OPSM 301 Operations Management
Class 22:Aggregate Planning (Chapter 13)
Koç University
Zeynep [email protected]
Announcements
Reminder: Midterm 2 next Tuesday on 20/12 at 17:00 CAS-Z08
Aggregate Planning: will skip AP in services; however OPSM 405 Service Operations Management has an extensive module on this topic
Linear Programming: Quantitative Module B; will skip graphical solution and sensitivity analysis parts
Example 2: Finding Cu and Co
A textile company in UK orders coats from China. They buy a coat from 250€ and sell for 325€. If they cannot sell a coat in winter, they sell it at a discount price of 225€. When the demand is more than what they have in stock, they have an option of having emergency delivery of coats from Ireland, at a price of 290.
The demand for winter has a normal distribution with mean 32,500 and std dev 6750.
How much should they order from China??
Operations Planning
Order Scheduling
Material RequirementPlanning
Master ProductionScheduling
Daily workforce and customerscheduling
Weekly workforce andCustomer scheduling
Aggregate Planning
Strategic CapacityPlanning
Process Planning
Long
range
Medium range
Short
range
Manufacturing Service
Relationships of the Aggregate Plan
AggregatePlan for
Production
DemandForecasts,
orders
MasterProduction
Schedule, and MRP systems
Detailed WorkSchedules
ExternalCapacity
Subcontractors
Inventory OnHand
Raw MaterialsAvailable
Work Force
Marketplaceand Demand
Research andTechnology
ProductDecisions
ProcessPlanning & Capacity
Decisions
Provides the quantity and timing of production for intermediate future– Usually 3 to 18 months into future
Combines (‘aggregates’) production– Often expressed in common units
• Example: Hours, dollars, equivalents (e.g., FTE students)
Involves capacity and demand variables
Aggregate Planning
Meet demand Use capacity efficiently Meet inventory policy Minimize cost
– Labor
– Inventory
– Plant & equipment
– Subcontract
Aggregate Planning Goals
Aggregate Planning StrategiesPure Strategies
Capacity Options — change capacity:– changing inventory levels (recall from
earlier session that these are known as seasonal inventory)
– varying work force size by hiring or layoffs– varying production capacity through
overtime or idle time– subcontracting– using part-time workers
Aggregate Planning StrategiesPure Strategies
Demand Options — change demand:
– influencing demand– backordering during high demand periods– counterseasonal product mixing
Aggregate Scheduling Options - Advantages and Disadvantages
Option Advantage Disadvantage SomeComments
Changinginventory levels
Changes inhuman resourcesare gradual, notabruptproductionchanges
Inventoryholding costs;Shortages mayresult in lostsales
Applies mainlyto production,not service,operations
Varyingworkforce sizeby hiring orlayoffs
Avoids use ofother alternatives
Hiring, layoff,and trainingcosts
Used where sizeof labor pool islarge
Option Advantage Disadvantage SomeComments
Varyingproduction ratesthrough overtimeor idle time
Matches seasonalfluctuationswithouthiring/trainingcosts
Overtimepremiums, tiredworkers, may notmeet demand
Allowsflexibility withinthe aggregateplan
Subcontracting Permitsflexibility andsmoothing of thefirm's output
Loss of qualitycontrol; reducedprofits; loss offuture business
Applies mainlyin productionsettings
Advantages/Disadvantages - Continued
Advantages/Disadvantages - Continued
Option Advantage Disadvantage SomeComments
Using part-timeworkers
Less costly andmore flexiblethan full-timeworkers
Highturnover/trainingcosts; qualitysuffers;schedulingdifficult
Good forunskilled jobs inareas with largetemporary laborpools
Influencingdemand
Tries to useexcess capacity.Discounts drawnew customers.
Uncertainty indemand. Hard tomatch demand tosupply exactly.
Createsmarketing ideas.Overbookingused in somebusinesses.
Advantage/Disadvantage - Continued
Option Advantage Disadvantage SomeComments
Back orderingduring high-demand periods
May avoidovertime. Keepscapacity constant
Customer mustbe willing towait, butgoodwill is lost.
Many companiesbackorder.
Counterseasonalproducts andservice mixing
Fully utilizesresources; allowsstable workforce.
May requireskills orequipmentoutside a firm'sareas ofexpertise.
Risky findingproducts orservices withopposite demandpatterns.
The Extremes
Level Strategy
Chase Strategy
Production equals
demand
Production rate is constant
Example 1:M
onth
ly s
ales
for
ecas
ts (
$ m
illi
on)
Jan
Feb
Mar
Apr
May
Jun.
July
Aug
Sep
t.
Oct
.
Nov
.
Dec
.
7.6 8.4 10.2 9.0 11.8 7.0 8.6 12.6 14.4 12.8 15.8 11.8
Total sales for the year = $130 million
Cumulative ChartC
umul
ativ
e sa
les
fore
cast
s ($
mil
lion
)
Jan
Feb
Mar
Apr
May
Jun.
July
Aug
Sep
t.
Oct
.
Nov
.
Dec
.
120-
Chase Strategy
Cum
ulat
ive
sale
s fo
reca
sts
($ m
illi
on)
Jan
Feb
Mar
Apr
May
Jun.
July
Aug
Sep
t.
Oct
.
Nov
.
Dec
.
120-
Cumulative sales and
cumulative production
Level Strategy
Cum
ulat
ive
sale
s fo
reca
sts
($ m
illi
on)
Jan
Feb
Mar
Apr
May
Jun.
July
Aug
Sep
t.
Oct
.
Nov
.
Dec
.
120-
Cumulative sales
Cumulative production
shortage
excess
Labor Capacity Requirements
January 253 20 1581 28.4 3099February 280 21 1667 29.6 5933March 340 23 1848 33.1 8037April 300 20 1875 33.7 9737May 393 22 2235 40.2 9706…. … … ….. …. ….December 393 20 2458 44.2 0Total 4333 243 2229 40 7035
Sales i
n
labor
-hou
rs
(000
)s Wor
king
days
Variab
le wor
k
force Vari
able
work
week Vari
able
inven
tory
Chase Strategy Level Strategy
Illustration of calculations
Level production– Total sales = $130 million– Total labor-hours required = $130 million/$30 = 4.333 M
labor-hrs.– Total hours = 243 days . 8 hrs/day = 1944 hrs– Number of workers = 4.333 M / 1944 = 2229
Variable workforce for January– Sales in labor-hours = $7.6 M /$30 = 253,333– Working hours = 20 days . 8 hrs/day = 160 hours– Variable work force = 1581
Variable workweek for January– Sales in labor-hours = $7.6 M /$30 = 253,333– Number of workers = 2229 (average required, constant)– Variable monthly load for a worker = 253,333/2229 = 113.65– Variable workweek = 113.65/4 = 28.4 hours/week
Variable inventory for January (Level production)– Production in January =
(2229 workers)(20 days/month)(8 hrs/day) = 356,640– Demand for January = 253,333 (labor-hours)– Inventory = 103,307 labor-hours– Inventory ($) = (103,307)($30/labor-hour) = $309,920
Evaluating Alternatives
Hiring cost = $200 per employee Firing cost = $500 per employee Regular labor cost = $5 per hour Overtime premium cost = $2.5 per hour Undertime premium cost = $3 per hour Inventory carrying cost = 2% per month
(applied to the monthly ending inventory) Beginning labor force = 1,583 persons Beginning inventory = 0
Alternative 1: Variable Workforce
Zero-inventory, hire-fire as requiredStarting Required Hire-fire CostWorkforce Workforce
January 1,583 1,583 0 0February 1,583 1,667 84 $16,800 March 1,667 1,848 181 $36,200April 1,848 1,875 27 $5,400May 1,875 2,235 360 $72,000June 2,235 1,326 -909 $454,500 …. ….. ……. ……. ……...December3,292 2,458 -834 $417,000Total $2,708,300
Alternative 2: Level Production
constant worforce :2229, Variable Inventory
Initial hire = (2229-1583) = 646 Cost = 129,200
Initial Production Required Ending Cost Inventory (labor-hours) Inventory
January 0 356,640 253,333 103,307 $61984.2…. ….. ……. ……. ……...
Total $1,882,420
Example 2:
National Steel Corporation (NSC) produces a special-purpose steel used in the aircraft and aerospace industries. The Sales Department of NSC has received orders of 2400, 2200, 2700, and 2500 tons of steel for each of the next 4 months. NSC can meet these demands by producing the steel, by drawing from its inventory, or by using any combination of the two alternatives.
The production costs per ton of steel during each of the next 4 months are projected to be $7400, $7500, $7600, and $7650. Because costs are rising each month-due to inflationary pressures- NSC might be better off producing more steel than it needs in a given month and storing the excess.
Production capacity cannot exceed 4000 tons in any one month. The monthly production is finished at the end of the month, at which time the demand is met. Any remaining steel is then stored in inventory at a cost of $120 per ton for each month it remains there.
If the production level is increased from one month to the next, then the company incurs a cost of $50 per ton of increased production to cover the additional labor and/or overtime. Each ton of decreased production to cover the additional labor and/or overtime. Each ton of decreased production incurs a cost of $30 to cover the benefits of unused employees.
The production level during the previous month was 1800 tons, and the beginning inventory is 1000 tons. Inventory at the end of the fourth month must be at least 1500 tons to cover anticipated demand.Formulate a production plan for NSC that minimizes the total costs over the next 4 months.
Data for the Production-Planning Problem of NSC
Month 1 2 3 4
Demand (tons) 2400 2200 2700 2500Production cost ($/ton) 7400 7500 7600 7650Inventory cost ($/ton/month) 120 120 120 120 Starting inventory = 1000 tonsEnding inventory (at the end of 4th month) = 1500 tonsStarting production level = 1800 tonsCost of changing production level = $50 per ton (increase)
$30 per ton (decrease)