P4-1
Harold Grey owns a small farm in the Salinas Valley that grows apricots. The apricots are
dried on the premises and sold to a number of large supermarket chains. Based on past
experience and committed contracts, he estimates that sales over the next five years in
thousands of packages will be as follows:
Year Forecasted Demand
(thousands of packages)
1
300
2
120
3
200
4
110
5
135
Assume that each worker stays on the job for at least one year, and that Grey currently has
three workers on the payroll. He estimates that he will have 20,000 packages on hand at the
end of the current year. Assume that, on the average, each worker is paid $25,000 per year
and is responsible for producing 30,000 packages. Inventory costs have been estimated to be
4 cents per package per year, and shortages are not allowed. Based on the effort of
interviewing and training new workers, Farmer Grey estimates that it costs $500 for each
worker hired. Severance pay amounts to $1,000 per worker.
a. Assuming that shortages are not allowed, determine the minimum constant workforce that
he will need over the next five years.
b. Evaluate the cost of the plan found in part (a).
P4-2
For the data given in P4-1, graph the cumulative net demand.
a. Graphically determine a production plan that changes the production rate exactly once
during the five years, and evaluate the cost of that plan.
b. Graphically determine a production plan that changes the production rate exactly twice
during the five years, and evaluate the cost of that plan.
P4-3
An implicit assumption made in P4-1 was that dried apricots unsold at the 'L. end of a year
could be sold in subsequent years. Suppose that apricots unsold at the end of any year must be
discarded. Assume a disposal cost of $0.20 per package. Resolve Problem 9 under these
conditions.
P4-4
The personal department of the A&M Corporation wants to know how many workers will be
needed each month for the next si5-month production period. The following is a monthly
demand forecast for the six-month period.
MONTH
Forecasted Demand
June
1,250
August
1,100
September
950
October
900
November
1,000
December
1,150
The inventory on hand at the end of June was 500 units. The company wants to maintain a
minimum inventory of 300 units each month and would like to have 400 units on hand at the
end of December. Each unit requires 5 employee-hours to produce, there are 20 working days
each month, and each employee works an 8-hour day. The workforce at the end of June was
35 workers.
a. Determine a minimum inventory production plan (i.e., one that allows arbitrary hiring and
firing).
b. Determine the production plan that meets demand but does not hire or fire workers during
the six-month period.
P4-5
A local semiconductor firm, Superchip, is planning its workforce and production levels over
the next year. The firm makes a variety of microprocessors and uses sales dollars as its
aggregate production measure. Based on orders received and sales forecasts provided by the
marketing department, the estimate of dollar sales for the next year by month is as follows:
Month
Production days
Predicted Demand
(in $1 0,000)
January
February
March
April
May
June
July
August
September
October
November
December
22
16
21
19
23
20
24
12
19
22
20
16
340
380
220
100
490
625
375
310
175
145
120
165
Inventory holding costs are based on a 25 percent annual interest charge. It is anticipated that
there will be 675 workers on the payroll at the end of the current year and inventories will
amount to $120,000. The firm would like to have at least $100,000 of inventory at the end
of December next year. It is estimated that each worker accounts for an average of $60,000 of
production per year (assume that one year consists of 250 working days). The cost of hiring a
new worker is $200, and the cost of laying off a worker is $400.
a. Determine the minimum constant workforce that will meet the predicted
b. Evaluate the cost of the plan determined in part (a).
P4-6
For the data in P4-5, determine the cost of the plan that changes the workforce size each
period to most closely match the demand.
P4-7
Graph the cumulative net demand for the Superchip data of P4-5. Graphically determine a
production plan that changes production levels no more than three times, and determine the
total cost of that plan.
P4-8.
Excelsior Springs, Ltd., schedules production of one end product, Hi-Sulphur, in batches of 80
units whenever the projected ending inventory balance in a quarter falls below 10 units. It takes
one quarter to make a batch of 80 units. Excelsior currently has 30 units on hand. The sales
forecast for the next four quarters is：
Quarter
Forecast
1
2
3
4
20
70
70
20
a. Prepare a time-phased MPS record showing the sales forecast and MPS for Hi-Sulphur.
b. What are the inventory balances at the end of each quarter?
c. During the first quarter, no units were sold. The revised forecast for the rest of the year is：
Quarter
Forecast
2
3
4
30
50
70
How does the MPS change?
P4-9.
Neptune Manufacturing Company’s production manager wants a master production schedule
covering next year’s business. The company produces a complete line of small fishing boats for
both saltwater and freshwater use and manufactures most of the component parts used in
assembling the products. The firm uses MRP to coordinate production schedules of the component
part manufacturing and assembly operations. The production manager has just received the
following sales forecast for next year from the marketing division：
Sales forecast (standard boats for each series)
st
Products lines
1 quarter
2nd quarter
3rd quarter
4th quarter
FunRay series
SunRay series
StingRay series
8,000
4,000
9,000
9,000
5,000
10,000
6,000
2,000
6,000
6,000
2,000
7,000
Total
21,000
24,000
14,000
15,000
The sales forecast is stated in terms of ” standard boats,” reflecting total sales volume for each of
the firm’s three major product lines．Another item of information supplied by the marketing
department is the target ending inventory position for each product line ． The marketing
department would like the production manager to plan on having the following number of
standard boats on hand at the end of each quarter of next year:
Product line
FunRay series
SunRay series
StingRay series
Quarterly target
ending inventory
(in standard boats)
3,000 boats
1,000 boats
3,000 boats
The inventory position for each product is:
Product line
FunRay series
SunRay series
StingRay series
Current
Inventory level
(in standard boats)
3,000 boats
1,000 boats
3,000 boats
The master production schedule is to specify the number of boats (in standard units) to be
produced for each product line in each quarter of next year on the firm’s single assembly line. The
assembly line can produce up to 15,000 standard boats per quarter (250 boats per day during the
60 days in a quarter).
Two additional factors are taken into account by the production manager in preparing the master
production schedule：the assembly line changeover cost and the inventory carrying cost for the
finished goods inventory. Each assembly line changeover costs $5,000, reflecting material
handling costs of changing the stocking of component parts on the line, adjusting the layout, and
so on. After some discussion with the company comptroller, the production manager concluded
that the firm’s inventory carrying cost is 10 percent of standard boat cost per year. The item value
for each of the product line standard units is:
Product line
Standard boats cost
FunRay series
SunRay series
StingRay series
$100
150
200
The master production scheduler has calculated the production lot sizes as 5,000, 3,000, and 4,000
units, respectively.
a. Develop a master production schedule for next year, by quarter, for each of Neptune’s fishing
boat lines. Identify any problems.
b. Verify the lot size calculations using the EOQ formula.
P4-10.
The MPS planner at Murphy Motors uses MPS time-phased records for planning end item
production．The planner is currently working on a schedule for the P24, one of Murphy’s
top-selling motors．The planner uses a production lot size of 70 and a safety stock of 5 for the P24
motor.
Week
1
2
3
4
5
6
7
8
Forecast
30
30
30
40
40
40
45
45
Orders
13
8
4
Available
Available to promise
MPS
On hand = 20
a. Complete the MPS time-phased record for product P24.
b. Can Murphy accept the following orders？Update the MPS time-phased record for accepted
orders.
Order
Amount
Desired week
1
2
3
4
40
30
30
25
4
6
2
3
P4-11.
Nino Spirelli has constructed the following (partial) time-phased MPS record:
Week
1
2
3
4
5
6
Forecast
20
30
20
30
20
30
Orders
14
8
6
50
50
Available
Available to promise
MPS
50
50
On hand = 5
a. Complete the record.
b. Are there any problems？
c. What's the earliest Nino can promise an order for 44 units?
d. Assume that an order for 15 is booked for week 4. Assume the order for 44
units in part c is not booked; recompute the record.
P4-12.
The Noname Computer Company builds a computer designated model ICU2. It imports the
motherboard of the computer from Taiwan, but the company inserts the sockets for the chips
and boards in its plant in Lubbock, Texas. Each computer requires a total of 90 64K DRAM
(dynamic random access memory) chips. Noname sells the computers with three add-in
boards and two disk drives. The company purchases both the DRAM chips and the disk
drives from an outside supplier. The product structure diagram for the ICU2 computer is
given in Figure 4-1. Suppose that the forecasted demands for the computer for weeks 6 to 11
are 220, 165, 180, 120, 75, and 300. The starting inventory of assembled computers in week 6
will be 75, and the production manager anticipates returns of 30 in week 8 and 10 in week 10.
a. Determine the MPS for the computers.
b. Determine the planned order release for the motherboards assuming a lot-for-lot scheduling
rule.
c. Determine the schedule of outside orders for the disk drives.
FIGURE 4-1 Product structure diagram for ICU2 computer (for Problem 4-12)
P4-13.
For the previous problem, suppose that Noname has 23,000 DRAM chips in inventory. It
anticipates receiving a lot of 3,000 chips in week 3 from another firm that has gone out of
business. At the current time, Noname purchases the chips from two vendors, A and B. A
sells the chips for less, but will not fill an order exceeding 10,000 chips per week.
a. If Noname has established a policy of inventorying as few chips as possible, what order
should it be placing with vendors A and B over the next six weeks?
b. Noname has found that not all the DRAM chips purchased function properly. From past
experience it estimates an 8 percent failure rate for the chips purchased from vendor A and a 4
percent failure rate for the chips purchased from vendor B. What modification in the order
schedule would you recommend to compensate for this problem?
P4-14.
a. Determine the planned order release for the motherboards in Problem 4 assuming that one
uses the EOQ formula to schedule production. Use K = $180 and h = 0.40.
b. Using the results from part (a), determine the gross requirements schedule for the DRAM
chips, which are ordered from an outside supplier. The order cost is $25.00, and the holding
cost is $0.01 per chip per week. What order schedule with the vendor results if the EOQ
formula is used to determine the lot size?
c. Repeat the calculation of part (b) for the add-in boards. Use the same value of the setup
cost and a holding cost of 28 cents per board per week.
P4-15.
The time-phased net requirements for the base assembly in a table lamp over the next six
weeks are
Week
1
2
3
4
5
6
Requirements 335 200 140 440 300 200
The setup cost for the construction of the base assembly is $200, and the holding cost is $0.30
per assembly per week.
a. What lot sizing do you obtain from the EOQ formula? b. Determine the lot sizes using the
Silver-Meal heuristic.
c. Determine the lot sizes using the least unit cost heuristic.
d. Determine the lot sizes using part period balancing.
e. Compare the holding and setup costs obtained over the six periods using the policies found
in parts (a) through (d) with the cost of a lot-for-lot policy.
P4-16.
Consider the example presented in Section 2 of this chapter of scheduling the production of
the valve casing assembly.
a. Suppose that the production capacity in any week is 100 valve casings. Using the algorithm
presented in this section, determine the planned order release for the valve casings.
b. What gross requirements schedule for the valves does the lot sizing you obtained in part (a)
give?
c. Suppose that the production capacity for the valves is 200 valves per week. Is the gross
requirements schedule from part (b) feasible? If not, suggest a modification in the planned
order release computed in part (a) that would result in a feasible gross requirements schedule
for the valves.
P4-17.
A single inventory item is ordered from an outside supplier. The anticipated demand for this
item over the next 12 months is 6, 12, 4, 8, 15, 25, 20, 5, 10, 20, 5, and 12. Current inventory
of this item is 4, and ending inventory should be 8. Assume a holding cost of $1 per period
and a setup cost of $40. Determine the order policy for this item based on
a. Silver-Meal.
b. Least unit cost.
c. Part Period balancing.
d. Which lot-sizing method resulted in the lowest cost for the 12 periods?
P4-18.
Two end products, EP1 and EP2, are produced in the Raleigh, North Carolina, plant of a large
manufacturer of furniture products located in the Southeast. The product structure diagrams
for these products appear in Figure 4-2. Suppose that the master production schedules for
these two products are
Week 18 19 20 21 22 23 24
EP1
120 112 76 22 56 90 210
EP2
62 68 90 77 26 30 54
Assuming lot-for-lot production, determine the planned order releases for components F, G,
and H.
FIGURE 4-2 Product structure diagrams (for Problem 4-18)
P4-19.
A component used in a manufacturing facility is ordered from an outside supplier. Because
the component is used in a variety of end products, the demand is high. Estimated demand (in
thousands) over the next 10 weeks is
Week
1
2
3
4
5
6
7
8
9
10
Demand
22
34
32
12
8
44
54
16
76
30
The components cost 65 cents each and the interest rate used to compute the holding cost is
0.5 percent per week. The fixed order cost is estimated to be $200. (Hint: Express h as the
holding cost per thousand units.)
a. What ordering policy is recommended by the Silver-Meal heuristic?
b. What ordering policy is recommended by the part period balancing heuristic?
c. What ordering policy is recommended by the least unit cost heuristic?
d. Which method resulted in the lowest-cost policy for this problem?
P4-20.
Cosmo's Camping Supplies sells two camping packages designed for hunters: Nomad and
Nimrod. It is a two-stage process that involves picking the appropriate items from inventory
and then packing them into a hunting knapsack. Cosmo is making his labor estimates for the
next four quarters for the picking and packing operations. The Nomad package requires 1.75
hours of labor and the Nimrod requires 2.45 hours. The Picking work center historically uses
55% of the labor resources and the Packing work center uses 45%. The production Schedule
for the next four quarters is given below:
Calculate the labor hours required in the picking and packing work centers for the next four
quarters.
Quarter
End product
1
2
3
4
Total
Nomad
450
500
300
350
1600
Nimrod
350
400
500
550
1800
P4-21.
Bisutti Cams has gathered data on labor-hour and machine-hour requirements for producing
its Racing Camshaft models RC1 and RC2:
1994
ProductionRC1(units) 1,400
ProductionRC2(units) 700
Labor-hoursRC1
450
Labor-hoursRC2
75
Machine-hoursRC1
125
Machine-hoursRC2
135
1995
1,500
820
580
90
145
160
1996
1,700
940
620
105
180
165
a. What planning factors should it use for 1997?
b. What capacity requirements for labor-hours and machine-hours would you project for 1997
if 50 percent of the labor-hours and machine-hours each were worked in departments 101 and
102? Use the quarterly summaries in the following master schedule to do the projections:
Quarter
1997 MPS
1
ProductRC1 400
ProductRC2 250
3
2
700
150
4
3
300
450
5
4
400
300
Total
1,800
1,150
P4-22.
Determine the capacity requirements in all work centers at erben Fabricators using the MPS,
resource profile , product structure, and lead time information given below for product Z and
all of its components. (Assume all usages are one, and that a new setup must be made in each
week at each work center.)
week
MPS of
Product Z
1
10
2
20
3
15
4
10
5
15
Z
M
N
O
P
P4-23.
Management at the Green Valley Furniture Company has just approved the following master
production schedule for its make-to-stock products:
End product
A
B
C
Week1
30
0
10*
Week2
0
40
0
Week3
0
36
0
Week4
10
0
30
*The remaining 10 units from a batch of 30 started last week.
a. The production control manager is concerned about capacity requirements for one
of the automatic machines in the firm's wood shop--the #10 molder whose fixed capacity is 40
hours per week. Prepare a rough-cut capacity plan for the #I0 molder using the resource
profile data below. What suggestions would you make?
Hours per unit of end product produced
Product
#10molder
Operation setback
A
0.1
1 week
B
1.5
1 week
C
0.1
1 week
The manager has been using the following to estimate capacity requirements:
Product
A
B
C
Weekly forecast of final product sales
Forecast(unit/week)
10
25
15
Product
A
B
C
Manager's estimated capacity requirements per week (#I0 molder)
Forecast
Resources/unit
Capacity requirements
10
0.1hour
1.0 hours/week
25
1.5hour
37.5 hours/week
15
0.1hour
1.5 hours/week
40.0 hours/week
Evaluate the rough-cut capacity planning procedure used by the production control manager.
P4-24.
Bisutti Cams has a specialized programmed machining center that produces racing camshafts
for Indianapolis 500 race cars. It takes about one day for the firm's programmed machining
center to produce a racing camshaft to exact tolerances. Consequently, the firm used a
two-week lead time to produce a "batch" of 10 camshafts. The current MRP record for the
camshafts is as follows:
Week
1
2
3
4
5
6
Gross requirements
2
8
5
8
6
5s
Scheduled receipts
0
10
0
0
0
0
0
2
7
9
3
8
10
10
0
10
0
0
Projected available
2
balance
Planned order release
Q = 10; LT = 2; SS = 2.
a. There was real concern whether the programmed machining center's capacity had been
managed correctly, especially since the firm was having difficulty meeting customer delivery
date promises. The programmed machining center designers had said the machine was
capable of producing two usable camshafts a day while operating. Bisutti's engineers had said
it wasn't correct to count on the "theoretical" capacity but to use 75 percent as the expected
output (1.5 camshafts per day). On the other hand, only over the past few nionths had the
company been able to consistently produce one usable camshaft per day. Which capacity
value do you think should be used? Why?
b. Given the preceding record, what are the capacity requirements over the next five weeks?
(You can assume the open order has been in progress for almost a week and has produced five
usable camshafts.) How do they compare to the three possible capacity measures? What
advice can you give the firm's management?
P4-25.
The finishing department of the Ragged Edges Company has just upgraded the finishing
machlne. The firm hoped the capac~tyw ould now be 20 units a day. The machine has been
tested one full day. Output fell two units short of what was planned, while input was exactly
as planned. To evaluate the machine's performance, Ragged Edges used a spreadsheet
program to create an inputloutput control report five days later, starting with the deviations
and backlog (5 units) from the end of the first day. The firm hoped to maintam a 4-unit
backlog.
a. What would the inputloutput control report look like if the firm planned inputs of 23, 14, 17,
20, and 22 units for each of the five days, and actually did input 22, 15, 21, 23, and 19 units,
while output was 22, 20, 20, 18, and 21 units? What observations do you have?
b. Suppose the actual input had been 25 units on the last day. What would the report look like
(assuming no other changes)? Would your comments change? What if the department
reported backlog (Instead of output) and told you that the actual backlog was zero for each of
the past four days?
c. What would the input/output control report be if the input had actually been 14, 18, and 20
in the past three days? What observations can you make?
Consider the example of Noname computers presented in this section.
a. What is the minimum cycle time that is possible? What is the minimum number of stations
that would theoretically be required to achieve this cycle time?
b. Based on the ranked positional weight technique, how many stations are actually required
for the cycle time indicated in part (a)?
c. Suppose that the owner of the company that sells Noname computers finds that he is
receiving orders for approximately 100 computers per day. How many separate assembly
lines are required assuming (i) the best five-station balance, (ii) the best six-station balance
(both determined in the text), and (iii) the balance you obtained in part (b)? Discuss the
trade-offs involved with each choice.