Aggregate Planning

Module 3

Module Learning Objectives

• At the end of this module student should be able to:– Interpret the changes in supply and demand (L3)– Examine different strategies of aggregate planning

and estimate the cost of each strategy (L4)– Illustrate the process of MRP (L3)

Aggregate Production PlanningWhy is it necessary?

• Demand fluctuations• Capacity fluctuations • Supply fluctuations• Difficulty level in altering production rates

– Production systems are complex and varying the rate of production requires prior planning and co-ordination with supplier and distributor

• Benefits of multi-period planning

Aggregate Production Planning is done in an organisation to match the demand with the supply on a period-by-period basis in a cost effective manner

Aggregate Production PlanningDecision Variables: An illustration

• The decisions involve – Amount of resources (productive capacity and labour hours) to be

committed – Rate at which goods and services needs to be produced during a

period – Inventory to be carried forward from one period to the next

• An example from Garment Manufacturing– Produce at the rate of 9000 metres of cloth everyday during the months of

January to March – Increase it to 11,000 metres during April to August – Change the production rate to 10,000 metres during September to December – Carry 10% of monthly production as inventory during the first 9 months of

production. – Work on a one-shift basis throughout the year with 20% over time during July to

October

Framework of Aggregate Planning

Forecast Capacity

Aggregate Production Plan

Master Production Schedule

Materials Requirements Planning Capacity Requirements Planning

Market Environment Resource Base and Technology

Business Plan

Marketing Plan Financial Plan

Production Plan(rough cut capacity)

Master Production Schedule

Materials Requirement

Plan

Capacity Requirement

Plan

Detailed Scheduling

Shop Floor Control

Level 1

Level 2

Level 3

Hierarchical Approach to Planning

AP Guidelines

• Determine the corporate policy regarding controllable variables• Use a good forecast as a basis for planning• Plan in appropriate capacity• Maintain as stable a work force as as is practical• Maintain needed control over inventories• Maintain flexibility to change• Respond to demand in controlled manner• Evaluate planning on a regular basis

Month DemandProdn. Days

Jan 220 22Feb 90 18Mar 210 21Apr 396 22May 616 22Jun 700 20Jul 378 21Aug 220 22Sep 200 20Oct 115 23Nov 95 19Dec 260 20

A firm has developed the following forecast (units) for an item which has a demand influenced by seasonal factors

a. Prepare a chart showing the daily demand requirements

b. Plot the demand as histogram and as a cumulative requirements

c. Determine the production rate required to meet average demand and plot this as dotted line

Month Demand Prodn. DaysDemand per day

Cu. Prodn. Days

Cu.Damand

Const Prodn @ 14

Cu. Prodn.

Av. Prodn.

Ending Inventory

Ending Inv. With 566

10 22 220 308 308 14 88 6545 40 310 252 560 14 250 816

10 61 520 294 854 14 334 90018 83 916 308 1162 14 246 81228 105 1532 308 1470 14 -62 50435 125 2232 280 1750 14 -482 8418 146 2610 294 2044 14 -566 010 168 2830 308 2352 14 -478 8810 188 3030 280 2632 14 -398 168

5 211 3145 322 2954 14 -191 3755 230 3240 266 3220 14 -20 546

13 250 3500 280 3500 14 0 566

Jan 220 22Feb 90 18Mar 210 21Apr 396 22May 616 22Jun 700 20Jul 378 21Aug 220 22Sep 200 20Oct 115 23Nov 95 19Dec 260 20

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

5

10

15

20

25

30

35

Demand per day

22 40 61 83 105 125 146 168 188 211 230 2500

5

10

15

20

25

30

35

Demand per day

22 40 61 83 105 125 146 168 188 211 230 2500

500

1000

1500

2000

2500

3000

3500

4000

Cu. Prodn. V/s Cu. Demand

Cu. Prodn. Days

Cu.

Dem

and

Jan

Feb Mar Apr

May Ju

n Jul

Aug Sep OctNov Dec

-800

-600

-400

-200

0

200

400

600

800

1000

Inventory Balance

Ending Inventory Ending Inv. With 566

Month

Un

its

Problem: An aggregate planner has estimated the following demand requirements for forthcoming work periods, which represent one complete demand cycle for them. A company expects the next demand cycle to be similar to this one.

Period Forecast

1 400

2 400

3 600

4 800

5 1200

6 1200

7 600

8 200

9 200

10 400

Plan 1: Vary the labour force from an initial capability of 400 units to whatever is required to meet the demand

Amount of Change

Incremental cost to change labour ($)

Increase Decrease

200 9000 9000

400 15000 18000

600 18000 30000

Go to

Plan 2: Maintain stable workforce capable of producing 600 units per period, and meet demand by overtime at a premium of $ 40 per unit, Idle time cost equivalent to $ 60 per unit.

Go to

Plan 3: Vary Inventory levels, but maintain a stable work force producing at an average requirement rate with no overtime or idle time. The carrying cost per unit per period is $20. ( the company can arrange to have whatever inventory level is required before period 1 at no additional cost

Go to Sheet 3

PROBLEM: Given the accompanying supply, demand, cost and inventory data for a firm that has a constant workforce and wishes to meet all demand ( that is with no back orders), allocate production capacity to satisfy demand at minimum cost.

Period

Supply Capacity (Units) Demand

(Units)Regular Time

Over Time

Subcontract

1 60 18 1000 100

2 50 15 1000 50

3 60 18 1000 70

4 65 20 1000 80Additional data:Initial Inventory = 20 unitsFinal Inventory = 25 unitsRegular Time cost / unit = Rs. 500

(Labour = 50% of the cost)Overtime cost / unit = Rs. 625Subcontracting cost / unit = Rs. 650Carrying cost / unit-period= Rs. 10

Monks 324

Go to

  Period 1 2 3 4Un used Capacity  

   Allocation Cost

Allocation Cost

Allocation Cost

Allocation Cost

Allocation Cost Capacity

Ini. Inventory  

Period 1

RT  

OT  

SC  

Period 2

RT  

OT  

SC  

Period 3

RT  

OT  

SC  

Period 4

RT  

OT  

SC  

     

Demand  

Michigan Manufacturing produces a product which has a six –month demand cycle, as shown. Each unit requires 10 worker-hours to be produced at a lobour cost of $6 per hour regular rate (or $ 9 per hour OT). The total cost per unit is estimated at $ 200, but units can be subcontracted at a cost of $ 208 per unit. There currently 20 workers employed in the subject department, and hiring and training cost for additional workers are $300 per person, where as layoff costs are $400 per person. Company policy is to retain a safety stock equal to 20% of the monthly forecast, and each month’s safety stock becomes beginning inventory for the next month. There are currently 50 units in stock carried at a cost of $ 2 per unit-month. Stockouts have been assigned a cost of $20 per month.

Jan Feb Mar Arp May JuneForecast Demand 300 500 400 100 200 300

Workdays 22 19 21 21 22 20

Worker Hour at 8 hours per day

Aggregate Planning for Services

1. Most services cannot be inventoried 2. Demand for services is difficult to predict 3. Capacity is also difficult to predict 4. Service capacity must be provided at the appropriate place

and time 5. Labor is usually the most constraining resource for services

Master Production Scheduling

Module 4

Why Master Production scheduling?

• To convert aggregate plan into detailed and short term plans

• To use resources optimally• To meet delivery terms• To effectively manage emergencies

ForecastingAggregate

Production Planning

MasterProductionScheduling

Materials PlanCapacity Plan

Actual Production

Market

Labour & Resources Vendors

Material Inflow

Order Inflow

Resource availability

Master Production Scheduling Linkages with APP & Forecasting

Master Scheduling guidelines

• Work from an aggregate production plan• Schedule common modules when possible• Load facilities realistically• Release orders on timely basis• Monitor inventory levels closely• Reschedule as required

Master Scheduling (Master Production Schedule-MPS)

• Functions:– Translate Aggregate Plan into specific end items– Evaluate alternative schedule– Generate Material Requirements– Generate Capacity Requirements– Facilitate information processing– Maintain valid priorities– Effectively utilize capacity

Master Scheduling• Problem: An appliance manufacturer produces a

motor assembly (X) that is used in several handheld appliances. They currently have 60 units in stock and will manufacture more in production runs (lots) of 90 units. Develop a tentative master schedule for the demand shown below

Inventory in hand = 60Production run = 90

Week

1 2 3 4 5 6 7 8 9 10

Customer forecast 5 30 40 50 40 50 50 50 50

Interplant forecast 5 5 5

Customer orders 40 40 30 10 10 5

Warehouse orders 15 10 5

Monks 346

Inventory in hand = 60Production run = 90

Week

1 2 3 4 5 6 7 8 9 10

Customer forecast 5 30 40 50 40 50 50 50 50

Interplant forecast 5 5 5

Customer orders 40 40 30 10 10 5

Warehouse orders 15 10 5

Total Requirements 55 55 65 55 60 50 50 50 55 50

Beginning Inventory 60 5 40 65 10 40 80 30 70 15

Production Required 90 90 90 90 90 90

Ending Inventory 5 40 65 10 40 80 30 70 15 55

Total Requirements = Sum of forecasts and ordersEnding Inventory = Beginning inventory + Production – Total requirements

• Problem: Take data from the previous example and maintain a safety stock of 20 unitsInventory in hand = 60Production run = 90Safety Stock = 20

Week

1 2 3 4 5 6 7 8 9 10

Customer forecast 5 30 40 50 40 50 50 50 50

Interplant forecast 5 5 5

Customer orders 40 40 30 10 10 5

Warehouse orders 15 10 5

Total Requirements 55 55 65 55 60 50 50 50 55 50

Beginning Inventory 60 95 40 65 100 40 80 30 80 25

Production Required 90 90 90 90 90 90

Ending Inventory 95 40 65 100 40 80 30 80 25 65

• Problem : Clear lake Foundry produces three types of casting (A, B,C) to customer order. The standard hours per unit and proposed delivery schedule over next five periods are shown below. Plant capacity is set at 620 standard hours per period, based on a single-shift operation.

• Arrange the data into tentative master schedule in a make-to-order format

• What changes would you recommend in order to better utilize the plant capacity

Monks 353

Product Standard hr/unit

Demand units /period

1 2 3 4 5

A 10 8 10 10 8 10B 60 4 8 2 2C 30 10 6 30 20

• Problem: Medical instrument Company markets two ultrasonic cardiograms to an international market ECHO 27 and VUE 5. The anticipated demand over the next six periods is as follows:

Monks 353

Expected Demand during period1 2 3 4 5 6

Domestic Orders ECHO 27 20 20 15 20 5 5VUE 5 35 30 20 20 10

International Orders ECHO 27 8 6 4 2

VUE 5 12 5 7 5Forecast ECHO 27 5 3 10 20 30 30

VUE 5 5 5 10 10 30

Additional Data: Beginning Inventory Lot Size Safety Stock

ECHO 27 64 40 10

VUE 5 50 60 20

Scheduling of OperationsA planning tool for the short term

• Provides an opportunity to make use of new information as we approach real time• A methodology to fine tune planning and decision making due to the occurrence of random events• Enables organizations to focus on micro-

resources, a single machine, a set of workers and so on. Such a focus is neither possible nor warranted at the medium or long term planning.

Planning Context in the short term

• How do we assign the jobs to various work centers? • Within each work center, how do we rank order the

jobs? • How do we assign other resources such as skilled

workers and material handling devices to the operating system?

• How do we react to a breakdown in the system? • How do we measure the performance of the

operating system?

SchedulingAlternative Terminologies

• Scheduling is defined as the process of rank ordering the jobs in front of each resource with a view to maximize some chosen performance measure

• Loading is defined as a planning methodology using which the resources in an operating system are assigned with adequate number of jobs during the planning horizon (of say a week)– Finite– Infinite

• Routing is defined as the order in which the resources available in a shop are used by the job for processing

• Sequencing is the ordering of operations of the jobs in the operating system

• Dispatching is defined as the administrative process of authorizing processing of jobs by resources in the operating system as identified by the scheduling system

Scheduling methods

• Forward• Backward

Intervals and Horizon of MPS

• Time Interval depends on – Type– Volume– Component lead time

Ex: Weekly, Monthly• Time Horizon

– Product Characteristics– Lead time

Issues

• Make to Stock• Make to Order

– Require more detailed scheduling, because• Quantities and items specified are unique• Employee work time must be carefully balanced

• Serve to Order

Scheduling Strategies

• Detailed scheduling of specific jobs– Change in orders, breakdowns, unexpected events ---

invalidate the plan• Airline services, doctors

• Cummulative Scheduling• Priority decision rules• Time frame ( weekly time buckets)• Direction of schedule (forward and Backward)

Finite and Infinite SchedulingThere are two main approaches to the allocation of tasks to work centers (i.e., groups of people and/or machines): finite and infinite loading. Finite loading allocates work to a work center up to a set limit, normally derived from an estimate of capacity. Work over and above this capacity is rejected. Such an approach is particularly relevant for operations where it is possible to limit the load (e.g., an appointment system can be created) or the cost of limiting capacity is not prohibitive Conversely, infinite loading allocates work to a work center that may exceed its theoretical capacity constraints. Such an approach is particularly relevant for operations where it is simply not possible to limit the load (e.g., an accident and emergency department in a busy city hospital). In complex planning and control activities where there are multiple stages, each with different capacities and with varying mix arriving at the facilities, such as a machine shop in an engineering company, the constraints imposed by finite loading may make loading calculations complex and not worth the considerable computational power that would be needed.

Scheduling and loading guidelines

• Provide a realistic schedule• Allow adequate time for operations• Allow adequate time before, between and after

operations• Don’t release all available jobs to shop• Don’t schedule all available capacity in the shop• Load only selected work centers• Allow for necessary changes• Gear shop responsibility to the schedule

Scheduling Methodology

• Gantt Charts• Schedule Boards• Computer Graphics

Gantt Chart

Scheduling Rules• Shortest processing time (SPT): Chooses the job with the least

processing time among the competing list and schedules it ahead of the others

• Longest processing time (LPT): The job with the longest processing time is scheduled ahead of other competing jobs

• Earliest Due Date (EDD): Establishes priorities on the basis of the due date for the jobs.

• Critical Ratio (CR): Critical ratio estimates the criticality of the job by computing a simple ratio using processing time information and due date. A smaller value of CR indicates that the job is more critical.

Timegocesmaining

DateCurrentDateDue

Workmaining

timemainingCRRatioCritical

sinPrRe

)(

Re

Re)(

• First Cum First Served (FCFS): Schedules jobs simply in their order of job arrival

• Random Order (RAN): Assign priorities to jobs on a random basis.

Scheduling RulesAn illustration of their application

Current time = 0

Job No.Processing

timeOrderarrival Due by CR

Random Number

1 12 1 23 1.92 0.233

2 9 2 24 2.67 0.857

3 22 3 30 1.36 0.518

4 11 4 20 1.82 0.951

Job No.

Rank ordering of jobs based on

LPT rule SPT Rule EDD CR FCFS RAN

1 3 2 4 3 1 1

2 1 4 1 4 2 3

3 4 1 2 1 3 2

4 2 3 3 2 4 4

Find the sequence of jobs using SPT, LPT, EDD, CR, FCFS, Random selection

LPT rule

SPT Rule

EDD

CR

FCFS

RAN

0 1 2 3 4 5 6 7 8 9 10

3

2

4

3

1

1

1

4

1

4

2

3

4

1

2

1

3

2

2

3

3

2

4

4

Job Sequence Processing timeTime to complete

Job Due time Lateness/Tardiness1 12 12 23 112 9 21 24 33 22 43 30 -134 11 54 20 -34

SPT 2 9 9 24 154 11 20 20 01 12 32 23 -93 22 54 30 -24

LPT 3 22 22 30 81 12 34 23 -114 11 45 20 -252 9 54 24 -30

EDD 4 11 11 20 91 12 23 23 02 9 32 24 -83 22 54 30 -24

Sequencing

• Johnson’s Rule– Number of Jobs and Machines

• 2 machines and “n” Jobs • 3 machines and “n” Jobs • m machines and “n” Jobs

• 2 jobs and “m” machines

Capacity Requirements Planning

Normal Capacity

Pull ahead Push back

1 2 3 4 5 60

10

20

30

40

50

60

70

80

90

30

60

80

70

30

10

Under loaded Capacity can be leveled by:

• Acquiring more work• Pulling work ahead that is scheduled for later

periods• Reduce normal Capacity

Overloads

• Eliminate unnecessary requirements• Rerouting jobs to alternative machines, workers, or work

centers• Splitting the jobs between two or more machines• Increasing normal capacity• Subcontracting• Increasing the efficiency of the operation• Pushing work back to later time periods• Revising the master schedule

Material Requirements Planning

• MRP• MRPII• ERP

Structure of MRP System

Material Requirements Planning

• MRP calculates and maintains an optimum manufacturing plan based on master production schedules, sales forecasts, inventory status, open orders and bills of material. If properly implemented, it will reduce cash flow and increase profitability. MRP will provide the ability to be pro-active rather than re-active in the management of inventory levels and material flow

http://www.inventorysolutions.org/def_mrp.htm

• MRP will plan production so that the right materials are at the right place at the right time. It is the single most powerful tool in guiding inventory planning, purchase management and production control. MRP is easy to operate and adds dramatically to profits.

Implementing or improving Material Requirements Planning can provide the following benefits for your

company• Reduced Inventory Levels • Reduced Component Shortages • Improved Customer Service • Improved Productivity • Simplified and Accurate

Scheduling • Reduced Purchasing Cost • Improve Production Schedules • Reduced Manufacturing Cost

• Reduced Lead Time • Less Scrap and Rework Higher

Production Quality • Improved Plant Efficiency • Inventory Reduced Overtime• Improved Supply Schedules • Improved Calculation of Material

Requirements • Improved Competitive Position

MRP uses the following elements to plan optimal inventory levels, purchases, production schedules and more:

• Master Production Schedule (MPS) • Bill of Materials (BOM) • Quantity on Hand (QOH) • Part Lead Times • Sales Order Quantities / Due Dates • Scrap Rate • Purchase Order Quantities / Due Dates • Safety Stock Requirements

Input to MRP

• Bill of materials• Master production schedule• Inventory status

Bill of Materials

• Roti• Shirt• Mechanical Watch• Car

Bill of Materials (BoM)Product Structure Diagram for a Single –Level bill of Materials

(W099)

Wheel barrow

Wheel Assembly (1)

Handle Assembly(1)Box (1) Paint(1)

1011

1020 1030 1042

BoM contd…

Part Number Description Quantity Units

1011 Box: deep size, aluminum

1 each

1020 Handle Assembly 1 each

1030 Wheel Assembly 1 each

1042 Paint: blue 1 pint

Part No. W099: Wheelbarrow

• Wheel

barrow• Whee

l Assembly (1)

• Handle

Assembly(

1)

• Box (1)

• Paint(1)

• 1011

• 1020 • 1030 • 1042

Bars(2) Grips(2)

Tire(1)

Bearings(2)Axle (1) Wheel(1)

2022 2025 2031 2032 2035

3026

Level 3

Level 0

Level 1

Level 2

Outputs from MRP System

MRP

To: MPS Planners•Simulation of proposed MPS•Rescheduling information for open orders ( due to cancellations, delays, shortages)

To: CRPOrder release information for load profiles

To: Purchase and In-house Production shops

•Changes to keep priorities valid•Order Releases•Planned order release

To: Management •Performance Measurement (of vendors, cost, quality, forecast accuracy etc) •Exception reports (on due dates, BoM files etc.)

MRP Logic

Net Requirements = Projected gross Requirements – Inv. on Hand + Scheduled Receipts

• Problem: a firm producing wheelbarrows is expected to deliver 40 wheelbarrows in week 1, 60 in week 4, 60 in week 6 and 50 in week 8. Among the requirements for each wheelbarrow are 2 handles bars, a wheel assembly, and one tire for the wheel assembly. The order quantities, lead times and inventories on hand at the beginning of the period 1 are shown below.90 wheel assemblies are also needed in period 5 for a garden tractor shipment. A shipment of 300 handlebars is already scheduled to be received at the beginning of the week 2. Complete the material requirements plan for handlebars , wheel assemblies and tires and show what quantities of orders must be released and when they must be released in order to satisfy the MPS.Part Order Quantity Lead Time (week) Inventory on hand

Handlebars 300 2 100

Wheel assembly 200 3 220

Tires 400 1 50

Master Production Schedule

Week No 1 2 3 4 5 6 7 8

Requirements 40 60 60 50

Order Quantity = 300Lead Time = 2 weeks

Week

Week No 1 2 3 4 5 6 7 8

Projected Requirements 80 120 120 100

Receipts 300 300

On hand Inventory (100) 20 320 320 200 200 80 80 280

Planned order release 300

End Item :Wheelbarrows

Component Material Plan: Handlebars

Order Quantity = 200Lead Time = 3weeks

Week

Week No 1 2 3 4 5 6 7 8Projected Requirements 40 60 90 60 50Receipts 200On hand Inventory (220) 180 180 180 120 30 170 170 120Planned order release 200

Component Material Plan : Wheel Assemblies

Order Quantity = 400Lead Time = 1 week

Week

Week No 1 2 3 4 5 6 7 8

Projected Requirements 40 60 60 50

Receipts 400

On hand Inventory (50) 10 10 10 350 350 290 290 240

Planned order release 400

Component Material Plan: Tire

Level Production Strategy Example 1

MonthDemand (in units)

Hrs. reqd. per unit of

productionDemand

(Hrs.)

No. of working

days

Working hours per

dayNo. of

workers

Capacity available

(Hrs.)

Supply - Demand

(Hrs.)April 250 100 25,000 23 8 125 23,000 (2,000) May 220 100 22,000 22 8 125 22,000 - June 300 100 30,000 21 8 125 21,000 (9,000) July 290 100 29,000 24 8 125 24,000 (5,000) August 260 100 26,000 22 8 125 22,000 (4,000) September 180 100 18,000 22 8 125 22,000 4,000 October 200 100 20,000 19 8 125 19,000 (1,000) November 220 100 22,000 23 8 125 23,000 1,000 December 250 100 25,000 21 8 125 21,000 (4,000) January 200 100 20,000 23 8 125 23,000 3,000 February 240 100 24,000 20 8 125 20,000 (4,000) March 270 100 27,000 24 8 125 24,000 (3,000)

Total 2880 100 288000 264 8 125 264000 (24,000) Average 240 100 24000 22 8 125 22000 (2,000)

Cost of level strategyExample 1.

Month

Supply - Demand

(Hrs.)

Supply - Demand (units)

Opening Inventory

Closing inventory

Average Inventory

Cost of Inventory

April (2,000) (20) 200 180 190 190,000 May - - 180 180 180 180,000 June (9,000) (90) 180 90 135 135,000 July (5,000) (50) 90 40 65 65,000 August (4,000) (40) 40 - 20 20,000 September 4,000 40 - 40 20 20,000 October (1,000) (10) 40 30 35 35,000 November 1,000 10 30 40 35 35,000 December (4,000) (40) 40 - 20 20,000 January 3,000 30 - 30 15 15,000 February (4,000) (40) 30 (10) 10 30,000 March (3,000) (30) (10) (40) (25) 80,000

825,000 Total cost of the plan

Chase strategy using OT/UT Example 2

Month

Supply - Demand

(Hrs.)Overtime

(Hrs)Undertime

(Hrs) OT/UT cost

April (2,000) 2,000 0 80,000 May - - 0 - June (9,000) 9,000 0 360,000 July (5,000) 5,000 0 200,000 August (4,000) 4,000 0 160,000 September 4,000 - 4000 80,000 October (1,000) 1,000 0 40,000 November 1,000 - 1000 20,000 December (4,000) 4,000 0 160,000 January 3,000 - 3000 60,000 February (4,000) 4,000 0 160,000 March (3,000) 3,000 0 120,000

1,440,000 Total cost of the plan

Chase strategy using Hire/LayoffExample 2

Month

Supply - Demand

(Hrs.)

No. of workers

hired

No. of workers laid off

Under time (Hrs)

Hiring/ Laying off & UT costs

April (2,000) 11 0 24 82,002 May - - 0 - - June (9,000) 54 0 72 403,226 July (5,000) 26 0 184 198,993 August (4,000) 23 0 48 171,415 September 4,000 - 22 128 112,560 October (1,000) 7 0 64 50,622 November 1,000 - 5 80 26,600 December (4,000) 24 0 32 179,211 January 3,000 - 16 56 81,120 February (4,000) 25 0 - 187,500 March (3,000) 16 0 72 118,628

1,611,876 Total cost of the plan

Evaluating alternative strategiesExample 4

Hours/unit 125 175 200 350

Type 1 Type 2 Type 3 Type 4 Type 1 Type 2 Type 3 Type 4 Total

April 100 40 60 10 12,500 7,000 12,000 3,500 35,000 May 90 30 30 5 11,250 5,250 6,000 1,750 24,250 June 80 50 50 10 10,000 8,750 10,000 3,500 32,250 July 130 40 70 20 16,250 7,000 14,000 7,000 44,250 August 70 30 30 15 8,750 5,250 6,000 5,250 25,250 September 90 50 50 5 11,250 8,750 10,000 1,750 31,750 October 100 40 50 10 12,500 7,000 10,000 3,500 33,000 November 110 30 40 15 13,750 5,250 8,000 5,250 32,250 December 60 60 80 5 7,500 10,500 16,000 1,750 35,750 January 110 20 30 10 13,750 3,500 6,000 3,500 26,750 February 120 40 40 5 15,000 7,000 8,000 1,750 31,750 March 140 50 70 10 17,500 8,750 14,000 3,500 43,750

Total 1200 480 600 120 150,000 84,000 120,000 42,000 396,000 Average 100 40 50 10 12,500 7,000 10,000 3,500 33,000

Forecast of motor demand (units)Month

Forecast of motor demand (hours)

Plan (a): Level Strategy Example 4

Plan 1

Month Demand (Hrs)

Production rate (Hrs)

Opening Inventory

(Hrs)

Production - Demand

(Hrs)

Closing Inventory

(Hrs)

Cost of inventory/backorder

April 35000 33000 0 (2000) (2000) 60,000 May 24250 33000 (2000) 8750 6750 50,625 June 32250 33000 6750 750 7500 106,875 July 44250 33000 7500 (11250) (3750) 168,750 August 25250 33000 (3750) 7750 4000 30,000 September 31750 33000 4000 1250 5250 69,375 October 33000 33000 5250 0 5250 78,750 November 32250 33000 5250 750 6000 84,375 December 35750 33000 6000 (2750) 3250 69,375 January 26750 33000 3250 6250 9500 95,625 February 31750 33000 9500 1250 10750 151,875 March 43750 33000 10750 (10750) 0 80,625

Avg. (12 months) 33000 1,046,250 Total cost of the plan

Plan (b): Half-yearly production ratesExample 4

Plan 2

Month Demand (Hrs)

Production rate (Hrs)

Opening Inventory

(Hrs)

Production - Demand

(Hrs)

Closing Inventory

(Hrs)

Cost of inventory/backorder

April 35000 32125 0 (2875) (2875) 86,250 May 24250 32125 (2875) 7875 5000 37,500 June 32250 32125 5000 (125) 4875 74,063 July 44250 32125 4875 (12125) (7250) 254,063 August 25250 32125 (7250) 6875 (375) 11,250 September 31750 32125 (375) 375 0 - October 33000 33875 0 875 875 6,563 November 32250 33875 875 1625 2500 25,313 December 35750 33875 2500 (1875) 625 23,438 January 26750 33875 625 7125 7750 62,813 February 31750 33875 7750 2125 9875 132,188 March 43750 33875 9875 (9875) 0 74,063

Avg. (first 6 months) 32125 787,500 Avg. (next 6 months) 33875

Total cost of the plan

Comparison of Plan (a) & (b)

0

50000

100000

150000

200000

250000

300000

350000

400000

Month

Cu

mu

lati

ve n

um

ber

of

ho

urs

Cumulative Demand Cumulative Production (Plan 1) Cumulative Production (Plan2)

Jan Feb MarApr May

Jun Jul Aug Sep Oct Nov Dec

Inventory

Back-orders

Plan (c): Chase Strategy with UT/OTExample 4

Plan 3

Month Demand (Hrs)

Production rate (Hrs)

Opening Inventory

(Hrs)

Production - Demand

(Hrs)

Closing Inventory

(Hrs)Cost of OT/UT

April 35000 31000 0 (4000) 0 80,000 May 24250 31000 0 6750 0 67,500 June 32250 31000 0 (1250) 0 25,000 July 44250 31000 0 (13250) 0 265,000 August 25250 31000 0 5750 0 57,500 September 31750 31000 0 (750) 0 15,000 October 33000 31000 0 (2000) 0 40,000 November 32250 31000 0 (1250) 0 25,000 December 35750 31000 0 (4750) 0 95,000 January 26750 31000 0 4250 0 42,500 February 31750 31000 0 (750) 0 15,000 March 43750 31000 0 (12750) 0 255,000

982,500 Total cost of the plan

Plan (d): Mixed StrategyExample 4

Plan 4

Month Demand (Hrs)

Production rate (Hrs)

Opening Inventory

(Hrs)

Production - Demand

(Hrs)

Closing Inventory

(Hrs)Cost of OT/UT

April 35000 31000 0 (4000) 0 100,000 May 24250 31000 0 6750 6750 33,750 June 32250 31000 6750 5500 5500 61,250 July 44250 31000 5500 (7750) 0 221,250 August 25250 31000 0 5750 5750 28,750 September 31750 31000 5750 5000 5000 53,750 October 33000 31000 5000 3000 3000 40,000 November 32250 31000 3000 1750 1750 23,750 December 35750 31000 1750 (3000) 0 83,750 January 26750 31000 0 4250 4250 21,250 February 31750 31000 4250 3500 3500 38,750 March 43750 31000 3500 (9250) 0 248,750

955,000 Total cost of the plan

Aggregate Production PlanningAlternative methods

• Optimal Methods– Linear Programming (LP)– Transportation– Dynamic Programming (DP)

• Heuristics– Trial & Error Methods (Examples 11.1. to 11.4.)– Generalised search methods– Linear Decision Rule (LDR)

• Simulation

StartIdentify parametersSetup the stopping

criterion

Generate one candidate solution.Evaluate the cost

Current solutionthe best?

Have we metthe stopping

criterion?

No

Yes Yes

End

No

Replace the best solution with the current solution

Search Procedure

0 2 4 6

80 82 84 86

120 122 124 126

105 107 109 111

80 82 84

120 122 124

105 107 109

Cb3 Cb4

Cc3 Cc4

Cb3 Cb4

80

120

105

Demand Requirements

Period 2 OP

Period 1 Period 2 Period 3 Period 4Supply

Constraints

25,000

Period 2 RP

Initial Inventory

Period 1 SC

Period 1 RP

Period 1 OP

80,000

16,000

13,000

100,000

Period 2 SC

Period 3 RP 65,000

Period 3 OP

Period 4 OP

Period 4 SC

Period 3 SC

Period 4 RP

100,000

80,000

16,000

100,000

80,000

16,000

100,000

105,000 57,000 76,000 110,000

Demand

Supply

A Transportation Problem

formulation for Aggregate Production

Planning (Example 11.5)

 Indicates no feasible

APP alternative available

Linear Programming Method for APP: An illustration

Cost parametersCr Per unit cost of regular productionCo Per unit cost of overtime productionCs Per unit cost of sub-contracted unitsCh Per unit cost related to hiring of workersCl Per unit cost related to laying off workersCi Per unit costs related to inventory

Decision variables for the time period “t”Rt Number of units produced in regular timeOt Number of units produced using over timeSt Number of units obtained through sub-contractingHt Number of additional units obtained though hiring of workersLt Number of units reduced through laying off workersIt Inventory during the period

Other parametersDt Projected Demand during the periodK Minimum amount to be sub-contracted

Maximum allowable OT as a proportion of regular production ( ) 10

Linear Programming Method for APP: An illustration…

NtLHRR tttt ,...,3,2,11

NtDSORII tttttt ,...,3,2,11

NtRO tt ,...,3,2,1

NtKSt ,...,3,2,1

NtISLHOR tttttt ,...,3,2,10,,,,,

N

ttitlthtstotrAPP ICLCHCSCOCRCTCMin

1

Objective function

Subject to the constraints

Over time constraint:

Sub-contracting constraint:

Amount Produced in regular time :

Inventory Balance Equation:

Non-negativity constraint:

Aggregate Production PlanningChapter Highlights

• Aggregate Production Planning (APP) serves to translate the business plans into operational decisions

• The decisions include – amount of resources (productive capacity and labour hours) to commit, – rate at which to produce – inventory to be carried forward from one period to the next

• APP is done to match the demand and the available capacity on a period-by-period using a set of alternatives available to modify demand and/or the supply

• Alternatives for modifying demand include reservation of capacity and methods of influencing (changing) the demand during a period

• Alternatives for modifying the supply include inventory variations, capacity adjustment and capacity augmentation

Aggregate Production PlanningChapter Highlights…

• APP exercise employs the two generic strategies; chase and level production. A chase strategy is often found to be expensive and hard to implement in organisations

• In reality a mixed strategy using a combination of alternatives is employed in an APP exercise. It uses a variety of alternatives for modifying supply.

• The structure of a transportation model lends itself to studying the APP problem

• Linear programming can also be used to model the APP problem• MPS involves dis-aggregation of product information and ensuring the

required capacity and material are available as per the plan