Lecture 2: Capacity Planning Flashcards Preview

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Flashcards in Lecture 2: Capacity Planning Deck (36):

Define the capacity of an operation, giving examples.

  • The maximum level of value-added activity over a period of time that the process can achieve under normal operating conditions (Slack et al.)
  • This can be defined in terms of input or output
  • Examples:
    • Air-conditioner plant – Number of units per week (output)
    • Brewery – Litres of beer produced per month (output)  
    • Steel mill – Tonnes per hour (output)
    • Electricity company – MW of electricity generated (output)
    • Hospital – Number of beds available (input)
    • Theatre – Number of seats (input)
    • University – Number of students (input)


Rough formula for the capacity of a process 

capacity = (hours available) / (hours per unit)


Define utilisation

A measure of the number of % of hours worked by equipment, line, staff etc. (Hill)


Qualitatively, what is efficiency?

A comparison of the actual output to the level of output expected (Hill)


Define capacity planning

The task of setting the effective capacity of an operation, so that it can respond to demand


List 6 challenges for capacity planning.

  1. Capacity is a soft, malleable constraint
  2. Capacity depends on everything: workers, machines etc.
  3. Capaticty frictions
    1. ​Lead times  - it can take years (usually 2-3) to build capacity
      • Examples: Mercedes (6 years|), Amazon Kindly backordered for 5.5 months
    2. Lumpiness - capacity is a step function
      • Can't increase capacity one unit at a time
    3. Fixed costs - usually irreversible once invested in
  4. Capacity decisions can be policital
  5. Measuring and valuing capacity shortfall is not obvious
    • E.g. difficult to characterise loyalty: gaining/losing customers for life (example: cars)
  6. Capacity investment involves long-term planning under uncertainty
    • ​​Arguably the greatest challenge for capacity strategy
    • A function of all the other challenges


Identify 4 key capacity decisions

  1. Sizing - how much capacity to invest in
  2. Timing - when to increase or reduce resources
  3. Type - what kinds of resources are best?
  4. Location - where should resources be located?


Outline the three main capacity drivers.

  1. Forecasting
    • ​​Average demand
    • Volatility
    • Separate planning from other uses
  2. Shortage cost
    • ​Volatility
    • Standard loss
    • Shortage penalty
    • Waiting cost, i.e. do customers have to be compensated?
    • Holding cost
  3. Safety capacity cost
    • ​Discount horizon and rate
    • Marginal cost of capacity, subcontracting, overtime/temp work, spot-market buying (immediate delivery)


State the difference between theoretical capacity and actual capacity.

Outline the main difficulties which inhibit perfect utilisation of a manufacturing system.

Theoretical capacity is the maximum possible output, while actual capacity is a realistic estimate of the achievable output rate.

The main difficulties which restrict capacity are:

  1. Lost time (planned)
    • Setup times
    • Switchover delays
  2. Lost time (unplanned)
    • ​​Breakdowns
    • Coordination conflicts (of equipment and labour)
    • Supply shortages
  3. Imbalances -> equipment idling
    • ​​Bottlenecks
    • Imbalances in task times
  4. Reduced yield
    • ​Quality problems
    • Slow-running equipment
  5. Variable conditions
    • ​Variability in process times -> buildup of inventory
    • Variability in raw material arrivals (supply)
    • Variability in order arrivals (demand)
    • Unplanned downtime


Define bottleneck in terms of manufacturing processes. What effect does this have on the whole system?

  • The task which restricts system capacity, either due to:
    • Processing time length
    • Processing time volatility
  • When capacity at each stage is not balanced, the capacity of the total system is limited by that of the bottleneck stage
  • Effectively creates two systems​:
    • Upstream is unneccesarily busy: queues as material waits to be serviced
    • Downstream is starved of full flow


Define set-up and state when it is required.

  • Any action or process required to prepare a machine to accomplish an operation
  • Required when the type/size/colour of the part being worked on is changed


How does batch size influence production capacity? Why might it not be possible to maximise batch size?

  • Only need to set up once per batch
  • For a larger batch size, set up time remains the same while run time increases
  • The average total time per component decreases
    • Proportionally less time "wasted" on setup
  • Capacity is thus increased
  • However, increasing batch size increases inventory held in the system - not always achievable
  • (NB if setup times are 0, batch size has no influence on capacity)


Outline the impacts of reducing setup times on a manufacturing system

Reducing setup times has a ripple effect in the system, eliminating hidden costs

  1. Smaller batch sizes become economical
  2. Reduced cost of setup labour required
  3. Increased production capacity (on bottlenecks)
  4. Reduced scale of potential quality problems, and hence waste (since avg time per unit is reduced)


Illustrate, using an equation, the impact break downs can have on a production system

  • If a process has n workstations, each with a probability P(breakdown) of breaking down at any given time:
    • P(completing a product) = (1 - P(breakdown))n
  • This gives the % of production that will be delayed or even lost (if it is assumed products are wasted as a result of breakdown)
  • Shows the importance of breakdown-free production and routine maintenance
  • The effect is exaggarated if a new setup is required after an interruption


Give the formua for the Overall Equipment Effectiveness, explaining each of the components

OEE = AR * PR * QR

(max. available time) - (availability losses) = (Total Operating time)

  • Availability losses include:
    • Unplanned down time
    • Setup and changeover
    • Breakdown failures
  • AR = availabiltiy rate = (total op time)/(max. available time

(total op time) - (speed losses) = (net op time)

  • Speed losses include
    • Equipment idling
    • Slow running equipment
  • PR = perdormance rate = (net op time)/(total op time)

(net op time) - (quality losses) = (valuable op time)

  • QR = quality rate = (valuable op time)/(net op time)


Outline how real demand differs from ideal demand

Ideal demand is smooth and predictable

  • Total demand = maximum output capacity of resources
  • Any changes are perfectly forecast, in sufficient time to allow capacity change

Real demand us usually not predictable

  • It has peaks, e.g. lunchtime, weekends, summer etc,
  • Demand varies through the product life cycle and competition


Identify the 3 key steps in capacity planning and control

  1. Measure aggregate demand and capacity
  2. Identify the alternative capacity plans
  3. Choose the most appropriate capacity plan


Outline 2 key issues in balancing capacity and demand. 

  1.  Trade-off between unacceptable queuing times and unnacceptably low utilisation of servers/machines (capacity)
  2. Effect of variation in inter-arrival and service/processing times
    • Capacity and demand rarely match


Outline the 3 basic strategies for long-term capacity planning

  1. Capacity lead: capacity always exceeds demand
    • ​​Sufficient capacity to meet demand
    • Capacity cushion
    • Low impact of start-up problems
    • Low utilisation
    • Risk of over-capacity
    • Requires early capital spending
  2. Capacity lag: demand always exceeds capacity
    • Sufficient demand for full working capacity
    • No capacity cushion
    • High impact of start-up problems
    • Insufficient capacity to meet demand
    • No risk of over-capacity
    • Capital spending is delayed
  3. Smoothing with inventory
    • Inventory is built when over capacity
    • Used up when under capacity


Outline the 4 possible options for medium-term capacity planning

  1. Level capacity plan
    • Processing capacity is set at a uniform level throughout the planning period, regardless of the fluctuations in forecast demand
  2. Chase demand plan
    • Attempts to match capacity closely to the varying levels of forecast demand
  3. Optimal capacity plan
    • Balances the costs of levelling and varying the capacity
  4. Demand management
    • Change demand to suit capacity


Describe level capacity planning in detail, giving the advantages and disadvantages.

Capacity at uniform level throughout the planning period

  • Same number of staff operate the same processes
  • Finished goods transferred to inventory in anticipation of sales at later time
  • Suitable for non-perishable goods


  • Stable employment patterns
  • High process utilisation
  • High productivity with low unit costs


  • Considerable inventory costs
  • Decision-making: what to produce for inventory vs. immediate sale
  • High over/under utilisation levels for service operations


Steps in calculating the total cost of a level capacity plan, given demand forecasts

  1. Calculate cumulative net demand (A)
    • Adjust for existing inventory, and the inventory needed at the end of the forecast period
  2. Calculate the cumulative no. of units each worker is able to produce (B)
  3. Calculate the ratio A/B -> number of workers needed
  4. Hire the maximum needed number of workers
  5. Calculate cumulative production
  6. Calculate the ending inventory for each period
  7. Use the above to calculate the total cost:
    • Coast of hiring + cost of storing inventory


Steps in calculating the total cost of a chase demand plan, given demand forecasts

  1. Calculate the forecasted net demand (A)
    • Adjust for existing inventory and the inventory required at the end of the period
  2. Calculate the no. of units each worker is able to produce (B)
  3. Calculate the ratio A/B -> number of workers needed
  4. Hire the exact number needed for each month, and fire them when no longer needed
  5. Calculate cumulative production
  6. Calculate the ending inventory for each period
  7. Use the above to calculate the total cost:
    • Coast of hiring/firing + cost of storing inventory


Describe optimal capacity planning. Give one simple model that can be used for this.

Mathematical programming is used to find the best or optimal solution to a problem that requires

  • A decision or set of decisions, about
  • How best to use limited resources, in order to
  • Achieve a state goal of objectives

A Linear Programming (LP) model seeks to maximise or minimise a linear objective function, subject to a set of linear constraints, by determining values of nonnegative real decision variables.

  • Constraints could be e.g. have to satisfy demand, workers have to be fully utilised etc.


List 4 options for short-term capacity planning 

  1. Manage order mix
  2. Schedule downtime appropriately
  3. Overtime planning
  4. Outsourcing


List 4 key considerations in the analysis of queues

  1. The average time a customer/order spends:
    • In the system
    • In the queue
  2. The average length of the queue
  3. The average resource utilisation
  4. When it is justified to increase resources


Describe how a queue-server system can be modelled as a discrete system. 

Derive the formulae for average number of customers in the system, N, and average queue length, Nq


  • Arrival rate = λ
  • Service rate = μ
  • Assume λ/μ
  • Arrival rate < service rate, so the queue is decreasing


  • Let ρ = λ/µ
  • Let pi = probability of i orders being in the system after reaching equilibrium

At equilibrium, when pi is not changing:

  • Rate of items arriving in one state = rate of items leaving that state (since the probability of each state stays the same)
  • Node 0: µp1= λp→ p1 = ρp0
  • Node 1 → p2 = ρp1 = ρ2p0
  • etc.

Generalise the above:

  • pN+1 = ρpN = ρN+1p0

Noting that [p0 + p1 + p2 + … + pi + … ] = 1

 → p0 [1 + ρ + ρ2 + ρ3 + … + ρi]= 1

→p0/(1- ρ) = 1 (geometric series, assuming i → ∞)

Hence, we have:

  • p0 = 1 – ρ
  • pi = ρi(1- ρ)

Average number of customers in the sysem, N:

= Sum (i=0 to i=∞)[ipi],

i.e. sum[(no. of items in the queue)*(probability of there being that many items) 

= Sum (i=0 to i=∞)[iρi(1- ρ)]

= ρ/(1 – ρ) [why?]

Average queue length, Nq

=  Sum (i=0 to i=∞)[(i-1)pi]

= (ρ/(1 – ρ)) - (1 - p0)

=  (ρ/(1 – ρ)) - ρ

= (ρ2/(1 - ρ))


List three other cases which the basic queuing model (Little's Law) can be used to analyse

  1. Multiple queues, multiple server channels
  2. Single queue, multiple server channels
  3. Single queue, multiple stages


Give the formula for Little's Law

Derive expressions for average time spent in the system, W, average waiting time, Wq, and server utilisation

Little's Law: N = λW

  • W = Average time spent in the system
  • N = Average number of items in the system
  • λ  = Arrival rate


W = λ / N

  • Define ρ = λ/μ, where μ is service rate
  • We can show that N = ρ/(1-ρ)
  • Giving W = λ/((λ/μ)/(1-λ/μ))

= 1/(μ(1-ρ))

Wq = W - 1/μ

  • (average time spent in system, minus time spent being served)

= ρ/(μ(1-ρ))


Outline 3 key trade offs in capacity planning

  1. Inventory cost vs. the cost of changing capacity
  2. Flexibility vs. quality
  3. Customer satisfaction vs. employee satisfaction


Describe the Centre of Gravity method

  • The CoG method performs a production volume weighted distance calculation
  • Used to find the location that minimises transport costs
  • Based on the idea that all possible locations have a "value", which is the sum of all transportation costs to and from that location
  • The best location, i.e. the one that minimises costs, is represented by the weighted CoG of all points to and from which goods are transported
  • (give CoG formulae, defining each letter)


Outline the advantages and limitations of the Centre of Gravity method.


  1. Objective
  2. Quantitative
  3. Useful for searching for sites


  1. Depends on the actual transportation distance
  2. Local infrastructure and incentives
    • Access to ports
    • Location relative to transportation networks
  3. Financial/regulatory considerations:
    • Financial: exchange tariffs, taxes, shipping costs
    • Regulatory: employment, environmental, safety/construction
  4. Social factors:
    • Availability, cost and skill of local labour force, 
    • Culture e.g. ethics and language,
    • Proximity to markets
  5. Location of supplier base/ availability of alternative suppliers
  6. One-dimensional
    • Assumes transportation costs are a function of distance and number of units transported only
  7. May not be suitable sites close to the CoG


Describe the load-distance method for determining location. Give the advantages and disadvantages of this method.

Used to choose the best location among available choices:

  1. Plot locations and destinations on a x-y grid map
  2. Calculate load for each destination
    • E.g. tons of good transported per month
  3. Calculate distance from each potential location
    • E.g. Euclidean, rectilinear etc.
  4. Calculate weighted (load * distance) sum for each location
  5. Choose the location with the lowest load*distance


  1. Objective
  2. Quantitative
  3. Useful for evaluating candidate sites


  1. One dimensional
  2. Need target sites to already have been identified
    Depends on the actual transportation distance
  3. Local infrastructure and incentives
    • Access to ports
    • Location relative to transportation networks
  4. Financial/regulatory considerations:
    • Financial: exchange tariffs, taxes, shipping costs
    • Regulatory: employment, environmental, safety/construction
  5. Social factors:
    • Availability, cost and skill of local labour force, 
    • Culture e.g. ethics and language,
    • Proximity to markets
    • Location of supplier base/ availability of alternative suppliers


What is a heuristic?

A simple "rule of thumb" method that seems to work

  • Easy to understand (common-sense)
  • Can be efficient
  • Not necessarily optimal (but good enough)
  • May not be evident why it works


List 3 methods that can be used to aid distribution decisions

  1. Simulation
  2. Optimisation
  3. Heuristics, e.g. the NorthWest Corner Method


What are distribution decisions concerned with?

  • How much to distribute
  • From which factories to which distribution centres
  • Given:
    • Associated costs
    • Supply and demand constraints