# اريد ان اعرف اشياء عن تخطيط الانتاج



## مؤيد الاسلام (9 أغسطس 2011)

السلام عليكم ورحمة الله
انا مهندس حديث التخرج 2011
من انتاج واود ان اعرف ماهي الكتب التي اقرا فيها كي اعمل مهندس تخطيط انتاج
انا اقرا في :
1- operation mangnment
2-operation research

هل هناك اشياء اخري واريد ان اعرف اذا حصلت علي مثل هذه الوظيفة كيف اطور نفسي وانجح فيها 
شكررا جزيلا وجزاكم الله خير


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## فهد الفهد (5 يناير 2012)

*ألف مبروك التخرج*

*وبالتوفيق ان شاء الله*


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## محمد فوزى (9 يناير 2012)

*​*1
3-1
MDP 532:
Production Planning and Control
1st Year Diploma
Dr. Sherif Fahmy
Mechanical Design & Production Department, Cairo University
3-2
Chapter 3
Aggregate Planning
2
3-3
Introduction
3-4
Introduction
• Goal: To plan gross work force levels and set firmwide
production plans.
• Concept is based on the idea of an aggregate unit of
production.
• Most direct approach is to express aggregate units
using generic measures: weight (tons of steel),
volume (gallons of gasoline), time (worker-hours), or
dollars of sales.
3
3-5
Overview of the Problem
Suppose that D1, D2, . . . , DT are the forecasts of demand for
aggregate units over the planning horizon (T periods.) The
problem is to determine both work force levels (Wt) and
production levels (Pt ) to minimize total costs over the T
period planning horizon.
 Aggregate Planning addresses the problem of deciding how
many employees (workers) to retain over the planning
period and the quantity and mix of products to be produced.
3-6
Issues in Aggregate Planning
• Smoothing: Refers to the costs that result from making changes
in production and workforce levels (hiring and firing).
• Poor image. Difficulty of finding workers to hire.
• Bottleneck Planning: Problem of meeting peak demand because
of capacity restrictions (sudden changes).
• Planning Horizon: If too short, cannot anticipate sudden
changes. If too long, forecasts become unreliable
• End-of-horizon effect: Zero inventory.
• Treatment of Demand: Demand is assumed known: input models
have zero forecast error.
• Enables manager to focus systematic changes but no buffer for
errors.
4
3-7
Costs in Aggregate Planning
1. Smoothing Costs: changing size of the work force
and changing levels of production.
Linear Function: Constant
dollar amount charged
for hired (fired) worker
3-8
Costs in Aggregate Planning
2. Holding Costs:
• Major Factor: opportunity cost of dollars invested in
inventory
• Assumed to be linear in the number of units inventory:
dollars per unit held per planning period.
• Assumed to be charged on inventory remaining at the end of
planning period.
3. Shortage Costs:
• Cost of demand exceeding stock on-hand: Lost sales
• Assumed to be linear like holding costs.
5
3-9
Costs in Aggregate Planning
Back-orders Positive
Inventory
Slope = C
P
Slope = C
i
$ Cost
Inventory
Shortage Cost Holding Cost
3-10
Costs in Aggregate Planning
4. Regular Time Costs:
• Cost of producing one unit of output during regular hours.
• Payroll costs, direct & indirect material, and other manufacturing
expenses (overheads).
5. Over-time and sub-contracting costs
6. Idle time costs:
• Underutilizing workforce.
6
3-11
Obtaining Aggregate Units
• When the types of items produced are similar, an average
item is computed to be used as the aggregate unit.
• If the product types are very different, generic units have
to be used: weight, volume, dollar values,…
3-12
Example 3.1: Average Item
One plant produced 6 models of washing machines:
Model # hrs. Price % sales
A 5532 4.2 285 32
K 4242 4.9 345 21
L 9898 5.1 395 17
L 3800 5.2 425 14
M 2624 5.4 525 10
M 3880 5.8 725 06
Question: How do we define an aggregate unit based on
labor hours here?
7
3-13
Example 3.1: Average Item
• Price is not always proportional to worker hours: why?
• The aggregate unit to be used:
• Fictitious washing machine that requires:
0.32(4.2) + 0.21(4.9) + 0.17(5.1) + 0.14(5.2) +0.10(5.4) + .06(5.8)
= 4.856 labor hours.
3-14
Solution Methods
• Approximate Methods: These are solved by hand or by
straightforward graphical techniques:
• Level (Constant Workforce) Plan:
• Constant production and workforce levels over the whole
planning horizon
• Minimum smoothing costs
• Chase (Zero-Inventory) Plan:
• Tracks the cumulative net demand curve as closely as
possible each period
• Minimum inventory costs
• Mixed Strategies
• Linear Programming
8
3-15
Linear Programming
• Linear Programming provides a means of solving aggregate
planning problems optimally.
• The LP formulation is fairly complex requiring 8T variables and
3T constraints, where T is the length of the planning horizon.
Clearly, this can be a hard linear program.
• Does not take into account management policies (ex: avoid
hiring and firing as much as possible).
• Out of our Scope but good for further research.
3-16
Aggregate Planning Example
(Example 3.2 page 133)
• The company is interested in determining work force and
production levels for the next 6 months (Jan – Jun).
Forecasted demands (working days) for Jan-Jun: 1280 (20),
640 (24), 900 (18), 1200 (26), 2000 (22), and 1400 (15).
• Cost of hiring = $500, cost of firing = $1000, and holding
cost/month = $80.
• Starting inventory at the beginning of January is 500 and the
firm would like to have 600 units on hand at the end of June.
There are currently 300 workers employed.
• Problem: Find best monthly production (worker) levels.
9
3-17
Aggregate Planning Example
• First step in solution is to account for starting and ending
inventories:
• Define the net predicted demand:
• Subtract the initial inventory from the demand in
period 1.
• Net Predicted demand in January = 1280 -500 = 780
• Add the ending inventory to the demand in the last
period (period T).
• Net predicted demand in June = 1400+600 = 2000
3-18
Aggregate Planning Example
• Second step in solution is to translate aggregate production
units to workforce levels:
• Define K = number of aggregate units produced by one
worker in one day.
• K is obtained from past data by dividing the amount of
production by the used number of days by the available
number of workers:
• In the example and from past data, 245 units were
produced in 22 days by 76 workers.
• Therefore K = 245/(22 x 76) = 0.14653 units/worker/day
10
3-19
Solving the Problem: Chase Strategy
Month # of Working
days
Number of units
produced per worker
(K x days)
Net Predicted
Demand
Min # of
Workers
Jan 20 2.931 780 267
Feb 24 3.517 640 182
March 18 2.638 900 342
April 26 3.810 1200 315
May 22 3.224 2000 621
June 15 2.198 2000 910
Rounded Up
Workforce level is adjusted every month to exactly cover the
predicted demand.
3-20
Solving the Problem: Chase Strategy
Month Min # of
Workers
#
Hired
#
Fired
Number of
units
produced
per
worker
Number
of units
produced
Cum
Prod
Cum
Demand
Ending
Inventory
Jan 267 33 2.931 783 783 780 3
Feb 182 85 3.517 640 1423 1420 3
Mar 342 160 2.638 902 2325 2320 5
April 315 27 3.810 1200 3525 3520 5
May 621 306 3.224 2002 5527 5520 7
June 910 289 2.198 2000 7527 7520 7
Total 755 145 30
Total Cost of Plan = 500(755) + 1000(145) + 80(30) = $524900
Adjust for ending Inventory (600) = 524900 + 80(600) = $572,900
11
3-21
Solving the Problem: Constant Workforce
Month Number of
units
produced
per worker
(K x days)
Cum
Demand
Cum # of
units
produced
per worker
Ratio
Jan 2.931 780 2.931 267
Feb 3.517 1420 6.448 221
March 2.638 2320 9.086 256
April 3.810 3520 12.896 273
May 3.224 5520 16.190 343
June 2.198 7520 18.318 411
In order to guarantee that no shortages occur, level is set to
cover the minimum workforce for every month.
Maximum
3-22
Solving the Problem: Constant Workforce
Mont
h
Number of
units
produced
per worker
(K x days)
Monthly
Production
(x 411)
Cum.
Production
Cum
Demand
Ending
Inventory
Jan 2.931 1205 1205 780 425
Feb 3.517 1445 2650 1420 1230
March 2.638 1084 3734 2320 1414
April 3.810 1566 5300 3520 1780
May 3.224 1325 6625 5520 1105
June 2.198 903 7528 7520 8
Total 5962
Therefore we need 411 workers for the whole period, hence
we need to hire another 111 workers.
Total Cost for plan = 500(111) + 80(5962+600) = $580460
12
3-23
Solving the Problem: Mixed Strategy
Just one
modification in
workforce level
3-24
Solving the Problem: Mixed Strategy
• What we can do is cover the cumulative net demand with
minimum inventory and minimum workforce level changes.
• According to the figure, we will cover the cumulative demand in
the first 4 months by one workforce level (273 workers) in each
of the first 4 months.
• This will lead to zero inventory at the end of April.
• In May and June, 738 workers will be needed to produce the
cumulative of 4000 units.
• The total cost of this plan = $379500 (from LP)
13
3-25
Assignment
• Solve Problem 13 page 140.​


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## Hima El-Gendy (14 يوليو 2013)

محمد فوزي :75:


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## أحمد دعبس (15 يوليو 2013)

*اتفضل يا بشمهندس

ط¹ط±ط¨ ط´ظٹط± - i-t-o-m-rar
ط¹ط±ط¨ ط´ظٹط± - o-m-rar*​


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