© 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Chapter 11 Capacity Planning And Aggregate Production Planning

2000 by Prentice-Hall, Inc2 Demand versus Capacity  Demand  desired level of products of services  Capacity  necessary level of productive resources for a firm

2000 by Prentice-Hall, Inc3 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Capacity Planning  Establishes overall level of productive resources  Affects lead-time responsiveness, cost & competitiveness  Determines when and how much to increase capacity How do you alter demand or capacity?

2000 by Prentice-Hall, Inc4 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Capacity Expansion Issues  Volume & certainty of anticipated demand  Strategic objectives for growth  Costs of expansion & operation  Incremental or one-step expansion

2000 by Prentice-Hall, Inc5 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Capacity Expansion Strategies Units Capacity Time Demand Units Capacity Time Demand Units Capacity Time Demand Units Incremental expansion Time Demand Capacity lead strategy Capacity lag strategy Average capacity strategyIncremental vs. one-step expansion One-step expansion

2000 by Prentice-Hall, Inc6 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Economies & Diseconomies Of Scale 250 room hotel Average cost per unit Best operating level 500 room hotel 1000 room hotel Best operating level Best operating level Economies of scale Diseconomies of scale

2000 by Prentice-Hall, Inc7 Aggregate Planning  Long-term perspective  Number of facilities  Facility size  Intermediate perspective  Inventory policies  Production rates  Staffing levels

2000 by Prentice-Hall, Inc8 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Aggregate Production Planning (APP)  Matches market demand to company resources  Plans production 6 months to 12 months in advance  Expresses demand, resources, and capacity in general terms  Develops a strategy for economically meeting demand  Establishes a companywide game plan for allocating resources

2000 by Prentice-Hall, Inc9 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Inputs and Outputs to Aggregate Production Planning Aggregate Production Planning Company Policies Financial Constraints Strategic Objectives Units or dollars subcontracted, backordered, or lost Capacity Constraints Size of Workforce Production per month (in units or $) Inventory Levels Demand Forecasts

2000 by Prentice-Hall, Inc10 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Aggregate Planning for Services 1. Most services can’t 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

2000 by Prentice-Hall, Inc11 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Strategies for Meeting Demand 1. Use inventory to absorb fluctuations in demand (level production) 2. Hire and fire workers to match demand (chase demand) 3. Maintain resources for high demand levels 4. Increase or decrease working hours (over & undertime) 5. Subcontract work to other firms 6. Use part-time workers 7. Provide the service or product at a later time period (backordering)

2000 by Prentice-Hall, Inc12 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Demand Distortion along the Supply Chain

2000 by Prentice-Hall, Inc13 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Planning Strategy Details  Level production - produce at constant rate & use inventory as needed to meet demand  Chase demand - change workforce levels so that production matches demand  Maintaining resources for high demand levels - ensures high levels of customer service  Overtime & under-time - common when demand fluctuations are not extreme

2000 by Prentice-Hall, Inc14 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Strategy Details - continued  Subcontracting - useful if supplier meets quality & time requirements  Part-time workers - feasible for unskilled jobs or if labor pool exists  Backordering - only works if customer is willing to wait for product/services

2000 by Prentice-Hall, Inc15 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e APP Using Pure Strategies Hiring cost = $100 per worker Firing cost = $500 per worker Inventory carrying cost = $0.50 pound per quarter Production per employee = 1,000 pounds per quarter Beginning work force = 100 workers QuarterSales Forecast (lb) Spring80,000 Summer50,000 Fall120,000 Winter150,000

2000 by Prentice-Hall, Inc16 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Level Production Time Production Demand Units

2000 by Prentice-Hall, Inc17 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Level Production Strategy SalesProduction QuarterForecastPlanInventory Spring80,000100,00020,000 Summer50,000100,00070,000 Fall120, ,000 50,000 Winter150,000100, ,000140,000 Cost = 140,000 pounds x 0.50 per pound = $70,000

2000 by Prentice-Hall, Inc18 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Chase Demand Time Units Production Demand

2000 by Prentice-Hall, Inc19 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Chase Demand Strategy SalesProductionWorkersWorkersWorkers QuarterForecastPlanNeededHiredFired Spring80,00080, Summer50,00050, Fall120,000120, Winter150,000150, Cost = (100 workers hired x $100) + (50 workers fired x $500) = $10, ,000 = $35,000

2000 by Prentice-Hall, Inc20 Ch © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Strategies for Managing Demand  Shift demand into other periods  incentives, sales promotions, advertising campaigns  Offer product or services with countercyclical demand patterns  create demand for idle resources

© 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Chapter 11 Supplement Operational Decision Making Tools: Linear Programming

2000 by Prentice-Hall, Inc22  Limited resources versus unlimited (or much greater) demand Why would that create difficulties for an operations manager?

2000 by Prentice-Hall, Inc23 Linear Programming (LP)  Developed by G.B. Dantzig in 1947  “linear” means that all the mathematical functions must be linear  “programming” is a synonym for planning

2000 by Prentice-Hall, Inc24 Ch 11 Supp - 2 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Linear Programming  Model consisting of linear relationships representing a firm’s objectives & resource constraints  Decision variables are mathematical symbols representing levels of activity of an operation  Objective function is a linear relationship reflecting objective of an operation  Constraint is a linear relationship representing a restriction on decision making

2000 by Prentice-Hall, Inc25 Typical areas of application:  Allocation of scarce resources – capacity planning  Production scheduling: assignments  Shipping patterns: transportation problems  Blending problems

2000 by Prentice-Hall, Inc26 Seven Conditions in problem situations for LP to pertain 1. Limited resources 2. An explicit objective 3. Linearity 4. Homogeneity 5. Divisibility 6. Non-negativity 7. Certainty

2000 by Prentice-Hall, Inc27 Procedure:  Develop a mathematical model to describe the word problem and then follow a sequence of steps that will lead to the best solution (if one exists) given the constraints

2000 by Prentice-Hall, Inc28 Ch 11 Supp - 3 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e General Structure Of Linear Programming (LP) Model Max/min z = c 1 x 1 + c 2 x c n x n subject to:a 11 x 1 + a 12 x a 1n x n  b 1 (or , =) a 21 x 1 + a 22 x a 2n x n  b 2 : a m1 x 1 + a m2 x a mn x n  b m x j = decision variables b i = constraint levels c j = objective function coefficients a ij = constraint coefficients

2000 by Prentice-Hall, Inc29 Components of the LP model: 1. Objective (or goal): 2. Objective function: 3. Decision variables: 4.Constraints Less than or equal to Greater than or equal to Equal to 5. Feasible region 6. Optimal solution 7. Parameter

2000 by Prentice-Hall, Inc30 Example of Lego Problem formulation : MAX 16T + 10C Subject to 2T + 1C <= 6 Large Legos 2T + 2C <= 8 Small Legos T >= 0, C >= 0

2000 by Prentice-Hall, Inc31 Ch 11 Supp - 4 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Linear Programming Model Formulation Resource requirements Labor ClayRevenue Product(hr/unit)(lb/unit)($/unit) Bowl1440 Mug2350 There are 40 hours of labor and 120 pounds of clay available each day Decision variables x 1 = number of bowls to produce x 2 = number of mugs to produce

2000 by Prentice-Hall, Inc32 Model Formulation: Step 1: Define the decision variables Step 2: Write out the objective function Step 3: Write out the constraints

2000 by Prentice-Hall, Inc33 Ch 11 Supp - 5 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Objective Function & Constraints Maximize Z = $40 x x 2 Subject to x x 2  40 hr (labor constraint) 4 x x 2  120 lb (clay constraint) x 1, x 2  0 Solution is x 1 = 24 bowls x 2 = 8 mugs Revenue = $1,360

2000 by Prentice-Hall, Inc34 Once the model has been formulated:  There are two alternative solution methods:  1. graphical solution  only useful if there are at most two decision variables  2. computer-generated solutions using the simplex method  two or more variables

2000 by Prentice-Hall, Inc35 Ch 11 Supp - 6 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Graphical Solution Method  1. Plot model constraint on a set of coordinates in a plane  2. Identify the feasible solution space on the graph where all constraints are satisfied simultaneously  3. Plot objective function to find the point on boundary of this space that maximizes (or minimizes) value of objective function

2000 by Prentice-Hall, Inc36 Ch 11 Supp - 7 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Graph Of Pottery Problem x1x1 x2x2 4 x x 2  120 lb x x 2  40 hr Area common to both constraints

2000 by Prentice-Hall, Inc37 Ch 11 Supp - 8 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Plot Objective Function $800 = 40x x 2 Optimal point x1x x2x2 B.

2000 by Prentice-Hall, Inc38 Ch 11 Supp - 9 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Computing Optimal Values A. x x 2 =  40 4 x x 2 =  x x 2 =  x x 2 =  x 2 = 40 x 2 = 8 x (8) =  40 x 1 =  24 Z = $50(24) + $50(8) Z = $1,360 8 B C x x 2 =  40 4 x x 2 =  x1x x2x2

2000 by Prentice-Hall, Inc39 Ch 11 Supp - 10 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Extreme Corner Points A. B C x 1 = 0 bowls x 2 =  20 mugs Z = $1,000 x 1 = 224 bowls x 2 =  8 mugs Z = $1,360 x 1 = 30 bowls x 2 =  0 mugs Z = $1, x1x x2x2

2000 by Prentice-Hall, Inc40 Ch 11 Supp - 11 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Objective Function Determines Optimal Solution A B C Optimal point: x 1 = 30 bowls x 2 =  0 mugs Z = $2, x1x x2x2 4 x x 2  120 lb x x 2  40 hr Z = 70 x x 2

2000 by Prentice-Hall, Inc41 Ch 11 Supp - 12 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e The Simplex Method  A mathematical procedure for solving linear programming problems according to a set of steps  Based on solving simultaneous equations & matrix algebra  Computers use the simplex method to solve linear programming problems

2000 by Prentice-Hall, Inc42 Ch 11 Supp - 19 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Minimization Linear Program Chemical contribution Nitrogen PhosphatePriceDecision Brand(lb/bag)(lb/bag)($/bag)variable Super-Gro246x 1 Crop-Quik433x 2 The farmer needs at least 16 pounds of nitrogen and 24 pounds of phosphate. Determine how many bags to buy to meet these requirements at minimum cost

2000 by Prentice-Hall, Inc43 Ch 11 Supp - 20 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Problem Formulation Minimize Z = $6 x x 2 Subject to 2 x x 2  16 lb of nitrogen 4 x x 2  24 lb of phosphate x 1, x 2  0 In converted form: Minimize Z = $6 x x S S 2 + M A 1 + M A 2 Subject to 2 x x 2 - S 1 + A 1  =  16 lb of nitrogen 4 x x 2 - S 2 + A 2  =  24 lb of phosphate x 1, x 2, S 1, S 2, A 1, A 2  0

2000 by Prentice-Hall, Inc44 Ch 11 Supp - 21 © 2000 by Prentice-Hall Inc Russell/Taylor Oper Mgt 3/e Graphical Solution x2x2 x1x1 x 1 = 0 bags of Super-Gro x 2 =  8 bags of Crop-Quik Z = $24 A B C Z = $6 x x 2