Chap 012

12-1 Aggregate Planning

William J. Stevenson

Operations Management

8th edition


Chapter 12Chapter 12

Aggregate planning


Planning HorizonPlanning HorizonAggregate planning: Intermediate-range

capacity planning, usually covering 2 to 12 months. The goal of aggregate planning is to achieve a production plan that will effectively utilize the organization’s resources to satisfy expected demand.

Shortrange

Intermediate range

Long range

Now 2 months 1 Year


Organizations make capacity decisions on three levels: Short-range plans (Detailed plans)

Machine loading Job assignments

Intermediate plans (General levels) Employment Output, and inventories

Long-range plans Long term capacity Location / layout

Overview of Planning LevelsOverview of Planning Levels


Planning SequencePlanning Sequence

Business PlanEstablishes operationsand capacity strategiesEstablishes operationsand capacity strategies

Aggregate plan Establishesoperations capacity

Establishesoperations capacity

Master schedule Establishes schedulesfor specific products

Establishes schedulesfor specific products

Corporatestrategies

and policies

Economic,competitive,and political conditions

Aggregatedemand

forecasts

Figure 12.1


Overview of aggregate planningOverview of aggregate planning

Aggregate planning begins with a forecast of aggregate demand for the intermediate range.

This is followed by a general plan to meet demand requirements by setting output, employment, and finished-goods inventory or service capacities.

Managers must consider a number of plans, each of which must be examined in light of feasibility and cost.

If a plan is reasonably good but has minor difficulties, it may be reworked.

Aggregate plans are updated periodically, often monthly, to take into account updated forecast and other changes.


Resources Workforce/production rate Facilities and equipment

Demand forecast Policies

Subcontracting Overtime Inventory levels Back orders

Costs Inventory carrying Back orders Hiring/firing Overtime Inventory changes subcontracting

Aggregate Planning InputsAggregate Planning Inputs


Total cost of a plan Projected levels of:

Inventory Output Employment Subcontracting Backordering

Aggregate Planning OutputsAggregate Planning Outputs


Aggregate Planning StrategiesAggregate Planning Strategies

Proactive Involve demand options: Attempt to alter

demand to match capacity Reactive

Involve capacity options: attempt to alter capacity to match demand

Mixed Some of each


Pricing

Promotion

Back orders

New demand

Demand OptionsDemand Options


PricingPricing Pricing differential are commonly used to shift demand

from peak periods to off-peak periods, for example: some hotels offer lower rates for weekend stays Some airlines offer lower fares for night travel Movie theaters offer reduced rates for matinees Some restaurant offer early special menus to shift some of

the heavier dinner demand to an earlier time that traditionally has less traffic.

To the extent that pricing is effective, demand will be shifted so that it correspond more closely to capacity.

An important factor to consider is the degree of price elasticity of demand; the more the elasticity, the more effective pricing will be in influencing demand patterns.


PromotionPromotion

Advertising and any other forms of promotion, such as displays and direct marketing, can sometimes be very effective in shifting demand so that it conforms more closely to capacity.

Timing of promotion and knowledge of response rates and response patterns will be needed to achieve the desired result.

There is a risk that promotion can worsen the condition it was intended to improve, by bringing in demand at the wrong time.


Back orderBack order

An organization can shift demand to other periods by allowing back orders. That is , orders are taken in one period and deliveries promised for a later period.

The success of this approach depends on how willing the customers are to wait for delivery.

The cost associated with back orders can be difficult to pin down since it would include lost sales, annoyed or disappointed customers, and perhaps additional paperwork.


New demandNew demand

Manufacturing firms that experience seasonal demand are sometimes able to develop a demand for a complementary product that makes use of the same production process. For example, the firms that produce water ski in the summer, produce snow ski in the winter.


Hire and layoff workers Overtime/slack time Part-time workers Inventories Subcontracting (in- out)

Capacity OptionsCapacity Options


Aggregate Planning StrategiesAggregate Planning Strategies

Maintain a level workforce

Maintain a steady output rate

Match demand period by period

Use a combination of decision variables


Basic StrategiesBasic Strategies

Level capacity strategy:

Maintaining a steady rate of regular-time output while meeting variations in demand by a combination of options such as: inventories, overtime, part-time workers, subcontracting and back orders.

Chase demand strategy:

Matching capacity to demand; the planned output for a period is set at the expected demand for that period.


Chase ApproachChase Approach

Advantages

Investment in inventory is low

Labor utilization is high

Disadvantages

The cost of adjusting output rates and/or workforce levels


Level ApproachLevel Approach

Advantages

Stable output rates and workforce levels

Disadvantages

Greater inventory costs

Increased overtime and idle time

Resource utilizations vary over time


Techniques for aggregate planning are classified into two categories:

Informal trial-and-error techniques (frequently used)

Mathematical techniques

Techniques for Aggregate PlanningTechniques for Aggregate Planning


1. Determine demand for each period

2. Determine capacities (regular time, over time, and subcontracting) for each period

3. Identify policies that are pertinent

4. Determine units costs for regular time, overtime, subcontracting, holding inventories, back orders, layoffs, and other relevant costs

5. Develop alternative plans and compute the costs for each

6. Select the best plan that satisfies objectives. Otherwise return to step 5.

A general procedure for Aggregate A general procedure for Aggregate PlanningPlanning


Mathematical TechniquesMathematical Techniques

Linear programming: Methods for obtaining optimal solutions to problems involving allocation of scarce resources in terms of cost minimization.

Linear decision rule: Optimizing technique that seeks to minimize combined costs, using a set of cost-approximating functions to obtain a single quadratic equation.

Simulation models: Developing a computerized models that can be tested under a variety of conditions in an attempt to identify reasonably acceptable (although not always optimal) solutions to problem.


Summary of Planning TechniquesSummary of Planning Techniques

Technique Solution Characteristics

Graphical/charting Trial and error

Intuitively appealing, easy to understand; solution not necessarily optimal.

Linear programming

Optimizing Computerized; linear assumptions not always valid.

Linear decision rule

Optimizing Complex, requires considerable effort to obtain pertinent cost information and to construct model; cost assumptions not always valid.

Simulation Trial and error

Computerized models can be examined under a variety of conditions.

Table 12.7


Linear programmingLinear programming Linear programming models are methods for obtaining

optimal solutions to problems involving the allocation of scarce resources in terms of cost minimization or profit maximization.

With aggregate planning, the goal is usually to minimize the sum of costs related to regular labor time, overtime, subcontracting, carrying inventory, and cost associated with changing the size of the workforce. Constraints involve the capacities of the workforce, inventories, and subcontracting.

The aggregate planning problem can be formulated as a transportation problem (special case of linear programming.


Aggregate planning notationAggregate planning notation

r = regular production cost per unit

t = overtime cost per unit

s = subcontracting per unit

h = holding cost per unit

b = backorder cost per unit per period

n = number of periods in planning horizon

12-28 Aggregate PlanningTransportation notation for aggregate Transportation notation for aggregate

planningplanningPeriod

1Period

2Period

3… Period n Unused

capacitycapacity

Period Beginning inventory

0 h 2h (n-1)h 0 I0

1 Regular r r+h r+2h r+(n-1)h 0 R1

Overtime t t+h t+2h t+(n-1)h 0 O1

subcontract s s+h s+2h s+(n-1)h 0 S1

2 Regular r+b r r+h r+(n-2)h 0 R2

Overtime t+b t t+h t+(n-2)h 0 O2

subcontract s+b s s+h s+(n-2)h 0 S2

3 Regular r+2b r+b r r+(n-3)h 0 R3

Overtime t+2b t+b t t+(n-3)h 0 O3

subcontract s+2b s+b s s+(n-3)h 0 S3

demand D1 D2 D3 Dn total


notesnotes Regular cost, overtime cost, and subcontracting cost are at

their lowest cost when output is consumed in the same period it is produced.

If goods are made available in one period but carried over to later period, holding costs are incurred at the rate of (h) per period.

Conversely, with back orders, the unit cost increases as you move across a row from right to left, beginning at the intersection of a row and column for the same period.

Beginning inventory is given a unit cost of 0 if it is used to satisfy demand in period 1. however, if it is held over for use in later periods, a holding cost of h per unit is added for each period.


ExampleExample Given the following information set up the problem in a transportation table and

solve for the minimum cost plan.

period

1 2 3

demand 550 700 750

Capacity

Regular 500 500 500

Overtime 50 50 50

subcontract 120 120 100

Beginning inventory 100

Costs

Regular time $60 per unit

80 per unit

90 per unit

$1 per unit per month

$3 per unit per month

Overtime

Subcontract

Inventory carrying cost

Back order cost


SolutionSolution The transportation table and solution are shown in the next slide.

Some entries require additional explanation:a. Inventory carrying cost, h = $1 per unit per period. Hence, units

produced in one period and carried over to a later period will incur a holding cost that is a linear function of the length of time held.

b. Linear programming models of this type require that supply (capacity) and demand be equal. A dummy column has been added (nonexistent capacity) to satisfy that requirement. Since it does not “cost” anything extra to not use capacity in this case, cell costs of $0 have been assigned.

c. No backlogs were needed in this exampled. The quantities (e.g., 100, 450 in column 1) are the amounts of

output or inventory that will be used to meet demand requirements. Thus, the demand of 550 units in period 1 will be met using 100 units from inventory and 450 obtained from regular time output.


Initial solution using northwest cornerInitial solution using northwest corner

Period 1

Period 2

Period 3

Unused capacity

capacity


0 1 2 0 100

1 Regular 60 61 62 0 500

Overtime 80 81 82 0 50

subcontract 90 91 92 0 120

2 Regular 63 60 61 0 500

Overtime 83 80 81 0 50


3 Regular 66 63 60 0 500

Overtime 86 83 80 0 50


demand 550 700 750 90 2090

100

450 50

50

120

480

120

500

50

10

20

50

90

Total cost is

$124910


Optimal solutionOptimal solution

Period 1

Period 2

Period 3

Unused capacity

capacity


0 1 2 0 100

1 Regular 60 61 62 0 500

Overtime 80 81 82 0 50


2 Regular 63 60 61 0 500

Overtime 83 80 81 0 50


3 Regular 66 63 60 0 500

Overtime 86 83 80 0 50


demand 550 700 750 90 2090

100

450 50

50

30

500

50

20 100

500

50

100

90

Total cost is

$124730


Trial and error techniquesTrial and error techniques

Trial and error approaches consist of developing simple tables or graphs that enable planners to visually compare projected demand requirements with existing capacity.

Different plans are conducted and evaluated in terms of their overall costs. The one with the minimum cost will be chosen.

The disadvantage of such techniques is that they do not necessarily result in the optimal aggregate plan.


AssumptionsAssumptions

1. The regular output capacity is the same in all periods.2. Cost ( back order, inventory, subcontracting, etc) is a linear

function composed of unit cost and number of units.3. Plans are feasible; that is, sufficient inventory capacity exists to

accommodate a plan, subcontractors with appropriate quality and capacity are standing by, and changes in output can be made as needed.

4. All costs associated with a decision option can be represented by a lump sum or by unit costs that are independent of the quantity involved

5. Cost figures can be reasonably estimated and are constant for the planning horizon.

6. Inventories are built up and drawn down at a uniform rate and output occurs at a uniform rate throughout each period.


Some important relationshipsSome important relationshipsNumber of number of number of new number of laid-off

Workers in = workers at end of + workers at start - workers at start of

A period the previous period of the period the period

Inventory inventory production amount used to

At the end of = at the end of + in the - satisfy demand in

A period previous period current period current period

Cost for output cost hire/layoff inventory back order = + + +a period (Reg + OT + subcontract) cost cost cost

Averageinventory

Beginning Inventory + Ending Inventory 2

=


Cost calculationCost calculation

Type of cost How to calculate

Output

Regular Regular cost per unit × Quantity of regular output

Overtime Overtime cost per unit × Overtime quantity

Subcontract Subcontract cost per unit × subcontract quantity

Hire/layoff

Hire Cost per hire × number hired

Layoff Cost per layoff × number laid off

Inventory Carrying cost per unit × average inventory

Back order Back-order cost per unit × number of back order unit


Example 1Example 1 Planners for a company that makes several models of skateboards are about to prepare the

aggregate plan that will cover six periods. They now want to evaluate a plan that calls for a steady rate of regular output, mainly using inventory to absorb the uneven demand but allowing some backlog. Overtime and subcontracting are not used because they want a steady output. They intend to start with zero inventory on hand in the first period. Prepare an aggregate plan and determine its cost using the following information. Assume a level of output rate of 300 unit per period with regular time. Note that the planned ending inventory is zero. There are 15 workers, and each can produce 20 units per period.

period 1 2 3 4 5 6 total

forecast 200 200 300 400 500 200 1800

Cost:

Regular time = $2 per skateboard

Overtime = $3 per skateboard

Subcontract = $6 per skateboard

Inventory = $1 per skateboard per period on average inventory

Back orders = $5 per skateboard per period


Solution: example 1Solution: example 1Period 1 2 3 4 5 6 total

Forecast 200 200 300 400 500 200 1800Output

Regular 300 300 300 300 300 300 1800 Overtime - - - - - -

Subcontract - - - - - -

Output-forecast 100 100 0 (100) (200) 100 0Inventory

Beginning 0 100 200 200 100 0

Ending 100 200 200 100 0 0

Average 50 150 200 150 50 0 600Backlog 0 0 0 0 100 0 100Cost

Output

Regular $600 600 600 600 600 600 $3600 Overtime - - - - - -

Subcontract - - - - - -

Hire/layoff - - - - - -

Inventory $50 150 200 150 50 0 $600 Back order 0 0 0 0 500 0 $500Total $650 750 800 750 1150 600 $4700


Example 2Example 2

After reviewing the plan developed in the preceding example, planners have decided to develop an alternative plan. They have learned that one is about to retire from the company. Rather than replace that person, they would like to stay with the smaller workforce and use overtime to make up for lost output. The reduced regular time output is 280 units per period. The maximum amount of overtime output per period is 40 units. Develop a plan and compare it to the previous one.


Solution: example 2Solution: example 2Period 1 2 3 4 5 6 total

Forecast 200 200 300 400 500 200 1800Output

Regular 280 280 280 280 280 280 1680 Overtime 0 0 40 40 40 0 120 Subcontract - - - - - -

Output-forecast 80 80 20 (80) (180) 80 0Inventory

Beginning 0 80 160 180 100 0

Ending 80 160 180 100 0 0

Average 40 120 170 140 50 0 520Backlog 0 0 0 0 80 0 80Cost

Output

Regular $560 560 560 560 560 560 $3360 Overtime 0 0 120 120 120 0 360 Subcontract - - - - - -

Hire/layoff - - - - - -

Inventory $40 120 170 140 50 0 $520 Back order 0 0 0 0 400 0 $400Total $600 680 850 820 1130 560 $4640


Comment: example 2Comment: example 2 The amount of overtime that must be scheduled has to

make up for lost output of 20 units per period for six periods, which is 120. this is scheduled toward the center of the planning horizon since that is where the bulk of demand occurs. Scheduling it earlier would increase inventory carrying costs; scheduling it later would increase backlog cost.

Overall the total cost for this plan is 44640, which is $60 less than the previous plan.

Regular time production cost and inventory cost are down, but there is overtime cost, however, this plan achieves savings in back order cost, making it somewhat less costly overall than the plan in example 1


Aggregate planning for services takes into account projected customer demands, equipment, capacities, and labor capabilities. The resulting plan is a time-phased projection of service staff requirements.

Aggregate planning for manufacturing and aggregate planning for services share similarities in some respect, but there are some important differences which are:

Services occur when they are rendered

Demand for service can be difficult to predict

Capacity availability can be difficult to predict

Labor flexibility can be an advantage in services

Aggregate Planning in ServicesAggregate Planning in Services


Disaggregating the aggregate planDisaggregating the aggregate plan For the production plan to be translated into meaningful terms of

production, it is necessary to disaggregate the aggregate plan. This means breaking down the aggregate plan into specific product

requirements in order to determine labor requirements (skills, size of workforce), materials, and inventory requirements.

To put the aggregate production plan into operation, one must convert, or decompose, those aggregate units into units of actual product or services that are to be produced or offered.

For example, televisions manufacturer may have an aggregate plan that calls for 200 television in January, 300 in February, and 400 in March. This company produce 21, 26, and 29 inch TVs, therefore the 200, 300, and 400 aggregate TVs that are to be produced during those three months must be translated into specific numbers of TVs of each type prior to actually purchasing the appropriate materials and parts, scheduling operations, and planning inventory requirements.


Master schedulingMaster scheduling The result of disaggregating the aggregate plan is a master schedule

showing the quantity and timing of specific end items for a scheduled horizon, which often covers about six to eight weeks ahead.

The master schedule shows the planned output for individual products rather than an entire product group, along with the timing of production.

It should be noted that whereas the aggregate plan covers an interval of, say, 12 months, the master schedule covers only a portion of this. In other words, the aggregate plan is disaggregated in stages , or phases, that may cover a few weeks to two or three months.

The master schedule contains important information for marketing as well as for production. It reveals when orders are scheduled for production and when completed orders are to be shipped.


Aggregate Plan to Master ScheduleAggregate Plan to Master Schedule

Jan Feb Mar.

200 300 400

AggregatePlanning

Disaggregation

MasterSchedule

Figure 12.4

Aggregate plan

Type Jan. Feb. Mar

21 inch

100 100 100

26 inch

75 150 200

29 inch

25 50 100

total 200 300 400

Master schedule


Master SchedulingMaster Scheduling

Master schedule Determines quantities needed to meet demand Interfaces with

Marketing: it enables marketing to make valid delivery commitments to warehouse and final customers.

Capacity planning: it enables production to evaluate capacity requirements

Production planning Distribution planning


Master SchedulerMaster Scheduler

The duties of the master scheduler generally include:

Evaluates impact of new orders Provides delivery dates for orders Deals with problems such as:

Production delays Revising master schedule Insufficient capacity


Master Scheduling ProcessMaster Scheduling Process

MasterScheduling

Beginning inventory

Forecast

Customer orders

Inputs Outputs

Projected inventory

Master production schedule

Uncommitted inventory

Figure 12.6


Master scheduling processMaster scheduling process

Master production schedule (MPS): indicates the quantity and timing of planned production, taking into account desired delivery quantity and timing as well as on-hand inventory. The MPS is one of the primary outputs of the master scheduling process.

Rough-cut capacity Planning (RCCP): it involves testing the feasibility of a proposed master relative to available capacities, to assure that no obvious capacity constraints exist. This means checking capacities of production warehouse facilities, labor, and vendors to ensure that no gross deficiencies exist that will render the master schedule unworkable


Master scheduleMaster schedule

Inputs: Beginning inventory; which is the actual inventory

on hand from the preceding period of the schedule Forecasts for each period demand Customer orders; which are quantities already

committed to customers. Outputs

Projected inventory Production requirements The resulting uncommitted inventory which is

referred to as available-to-promise (ATP) inventory


Projected On-hand InventoryProjected On-hand Inventory

Projected on-handinventory

Inventory fromprevious week

Current week’srequirements

-=


Example: Master ScheduleExample: Master ScheduleA company that makes industrial pumps wants to prepare a master

production schedule for June and July. Marketing has forecasted demand of 120 pumps for June and 160 pumps for July. These have been evenly distributed over the four weeks in each month: 30 per week in June and 40 per week in July.

Now suppose that there are currently 64 pumps in inventory (i.e., beginning inventory is 64 pumps), and that there are customer orders that have been committed for the first five weeks (booked) and must be filled which are 33, 20, 10, 4, and 2 respectively. The following figure (see next slide) shows the three primary inputs to the master scheduling process: beginning inventory, the forecast, and the customer orders that have been committed. This information is necessary to determine three quantities: the projected on-hand inventory, the master production schedule (MPS) and the uncommitted (ATP) inventory. Suppose a production lot size of 70 pumps is used.

Prepare the master Schedule


Solution: Master scheduleSolution: Master schedule

64 1 2 3 4 5 6 7 8Forecast 30 30 30 30 40 40 40 40

Customer Orders (committed) 33 20 10 4 2

Projected on-hand inventory 31 1 -29

JUNE JULY

Beginning Inventory

Customer orders are larger than forecast in week 1

Forecast is larger than Customer orders in week 2

Forecast is larger than Customer orders in week 3

Figure 12.8 The master schedule before MPS


Solution: The master scheduleSolution: The master schedule The first step you have to calculate the on hand inventory

Week Inventory from previous week

Requirements Net inventory before MPS

MPS Projected inventory

1 64 33 31 31

2 31 30 1 1

3 1 30 -29 70 41

4 41 30 11 11

5 11 40 -29 70 41

6 41 40 1 1

7 1 40 -39 70 31

8 31 40 -9 70 61


Solution: Master ScheduleSolution: Master Schedule The projected on-hand inventory and MPS are added to the master

schedule

Initial inventory

64

June July1 2 3 4 5 6 7 8

Forecast 30 30 30 30 40 40 40 40Customer orders (committed)

33 20 10 4 2

Projected on hand inventory

31 1 41 11 41 1 31 61

MPS 70 70 70 70Available to promise inventory (uncommitted)

11 56 68 70 70


NotesNotes

The requirements equals the maximum of the forecast and the customer orders

The net inventory before MPS equals the inventory from previous week minus the requirements.

The MPS = run size, will be added when the net inventory before MPS is negative ( weeks 3, 5, 7, and 8).

The projected inventory equals the net inventory before MPS plus the MPS (70).


Solution: Master ScheduleSolution: Master Schedule

The amount of inventory that is uncommitted, and, hence, available to promise is calculated as follows:

Sum booked customer orders week by week until (but not including) a week in which there is an MPS amount. For example, in the first week, this procedure results in summing customer orders of 33 (week 1) and 20 (week 2) to obtain 53. in the first week, this amount is subtracted from the beginning inventory of 64 pumps plus the MPS (zero in this case) to obtain the amount that is available to promise [(64 + 0 – (33 + 20)] = 11


Time Fences in MPSTime Fences in MPS

Period

“frozen”(firm orfixed)

“slushy”somewhat

firm

“liquid”(open)

Figure 12.12

1 2 3 4 5 6 7 8 9

Time fences divide a scheduling time horizon into three sections or phases, sometimes referred as frozen, slushy, and liquid, in reference to the firmness of schedule:

Frozen phase: is the near-term phase that is so soon that delivery of a new order would be impossible, or only possible using very costly or extraordinary options such as delaying another delivery.

Slushy phase: is the next phase, and its time fence is usually a few periods beyond the frozen phase. Order entry in this phase necessitate trade-offs, but is less costly or disruptive than in frozen phase.

Liquid phase: is the farthest out on the time horizon. New orders or cancellations can be entered with ease

Chap 012

Documents

aggregate planning chapter

goal of aggregate planning

forecast of aggregate

aggregate plans

expected demand

demand patterns

seasonal demand

demand requirements