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Dr' Cholette DS855 Fall 2006


... changing capacity: hiring or layoff ($/worker) and cost of ... policy limits on overtime, layoffs, capital available, warehousing, stock-outs and backlogs ... – PowerPoint PPT presentation

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Title: Dr' Cholette DS855 Fall 2006

Dr. Cholette DS855 Fall 2006
Aggregate Planning in the Supply Chain
  • Role of aggregate planning in a supply chain
  • The aggregate planning problem
  • Aggregate planning strategies
  • Implementing aggregate planning in practice

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

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?

Aggregate Planning Scope
  • All supply chain stages should be included in an
    aggregate plan to optimize supply chain
  • For now we will ignore transportation issues and
    costs and focus on a single manufacturing
  • 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)

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
  • 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
Information Needed for an Aggregate Plan
  • Demand forecast in each period
  • Production costs
  • Machine costs
  • labor costs, regular time (/hr) and overtime
  • 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
  • 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

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!

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

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

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

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

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?

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
  • 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
  • But the days of 6-12 variable LPs are over

Aggregate Planning Example Red Tomato Tools, Inc.
  • Red Tomato makes a single product, a
    multi-purpose garden tool that generates 40 in
  • Customer demand is seasonal, peaking with spring
  • 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

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

Aggregate Planning (Define Objective Function)
Apologies to Finance gurus but for horizons of 1
year or less, we will not use NPVs
Aggregate Planning (Define Constraints Linking
  • 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
  • Is a Balance constraint. No spontaneous creation
    or destruction of workers outside hiring/firing

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?

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

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)

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

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

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
  • How many different types of constraints (aside
    from non-negativity and certain beginning/end
    conditions)? How many total constraint
  • What is our overall goal? Why can we take a

LP Formulation
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
  • 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

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

Increased Demand Fluctuation
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
  • I prefer to focus on minimizing the total
    inventory COST over the planning horizon rather
    than inventory LEVELS at any point in time

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?

What-If Scenario 3 Decrease Overtime Cost to
  • 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.

More Thoughts on Red Tomatos Planning Problem
  • What if our aggregate demand forecasts are
  • 786 review How often are real forecasts 100
  • What if demand is greater than anticipated?
  • What are some ways we can prepare for extra
    (either in terms of Safety Stock or Safety
  • 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

Building an Aggregate Plan An Exercise in Model
  • 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
  • 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
  • See formulateanaggplan.xls under the ADD directory

Aggregate Planning in Practice
  • Think beyond the enterprise to the entire supply
  • Make plans flexible because forecasts are always
  • Sensitivity Analysis shows where bottlenecks and
    potential improvements may lie
  • Rerun the aggregate plan as new information
  • 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

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

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?
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