Dr' Cholette DS855 Fall 2006

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Dr. CholetteDS855 Fall 2006
Aggregate Planning in the Supply Chain
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Outline

• Role of aggregate planning in a supply chain
• The aggregate planning problem
• Aggregate planning strategies
• Implementing aggregate planning in practice

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Role of Aggregate Planning in a Supply Chain

• Given
• Capacity is limited and has cost
• Lead times are greater than zero
• Aggregate planning is
• The process by which a company determines levels
  of capacity, production, subcontracting,
  inventory, stock-outs, and pricing over a
  specified time horizon
• Where the goal is to.
• maximize profit

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Aggregate Planning Scope

• Decisions are usually made at a product family
  (not SKU) level
• SKUS within product families tend to use same
  capacities, have similar costs
• Avoids too much detail- there might be 10 product
  families for 1500 SKUs
• The time frame is generally 3 to 18 months
• Too early to schedule by SKU
• Too late to make strategic, long term plans
  (build another plant)
• Answers question of How can a firm best use the
  facilities it has? with possibly Do we need to
  outsource or subcontract?

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Aggregate Planning Scope

• All supply chain stages should be included in an
  aggregate plan to optimize supply chain
  performance
• For now we will ignore transportation issues and
  costs and focus on a single manufacturing
  facility
• Avoid sub-optimization by silo. May need to
  incur more costs (outsourcing production) to
  maximize overall corporate profits
• Supply chains usually involve multiple firms. If
  these firms have close ties, it may be possible
  to optimize the efficiency of the entire supply
  chain (and share the efficiency gains)

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The Aggregate Planning Problem

• Given the demand forecast for each period in the
  planning horizon, determine the production level,
  inventory level, and the capacity level for each
  period that maximizes the firms profit over the
  planning horizon
• Specify the planning horizon
• Specify the duration of each period (time
  bucket)
• typically 1 month
• Specify key information required to develop an
  aggregate plan

or entire supply chains, if multi-firm, but we
will focus on a single firm
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Information Needed for an Aggregate Plan

• Demand forecast in each period
• Production costs
• Machine costs
• labor costs, regular time (/hr) and overtime
  (/hr)
• subcontracting costs (/hr or /unit)
• cost of changing capacity hiring or layoff
  (/worker) and cost of adding or reducing machine
  capacity (/machine)
• Labor/machine hours required per unit
• Material requirements per unit, material cost and
  availability
• Inventory holding cost (/unit/period)
• Stock-out or backlog cost (/unit/period)
• Yield rates, if applicable ( loss in production
  or inventory)
• Constraints physical or policy limits on
  overtime, layoffs, capital available,
  warehousing, stock-outs and backlogs

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Aggregate Plan Outputs

• Production quantity from regular time, overtime,
  and subcontracted time used to determine number
  of workers and supplier purchase levels
• Inventory held used to determine how much
  warehouse space and working capital is needed
• Backlog/stock-out quantity used to determine
  what customer service levels will be
• Machine capacity increase/decrease used to
  determine if new production equipment needs to be
  purchased or capacities need to be rededicated
• A poor aggregate plan can result in lost sales,
  lost profits, excess inventory, or excess
  capacity and overall sub-par profits!

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Aggregate Planning Strategies

• Trade-offs between capacity, inventory,
  backlog/lost sales
• Chase strategy using capacity as the lever
• Time flexibility from workforce or capacity
  strategy using utilization as the lever
• Level strategy using inventory as the lever
• Mixed strategy a combination of one or more of
  the first three strategies
• Will discuss further in Chapter 9

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1. Chase Strategy

• Production rate is synchronized with demand by
  varying machine capacity or hiring and laying off
  workers as the demand rate varies
• However, in practice, it is often difficult to
  vary capacity and workforce on short notice
• Expensive if cost of varying capacity is high
• Negative effect on workforce morale
• Results in low levels of inventory
• Should be used when inventory holding costs are
  high and costs of changing capacity are low

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2. Time Flexibility Strategy

• Can be used if there is excess machine capacity
• Workforce is kept stable, but the number of hours
  worked is varied over time to synchronize
  production and demand
• Can use overtime or a flexible work schedule
• Requires a flexible workforce, but avoids the
  morale problems of the chase strategy
• Low levels of inventory, lower utilization
• Should be used when inventory holding costs are
  high and capacity is relatively inexpensive

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3. Level Strategy

• Maintain stable machine capacity and workforce
  levels with a constant output rate
• Shortages and surpluses result in fluctuations in
  inventory levels over time
• Inventories that are built up in anticipation of
  future demand or backlogs are carried over from
  high to low demand periods
• Better for worker morale
• Large inventories and/or backlogs may accumulate
• Should be used when inventory holding and backlog
  costs are relatively low

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Tools for Creating an Aggregate Plan

• Some companies have not created explicit
  aggregate plans, and rely only on orders from
  warehouses or DCs to drive production schedules
  (pure pull system).
• This is acceptable only if products are not
  capacity intensive, or if maintaining a plant
  with low utilization is inexpensive. It also
  assumes material and labor inputs are flexible
  and available when needed
• For simple problems, it may be possible to
  produce a feasible plan by guessing. (No
  guarantee of optimality)
• Can be solved with heuristics and other automated
  methods, i.e. Theory of Constraints
• What tool is commonly used to produce an optimal
  aggregate plan?

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Linear Programming

• Assumes costs are linear
• Pure unit costs are the easiest
• Increasing marginal costs (e.g. regular labor
  20/hour, overtime 30/hour)
• Economies of scale harder to model, but possible
  (ignored for this class)
• Difficulty of solving increases with degree of
  detail
• Take a 1-year plan for a plant that monitors
  weekly production of 100 different SKUs. How
  many variables?
• have 10052 over 5000 production decision
  variables Pi,t
• If we could aggregate SKUs into 5 different
  product families, with monthly time buckets, how
  many variables do we have now?
• only have 512 60 decision variables for Pi,t
• Industry aggregate plans often have 10,000 to
  100,000 decision variables
• In this class will keep our problem scales well
  below that of industry (under 200 decision
  variables, the limit of the built in Excel
  solver)
• But the days of 6-12 variable LPs are over

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Aggregate Planning Example Red Tomato Tools, Inc.

• Red Tomato makes a single product, a
  multi-purpose garden tool that generates 40 in
  revenue
• Customer demand is seasonal, peaking with spring
  planting
• Red Tomato starts with 1000 of these tools in
  inventory, and we are expected to end with at
  least 500 in stock
• Red Tomato can backlog demand for a cost, but at
  the end of the time horizon, they want their
  backlog to be zero.
• Production costs are based primarily on parts and
  labor with no machine capacity issues
• They start with 80 employees can hire or fire
  workers for a fee, have them work a limited
  amount of overtime (no more than 10 hrs/mo per
  worker). They can also subcontract production out
  for a much higher fee
• There are 20 days of production per month
• Red Tomato would like to generate a 6 month plan
  that maximizes their profits (revenue net of
  costs)

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Aggregate Planning at Red Tomato Tools
Working through the aggregate planning problem
presented in Chapter 8
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Aggregate Planning- Costs
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Aggregate Planning (Define the Decision
Variables)

• Wt Workforce size for month t, t 1, ..., 6
• Ht Number of employees hired at start of month
  t, t 1, ..., 6
• Lt Number of employees laid off at start of
  month t, t 1, ..., 6
• Pt Production in month t, t 1, ..., 6
• It Inventory at the end of month t, t 1, ...,
  6
• St Number of units stocked out (backlogged) at
  end of month t, t 1, ..., 6
• Ct Number of units subcontracted for month t, t
  1, ..., 6
• Ot Number of overtime hours worked in month t,
  t 1, ..., 6

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Aggregate Planning(Define Objective Function)
Apologies to Finance gurus but for horizons of 1
year or less, we will not use NPVs
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Aggregate Planning (Define Constraints Linking
Variables)

• Workforce size for each month is based on hiring
  and layoffs ( workers employed end of Month 1
  workers employed at the start of Month 2)
• May end up with fractional workers, e.g. 73.4,
  which could be acceptable if we allow for
  part-time
• Is a Balance constraint. No spontaneous creation
  or destruction of workers outside hiring/firing

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Links Between Periods?

• Why not create 6 different LPs, each with 1
  period of a month? It would be easier for the
  computer to solve, after all! (as N increases,
  complexity and solution time goes up by Order of
  N3 or more)
• Why not solve 1-month problems sequentially? At
  end points, such as workers left at the end of
  the month 1 and then use that as the starting
  workers for month 2?

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Aggregate Planning (Constraints)

• Production for each month cannot exceed capacity
• (hence, have a limit rather than balance
  constraint)

or
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Aggregate Planning (Constraints)

• Inventory balance for each month. Inventory
  levels change if we a) produce (P) or
  sub-contract (C) units than we have demand for,
  either from this period (D) or prior ones (S)

or
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Aggregate Planning (Constraints)

• Over-time limit for each month, reflecting policy
  that no one worker can put in more than 10 hours
  of overtime.

or
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Further Conditions

• All of the variables are inherently non-negative
• We have a starting balance of 80 workers, 1000
  tools, and no backlog
• We have been told that we are not allowed to have
  any backlog and must have at least 500 tools in
  stock at the end of the planning horizon

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LP Formulation

• We now take a brief digression and look at the
  formulation in Excel, including the LP Solver
  configuration and the reports
• Some things to think about
• How many variables will we have?
• Which variables have memory- and why do we
  care?
• How many different types of constraints (aside
  from non-negativity and certain beginning/end
  conditions)? How many total constraint
  equations?
• What is our overall goal? Why can we take a
  shortcut

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LP Formulation
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LP Formulation Solver

• Decision variables are indexed to 1 thru 6, tp0
  exists only for initialization
• We have 4 types of constraints, plus 2 ending
  conditions
• Technically we should require variables to be
  integers (no laying off .2 people or making .3
  tools) but for now will leave as linear.
• Real industry LPs have numbers like 300K and 3M,
  so this is less of an issue
• Assume linear model and non-negativity both
  checked in Options

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What-if Scenarios

• Planners often run re-run their models to see how
  the plan might change if parameter values are
  different than expected
• Here are some realistic changes that would result
  in changes to the optimal plan at Red Tomato
• Increase the seasonal swings in demand
• Raise holding costs (from 2 to 6)
• Drop Over-time costs to 4.1 per hour

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Increased Demand Fluctuation
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Solution Comparison of What-If Scenario 1 vs.-
Base Case

• Major changes
• Increases Costs by 10,583
• Base Case costs 10,233 1,333
• Larger seasonal fluctuations 12,400 9,750
• Caveat The book treats beginning and end
  periods differently when calculating the average
  inventory position (see p.217). I find this
  overly fussy, and will thus use a simple average.
  
• Should I ask you to calculate this on a test,
  either method is correct, but my method is my
  easier!
• I prefer to focus on minimizing the total
  inventory COST over the planning horizon rather
  than inventory LEVELS at any point in time

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What-If Scenario 2 Increase Inventory Costs
from 2 to 6

• Major changes- costs increase over base case. In
  what way?
• Reduce inventory carried by.
• engaging in more workforce reductions as
  pre-building inventory for peak periods is no
  longer as cost effective
• subcontracting some demand out in peak periods
• We switch from what type of strategy to what?

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What-If Scenario 3Decrease Overtime Cost to
4.10

• Overall costs will decrease- but how?
• Reduce inventory carried by.
• Using Overtime
• Engaging in one more workforce reductions as we
  dont need to keep that extra person (and build
  inventory) around for peak- can use overtime to
  the limit in TP 4- our high demand month.

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More Thoughts on Red Tomatos Planning Problem

• What if our aggregate demand forecasts are
  incorrect?
• 786 review How often are real forecasts 100
  accurate?
• What if demand is greater than anticipated?
• What are some ways we can prepare for extra
  (either in terms of Safety Stock or Safety
  Capacity?)
• What if demand is less than anticipated- what
  will happen
• What is one way to keep costs lower if demand is
  greatly reduced and expected to stay low for
  awhile?

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Building an Aggregate PlanAn Exercise in Model
Evolution

• How does one understand, let alone create a large
  LP? Your options include
• Hire expensive consultants to build it for you
• Use a template (pre-existing aggregate plan) and
  change parameter values or modify to fit special
  needs
• Start with a simple model and iteratively improve
  until as complex as needed
• Excel Example a firm with 2 products would like
  to formulate an aggregate plan for the next 3
  months
• See formulateanaggplan.xls under the ADD directory

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Aggregate Planning in Practice

• Think beyond the enterprise to the entire supply
  chain
• Make plans flexible because forecasts are always
  wrong
• Sensitivity Analysis shows where bottlenecks and
  potential improvements may lie
• Rerun the aggregate plan as new information
  emerges
• Usually every time period, with revisions and
  future predictions
• Importance of aggregate planning grows as a
  firms capacity utilization increases
• Less room for mistakes in this era of low margins

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Review of Aggregate Planning

• Fundamental Tradeoffs
• Capacity (regular time, overtime, subcontracting)
• Inventory
• Backlog / lost sales
• Basic Strategies (covered further in Chapter 9)
• Chase strategy
• Time flexibility from workforce or capacity
• Level strategy
• Using Linear Programming to produce the aggregate
  plan will show which mixture of strategies is not
  only feasible, but optimal

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Summary of Learning Objectives

• What types of decisions are best solved by
  aggregate planning?
• What is the importance of aggregate planning as a
  supply chain activity?
• What kinds of information are needed to produce
  an aggregate plan?
• What are the basic trade-offs a manager makes to
  produce an aggregate plan?
• How are aggregate planning problems formulated
  and solved using Microsoft Excel?