference between aggregate planning in manufacturing and aggregate planning in services? Variable affecting services operations can increase the need for overtime, a costly alternative. Also, services operations often have unique rules concerning the hours an employee may work (e.g., airlines, and trucking). Also intangibility of the product can make the use of MRP difficult. 2. What are the basic controllable variables of a production planning problem? What are the four major costs? Basic controllable variables: production rate, work force levels, and inventories. Major costs: production costs (fixed and variable), production rate change costs, inventory holding costs, and backlog costs. 3. Distinguish between pure and mixed strategies in production planning. Pure strategies use only one variable to absorb demand fluctuations. Mixed strategies involve two or more pure strategies. 4. Define level scheduling. How does it differ from the pure strategies in production planning. A Japanese approach, level scheduling focuses on holding production constant over a period of time. It is more like a combination of strategies in that for the period it keeps work force constant, inventory low and depends on a demand backlog to pull products through. 5. How does forecast accuracy relate, in general, to the practical application of the aggregate planning models discussed in the Chapter? A highly accurate forecast encourages the use of deterministic techniques such as linear programming which in turn permits the development of near optimal plans. Clearly, though, any reduction in uncertainty enhances the likely accuracy of any production planning method. 6. In which way does the time horizon chosen for an aggregate plan determine whether it is the best plan for the firm? Many factors affect the selection of an appropriate time horizon. Perhaps, the most important is what the firm intends to plan during that time period. An aggregate plan implies a period of up to 18 months wherein the firm takes its forecast and plans production using inventory, work force size, overtime and under time, subcontracting, and backlogging orders to achieve a reasonable schedule at reasonable costs. A very stable firm in a very stable environment with a very stable demand really doesn’t need to go out very far with its aggregate plan. However, when there is variation, especially when this variation is considerable, then a longer aggregate
12-1
Chapter 12 - Sales and Operations Planning
plan will show the need to find subcontractors, new workforce availability, etc. Planning for these can start early. 7. Review the opening vignette, how does sales and operations planning help resolve product shortage problems? Sales and Operations planning helps reduce shortages by getting all the key players (sales, finance, operations and product development) to work tog ether to help balance supply and demand. When a firm does a good job of sales and operations planning it is less likely to have demand and supply so far out of balance that there is product shortages. The opening vignette shows that better communication between the executives my have averted the problem they are discussing. 8. How would you apply yield management concepts to a barbershop? A soft drink vending machine? The first step would be to determine when peak and off-peak times existed. For the barbershop, lower prices could be given during off-peak times. For example, price discounts could be given during days of the week, or times of the day when demand is low. Another approach would be to offer a discount and an appointment to people that walk-in during peak times, thus transferring them to an off-peak time. Hopefully, lack of capacity would not be a problem for a vending machine, so reallocating peak demand should not be an issue. But, trying to increase usage during non-peak times is difficult because most vending machine can charge only one price. However, new technology could allow the prices to be changed based on time of day, or even the day of the week. Therefore, during off-peak times, a lower price could be charged to stimulate sales.
12-2
Chapter 12 - Sales and Operations Planning
Problems
1. Answers will vary, but Production Plan 2 is very difficult to beat in terms of total cost. 2. Forecast Fall Winter Spring Summer
10000 8000 7000 12000
Beginnin Productio Productio Productio Overtime Actual Ending Workers g n required n hours n hours hours productio inventor hired inventory required available n y
Back order
500 -2300 0 200
Fall Winter
9500 10300 7000 11800
Overtime Hiring
19000 20600 14000 23600 Lay off
$23,000 $49,600
Spring Summer
$2,000
$4,000
Total
14400 14400 14400 14400
7200 10300 7200 11800
6200
Inventory Straight time
-2300 0 200 0
Workers laid off
20*
20
Total
$72,000 $95,000 $72,000 $121,60 0 $1,000 $72,000 $73,000 $118,000 $124,00 0 $413,60 0
*Workers hired = (23,600-14400)/(8*60) = 19.17 workers
3. Forecast February March April May
80000 64000 100000 40000 Back order
February March April
Beginnin Productio Productio Productio Overtime g n n hours n hours hours Inventory required required available
0 80000 0 64000 0 100000 -16000 56000 Overtime Hiring
20000 16000 25000 14000 Lay off
16000 16000 16000 16000
$201,250 $161,750 $555,000
$80000 $160,000
$240,000 $1,158,000
$320,00 $75,000 0
May Total
Total
$200,000 $160,000 $160,000
$1,750
*(20,000-16,000)/(8*20) = 25 workers
12-3
Ending Workers Workers inventor hired laid off y
80000 0 64000 0 84000 -16000 64000 8000
5000
Inventory Straight time
$1,250
Actual production
25* 25
Chapter 12 - Sales and Operations Planning
12-4
Chapter 12 - Sales and Operations Planning
4. Forecast Spring Summer Fall Winter
Beginning Productio Productio Productio Overtime Inventory n n hours n hours hours required required available
20000 10000 15000 18000 Back order
Spring Summer Fall Winter Total
1000 0 0 0 Overtime
19000 10000 15000 18000 Hiring
38000 20000 30000 36000 Lay off
28000 28000 20000 30000
10000
Inventory Straight time
$150,000 $2,500 $24,000
Ending Workers Workers inventor hired laid off y
19000 0 10000 0 15000 0 15000 -3000
20 25
Total
$280,000 $200,000 $300,000 $300,000
$4,000
Actual production
$430,000 $204,000 $302,500 $324,000 $1,260,500
5. Jan. Forecast Beginning inventory Production requirements Ending inventory
Feb.
March April
May
June
July
August Sept.
Oct.
Nov.
Dec.
Ave.
2500
3000
4000
3500
3500
3000
3000
4000
4000
4000
3000
3000
500
1250
1500
2000
1750
1750
1500
1500
2000
2000
2000
1500
3250
3250
4500
3250
3500
2750
3000
4500
4000
4000
2500
3000 3458.3
1250
1500
2000
1750
1750
1500
1500
2000
2000
2000
1500
1500
2500
3000
4000
3500
3500
3000
3000
4000
4000
4000
3000
3000 40500
500
1360
1720
1080
940
800
1160
1520
880
240
-400
3360
3360
3360
3360
3360
3360
3360
3360
3360
3360
3360
1360
1720
1080
940
800
1160
1520
880
240
-400
-40
320
1250
1500
2000
1750
1750
1500
1500
2000
2000
2000
1500
1500
110
220
Total Forecast Beginning inventory Production plan Ending inventory Safety stock Excess inventory Back order
20 400
40
Cost
-40 3360 40320
$403,200
350
$1,750
440
$8,800
Total
$413,750
Next, try increasing or decreasing the number of workers by one, and recalculate the total cost. A better solution may be found.
12-5
Chapter 12 - Sales and Operations Planning
6. There is more then one solution. January 30.00
January RT
3800
January OT
1200
45.00
February
April
May
40.00
45.00
50.00
55.00
50.00
55.00
60.00
65.00
70.00
30.00
35.00
40.00
45.00
50.00
55.00
60.00
65.00
50.00
40.00
45.00
50.00
55.00
60.00
30.00
35.00
40.00
50.00
55.00
30.00
35.00
35.00
March
June
200
February RT
40.00
February OT
55.00
March RT
50.00
March OT
65.00
April RT
60.00
April OT
75.00
May RT
70.00
May OT
85.00
June RT
80.00
June OT
95.00
85.00
75.00
65.00
55.00
45.00
0
0
0
0
0
0
5000
4000
6000
6000
5000
4000
Unfilled Demand Total Demand
3800 45.00
200 50.00 600
40.00
600
30.00 4000
55.00
45.00 1200
50.00
40.00
4000 65.00
55.00
45.00 1200
60.00
50.00
40.00 200
75.00
65.00
55.00
3800 45.00
50.00
1200 70.00
60.00
50.00
40.00
30.00 4000
Total Cost = $1,003,000
12-6
Unused Capacity
Total Capacity
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
0
4000
1200
1200
Chapter 12 - Sales and Operations Planning
January January RT
30.00
February
March
April
May
June
35.00
40.00
45.00
50.00
55.00
4000
January OT
45.00
50.00
55.00
60.00
65.00
70.00
February RT
40.00
30.00
35.00
40.00
45.00
50.00
50.00
55.00
60.00
65.00
1000
February OT
55.00
March RT
50.00
March OT
65.00
April RT
60.00
April OT
75.00
May RT
70.00
May OT
85.00
June RT
80.00
June OT
95.00
Unfilled Demand Total Demand
3000 45.00
1200 40.00 1000 55.00
30.00
50.00
40.00
50.00
55.00
45.00
3000 45.00
60.00 1200
50.00
40.00
30.00
3000 65.00
35.00
40.00
50.00
55.00
1000
55.00
45.00 1000
60.00
50.00
40.00
200 30.00
35.00
45.00
50.00
4000 75.00
65.00
55.00
1000 70.00
60.00
50.00
40.00
200 30.00
4000 85.00
75.00
65.00
55.00
45.00 1200
0
0
0
0
0
0
5000
4000
6000
6000
5000
4000
Total Cost = $1,165,000
12-7
Unused Capacity
Total Capacity
0
4000
1200
1200
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
0
4000
0
1200
Chapter 12 - Sales and Operations Planning
7.
April RT April OT
April A
April B
April C
May A
May B
May C
June A
June B
June C
July A
July B
July C
4
5
6
7
9
11
10
13
16
13
17
21 1500
200
600 6
7.50
700 9
600 +1M
9
11.5 0
14
5
6
12
15.5
19
15
19.5
24 700
100 +1M
+1M
4
7
9
11
10
13
16
May RT
1300 100
May OT
+1M
+1M
+1M
6
700 7.50
500 9
400 +1M
+1M
+1M
+1M
9
11.5 0
14
5
6
12
15.5
19 650
250 +1M
+1M
4
7
9
11
June RT
1800 200
June OT
+1M
+1M
+1M
+1M
+1M
+1M
6
900 7.50
700 9
350 +1M
+1M
+1M
+1M
+1M
+1M
+1M
9
11.5 0
14
5
6
900
550 +1M
+1M
4
July RT
1700 900 +1M
+1M
+1M
+1M
+1M
+1M
+1M
+1M
+1M
6
800
7.50
9
July OT
850 650
200
Unfilled Demand Demand
Supply
50 50 800
600
700
600
700
500
800
900
700
Objective value = 55,300. There are alternative optimal solutions, such as:
12-8
120 0
1100
850
Chapter 12 - Sales and Operations Planning
April RT April OT
April A
April B
April C
May A
May B
May C
June A
June B
June C
July A
July B
July C
4
5
6
7
9
11
10
13
16
13
17
21 1500
100
600 6
7.50
700
100 9
9
11.5 0
14
5
6
12
15.5
19
15
19.5
24 700
700 +1M
+1M
+1M
4
7
9
11
10
13
16
May RT
1300 700
May OT
+1M
+1M
+1M
6
7.50
500 9
100 9
11.5 0
14
+1M
+1M
+1M
15.5
19 650
600 +1M
12 50
+1M
+1M
4
5
6
7
9
11
June RT
1800 900
June OT
+1M
+1M
+1M
+1M
+1M
+1M
6
7.50
700 9
800 +1M
+1M
+1M
+1M
+1M
+1M
+1M
200 9
11.5 0
14
5
6
900
100 +1M
+1M
4
July RT
1700 900 +1M
+1M
+1M
+1M
+1M
+1M
+1M
+1M
+1M
6
800
7.50
9
July OT
850 650
200
Unfilled Demand Demand
Supply
50 50 800
600
700
600
700
500
Objective value = 55,300
12-9
800
900
700
120 0
1100
850
Chapter 12 - Sales and Operations Planning
8. Number of workers = (6700-200)10/(249*8) = 32.6 or 33 workers Monthly production (except July) = 22(8)33/10 = 580 units/month Forecast Beginning inventory Available Production Ending inventory
Jan. Feb. March April May June July August Sept. Oct. Nov. Dec. Total 600 800 900 600 400 300 200 200 300 700 800 900 6700 200 180 0 0 0 180 460 444 824 1104 984 764 580
580
580
580
580
580
184
580
580
580
580
580
180
-40
-320
-20
180
460
444
824
1104
984
764
444
Total
Costs Lost Sales Inventory Total
6564
800 900 900
800
6400 6400
400 400
900 900
2300 2300
2220 2220
4120 4120
5520 5520
4920 4920
3820 3820
7600 2220 26920 2220 34520
Since there appears to be excessive inventory costs, another plan should be attempted with 32 workers for comparison purposes.
9.
January February March
Forecast Beginnin Safety Producti Productio Working Workers Beginning Worker Product Ending g stock on n hours days needed workers hired ion inventor Inventor required required y y 1000 500 500 1000 10000 22 57 50 7 1003 503 1500 1200
503 751
750 600
1747 1049
17470 10490
19 21
115 63
57 115
58 -52
1748 1058
751 609
Cost Hiring Layoffs Total $13,000 $15,600 $28,600
Note, inventory cost are at the minimum because the inventory levels are at the safety stock levels. Therefore, only the cost of hiring and laying off workers has been included.
12-10
Chapter 12 - Sales and Operations Planning
10. Current capacity per Month 12 full-time employees = 2460 per month for a four month total of 9840 units 3 Part-time employees = 495 per month for a four month total of 1980 units Giving Total capacity for 11,820 units Capacity needed: Total demand is 12,100 – Current Inventory is 403 = Needed product is 11,697 Current Capacity meets demand and a reduction in part-time labor is not feasible May Demand is 3200 – 403 = 2797 This production minimizes carrying cost and only inventory cost is included in the table. Carrying cost would be $40*(.24/12) = $.80 per month May
June 0
May Fulltime
2460
May Temps
337
0
July
.80
1.60
2.40
.80
1.60
2.40
.80
1.60
.80
1.60
35 0
June Fulltime
2460 0
June Temps
305
190 0
July Fulltime
2460
July Temps
450
0
.80 .80 45 0
August Fulltime
2460 0
August Temps Unfilled Demand Total Demand
August
495 0
0
0
0
2797
2800
3100
3000
Total Cost = $216.00
12-11
Unused Capacity
Total Capacity
0
2460
123
495
0
2460
0
495
0
2460
0
495
0
2460
0
495
