Strategic Production Planning

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Production planning is the activity of establishing production goals over a future time period calledthe planning horizon. The objective is to plan theoptimal use of resources to meet stated productionrequirements.

A Framework

• Strategic– which products?

– How many of each?

– what factories?

– where located?

– what capacities?

– which technologies?

– time period in years

– focus on profit

– static or dynamic

• Tactical– how many workers?

– what inventory levels?

– what production rates?

– number of shifts/overtime?

– contracting out?

– time period in months

– focus on costs

– dynamic

A Hierarchy of Production PlanningForecast product demand for t periods in the planning horizon

Determine product mix,plant utilization & capacity

Determine work force levelsand production rates

Establish schedule and job sequencingby item by time period

Production tracking and controlMaterial Requirements Planning

Two workers discussingthe company’s productionplanning system.

Years

Months

Weeks/days

Three Levels of Planning

• Strategic– Everything subject to change

• Tactical– Infrastructure (e.g. factories, warehouses, products)

remains fixed– Resources (e.g. machinery, raw material, labor) may

change

• Operational– Infrastructure and resources are fixed– Basic question is how best to utilize them

Aggregate Planning

• Macro production planning• Products lumped together to form an aggregate

product• Aggregated products and capacity expressed in

terms of an average item if similar• If items are different, then money, production

hours, or weight (e.g. tons of steel) may be used• Translate demand forecasts into a blueprint for

planning staff and production levels• Can be applied to strategic or tactical planning

Spreadsheet Methods

• Zero inventory strategy– produce to meet monthly demand– no inventories– work force fluctuates

• Level production strategy– maintain constant production rate– inventory fluctuates– constant work force

Production Strategies

time

cumulativenumberof units constant production rate

demand curve

variable production rate

Production Strategy - Example

Constant labor force = 28Labor hrs per unit = 9Fraction direct labor = 0.75

Aval hrs per month per person = 144Cost of inventory per mo = $5Cost of stockouts per month = $30Hiring cost Firing cost$100 $500

Labor rate per month$1,500

Monthly

MonthSales forecast

1 2402 3563 4154 2895 3216 4007 3218 2689 543

10 45211 38712 34513 28614 43415 53216 23817 43118 54319 30520 36521 34222 40223 41224 398 Excel

Optimal Strategy

• Use Solver to minimize total cost (target cell)

• Change labor force each month (changing cells)

Strategy Total CostConstant Production $1,273,905Variable Production $1,202,000Optimal Production $1,007,684

Excel

A Static Strategic Planning ModelAssumptions

• deterministic– all input parameters are known

• selling price is fixed

• unit cost does not vary with production levels (no learning curve effect)

• demand is over a fixed planning horizon (static)

A Static Strategic Planning Model

Let xijk = the number of units of product i manufactured in factory j using technology (process) k

Ri = selling price of product i cijk = cost of producing one unit of product i in factory

j using technology k Di = forecasted demand for product i over planning horizon aiL = number of units or resource L required to produce

one unit of product i FjL = capacity of resource L at factory j

Static - demand rate of each product is constant over time.

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tjm = unit transportation cost from factory j to customer m Dim = demand for product i by customer m

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How can we work theSupply chain problem intothis plan?

This model is becomingquite interesting. How can I throw a fixed startupcost into this?

Let zij = 1 if product i is to be produced at factory j; 0 otherwise

fij = fixed cost of producing product i at factory j

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The Makit CompanyOur very first example…

The Makit Company makes a variety of products. They currently have excess capacity within two of their factories and are interested in introducing three new products: a gas trimmer, a gas driven edger, and a gas driven snow blower. Selling prices are estimated to be $200, $180, and $298 respectively. Determine the annual production levels that will maximize profit.

I think we need more information

to solve this problem?

Makit CompanyProduct Prod

1Prod 1 Prod

2Prod 2 Prod 3 Prod 3 Prod 3

Factory location

Dayton Tijuana Dayton Tijuana Dayton Dayton Tijuana

Per unit data         Process A

Process B

 

Production cost

$25 20 18 12 36 30 32

Material cost $40 30 24 24 18 18 16

Labor hr 12 12 23 23 18 6 18

Machine hr 2 2 6 6 5 11 5

Fixed setup cost

10000 15000 5000 6000 1000 120000 8000

PlantCapacities

Labor hours per year

Machine hrs per year

Dayton 82000 55000

Tijuana 60000 15000

Product Eastern region

Central region

Western region

Trimmer 100 145 234

Edger 200 120 285

Snowblower 125 280 362

MoreData

Annual Demand

Plant Eastern region

Central region

Western region

Dayton 5 8 10

Tijuana, Mexico

12 7 6

Distribution Costs$ per unit

Xijk = number of units of product i produced at plant j using process k

Yijl = number of units of product i produced at plant j and sent to region l

Zij = fixed cost of producing product i at plant j

 MAX Profit:

z = - 10000 Z11 - 15000 Z12 - 5000 Z21 - 6000 Z22 - 1000 Z311 - 12000 Z312 - 8000 Z32 + 135 X11 + 150 X12 + 138 X21 + 144 X22 + 244 X311 + 250 X312 + 250 X32 -5 Y111 - 8 Y112 - 10 Y113 - 12 Y121 - 7 Y122 - 6 Y123 -5 Y211 - 8 Y212 - 10 Y213 - 12 Y221 - 7 Y222-6 Y223 - 5 Y311 - 8 Y312 - 10 Y313 - 12 Y321 - 7 Y322 - 6 Y323

The Formulation

SUBJECT TORegional demands: 2) Y111 + Y121 = 100 3) Y211 + Y221 = 200 4) Y311 + Y321 = 125 5) Y112 + Y122 = 145 6) Y212 + Y222 = 120 7) Y312 + Y322 = 280 8) Y113 + Y123 = 234 9) Y213 + Y223 = 285 10) Y313 + Y323 = 362Plant capacities: 11) 12 X11 + 23 X21 + 18 X311 + 6 X312 <= 82000 12) 12 X12 + 23 X22 + 18 X32 <= 60000 13) 2 X11 + 6 X21 + 5 X311 + 11 X312 <= 55000 14) 2 X12 + 6 X22 + 5 X32 <= 15000

Eastern

Central

Western

Fixed costs: 15) - 10000 Z11 + X11 <= 0 16) - 10000 Z21 + X21 <= 0 17) - 10000 Z311 + X311 <= 0 18) - 10000 Z312 + X312 <= 0 19) - 10000 Z12 + X12 <= 0 20) - 10000 Z22 + X22 <= 0 21) - 10000 Z32 + X32 <= 0

Production – Distribution dependency: 22) - X11 + Y111 + Y112 + Y113 = 0 23) - X21 + Y211 + Y212 + Y213 = 0 24) - X311 - X312 + Y311 + Y312 + Y313 = 0 25) - X12 + Y121 + Y122 + Y123 = 0 26) - X22 + Y221 + Y222 + Y223 = 0 27) - X32 + Y321 + Y322 + Y323 = 0 ENDINT Z11 Z12 Z21 Z22 Z311 Z312 Z32

Product Prod 1

Prod 1

Prod 2

Prod 2

Prod 3 Prod 3 Prod 3

Factory location

Dayton

Tijuana

Dayton

Tijuana

Dayton Dayton Tijuana

          Process A

Process B

 

Units produced

  479   605 767    

               

Distribution              

Eastern region

  100   200 125    

Central region

  145   120 280    

Western region

  234   285 362    

The Solution – Max Profit = $309,064

A “Solver” Solution

Let me show you what solver can do with this problem.

Another Example?

Could you share with us another

example?

Production Planning – Strategic

 A manufacturer produces four household products fabricated from sheet metal. The production system consists of five production centers at two plants: stamping, drilling, assembly, finishing (painting and printing), and packaging. For a given month, the manufacturer must decide how much of each product to manufacture, and to aid in this decision, he has assembled the data shown in the following Tables. Furthermore, he knows that only 1000 square feet of the type of sheet metal used for products 2 and 4 will be available at each plant during the month. Product 2 requires 2.0 square feet per unit and product 4 uses 1.2 square feet per unit.

TABLE 1 Production Data

 PRODUCTION RATES IN HOURS PER UNIT

production

Department prod 1 prod 2 prod 3 prod 4 hours available Plant 1 Plant 2

 

Stamping 0.03 0.15 0.05 0.10 150 250Drilling 0.06 0.12 - 0.10 200 200Assembly 0.05 0.10 0.05 0.12 300 200Finishing 0.04 0.20 0.03 0.12 175 275Packaging 0.02 0.06 0.02 0.05 300 100

TABLE 2 Product Data

NET SELLING VARIABLE SALES POTENTIALProduct PRICE/UNIT COST/UNIT MINIMUM MAXIMUM

Plant 1 Plant 2

1 10 $6 5 1000 60002 25 $15 13 - 5003 16 $11 10 500 30004 20 $14 12 100 1000

TABLE 3 distribution costs

Plant /warehouse Warehouse 1 Warehouse 2Plant 1 $2 1Plant 2 3 4

Demands – as a percent of 40 % 60 %above sales potential

FormulationVariable definitions:

Xij = number of units of product i produced at plant jYijk = number of units of product i shipped from

plant j to warehouse k Profit = selling price

– variable cost – distribution costs MAX 4 X11 + 5 X12 + 10 X21 + 12 X22 + 5 X31 + 6 X32 + 6 X41 + 8 X42 - 2 Y111 - 2 Y211 - 2 Y311 - 2 Y411 - Y112 - Y212 - Y312 - Y412 - 3 Y121 - 3 Y221 - 3 Y321 - 3 Y421 - 4 Y122 - 4 Y222 - 4 Y322 - 4 Y422

Constraints

Department processing constraints

2) 0.03 X11 + 0.15 X21 + 0.05 X31 + 0.1 X41 <= 1503) 0.06 X11 + 0.12 X21 + 0.1 X41 <= 2004) 0.05 X11 + 0.1 X21 + 0.05 X31 + 0.12 X41 <= 3005) 0.04 X11 + 0.2 X21 + 0.03 X31 + 0.12 X41 <= 1756) 0.02 X11 + 0.06 X21 + 0.02 X31 + 0.05 X41 <= 300

7) 0.03 X12 + 0.15 X22 + 0.05 X32 + 0.1 X42 <= 2508) 0.06 X12 + 0.12 X22 + 0.1 X42 <= 2009) 0.05 X12 + 0.1 X22 + 0.05 X32 + 0.12 X42 <= 20010) 0.04 X12 + 0.2 X22 + 0.03 X32 + 0.12 X42 <= 27511) 0.02 X12 + 0.06 X22 + 0.02 X32 + 0.05 X42 <= 100

Plant 1

Plant 2

warehouse upper/lower bounds

12) Y111 + Y121 >= 40013) Y111 + Y121 <= 240014) Y211 + Y221 <= 20015) Y311 + Y321 >= 20016) Y311 + Y321 <= 120017) Y411 + Y421 >= 4018) Y411 + Y421 <= 40019) Y112 + Y122 >= 60020) Y112 + Y122 <= 360021) Y212 + Y222 <= 30022) Y312 + Y322 >= 30023) Y312 + Y322 <= 180024) Y412 + Y422 >= 6025) Y412 + Y422 <= 600

Warehouse 1

Warehouse 2

produce only what is to be shipped26) - X11 + Y111 + Y112 = 027) - X21 + Y211 + Y212 = 028) - X31 + Y311 + Y312 = 029) - X41 + Y411 + Y412 = 0 30) - X12 + Y121 + Y122 = 031) - X22 + Y221 + Y222 = 032) - X32 + Y321 + Y322 = 033) - X42 + Y421 + Y422 = 0

sheet metal constraint• 2 X21 + 1.2 X41 <= 1000 • 2 X22 + 1.2 X42 <= 1000

SolutionProd 1 Prod 2 Prod 3 Prod 4

Plant 1 2 1 2 1 2 1 2

3333.3 1680 440 1000 1200 100

Warehouse1 1680 200 1200 40

2 3333.3 240 1000 60

max profit = $25,120

Alternate Solution

Prod 1 Prod 2 Prod 3 Prod 4Plant 1 2 1 2 1 2 1 2

3333.3 880 440 1000 2000 100

Warehouse1 880 200 1200 40

2 3333.3 240 1000 800 60

max profit = $25,120

Production Planning

The Dynamic Case

Look, we must consider the fact that demands are

going to fluctuate significantly over the

next several years

Let xijt = number of units or product i produced by process j in period t

sit = number of units of product i sold in period t

Iit = number of units of product i in inventory at the end of period t

Decision Variables

Model Parameters

rit = revenue from selling one unit of product i in period tcijt = variable production cost of one unit of product i by process j in period tFit = maximum sales forecasted for product i in period taijk = units of resource k required for each unit of product i

produced by process j.bkt = number of units of resource k available in time

period tdit = inventory carrying cost for product i during period thijt = cost of changing production levels for product i

using process j in period t

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Turn-in Problem #3

This is a great exercisefor the student!

Due Monday September 28Web Submission