Define the capacity of an operation, giving examples.
 The maximum level of valueadded 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:
 Airconditioner 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)
 Airconditioner 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.
 Capacity is a soft, malleable constraint
 Capacity depends on everything: workers, machines etc.
 Capaticty frictions

Lead times  it can take years (usually 23) to build capacity
 Examples: Mercedes (6 years), Amazon Kindly backordered for 5.5 months

Lumpiness  capacity is a step function
 Can't increase capacity one unit at a time

Fixed costs  usually irreversible once invested in
 Capacity decisions can be policital
 Measuring and valuing capacity shortfall is not obvious
 E.g. difficult to characterise loyalty: gaining/losing customers for life (example: cars)
 Capacity investment involves longterm planning under uncertainty
 Arguably the greatest challenge for capacity strategy
 A function of all the other challenges

Lead times  it can take years (usually 23) to build capacity
 Examples: Mercedes (6 years), Amazon Kindly backordered for 5.5 months

Lumpiness  capacity is a step function
 Can't increase capacity one unit at a time
 Fixed costs  usually irreversible once invested in
 E.g. difficult to characterise loyalty: gaining/losing customers for life (example: cars)
 Arguably the greatest challenge for capacity strategy
 A function of all the other challenges
Identify 4 key capacity decisions

Sizing  how much capacity to invest in

Timing  when to increase or reduce resources

Type  what kinds of resources are best?

Location  where should resources be located?
Outline the three main capacity drivers.

Forecasting

Average demand
 Volatility
 Separate planning from other uses

Shortage cost
 Volatility
 Standard loss
 Shortage penalty
 Waiting cost, i.e. do customers have to be compensated?
 Holding cost

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

Lost time (planned)
 Setup times
 Switchover delays

Lost time (unplanned)
 Breakdowns
 Coordination conflicts (of equipment and labour)
 Supply shortages

Imbalances > equipment idling
 Bottlenecks
 Imbalances in task times

Reduced yield
 Quality problems
 Slowrunning equipment

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
 Processing time length
 Processing time volatility
 Upstream is unneccesarily busy: queues as material waits to be serviced
 Downstream is starved of full flow
Define setup 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)
 Proportionally less time "wasted" on setup
Outline the impacts of reducing setup times on a manufacturing system
Reducing setup times has a ripple effect in the system, eliminating hidden costs
 Smaller batch sizes become economical
 Reduced cost of setup labour required
 Increased production capacity (on bottlenecks)
 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 breakdownfree production and routine maintenance
 The effect is exaggarated if a new setup is required after an interruption
 P(completing a product) = (1  P(breakdown))^{n}
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
 Measure aggregate demand and capacity
 Identify the alternative capacity plans
 Choose the most appropriate capacity plan
Outline 2 key issues in balancing capacity and demand.
 Tradeoff between unacceptable queuing times and unnacceptably low utilisation of servers/machines (capacity)
 Effect of variation in interarrival and service/processing times
 Capacity and demand rarely match
 Capacity and demand rarely match
Outline the 3 basic strategies for longterm capacity planning

Capacity lead: capacity always exceeds demand
 Sufficient capacity to meet demand
 Capacity cushion
 Low impact of startup problems
 Low utilisation
 Risk of overcapacity
 Requires early capital spending

Capacity lag: demand always exceeds capacity
 Sufficient demand for full working capacity
 No capacity cushion
 High impact of startup problems
 Insufficient capacity to meet demand
 No risk of overcapacity
 Capital spending is delayed

Smoothing with inventory
 Inventory is built when over capacity
 Used up when under capacity
 Sufficient capacity to meet demand
 Capacity cushion
 Low impact of startup problems
 Low utilisation
 Risk of overcapacity
 Requires early capital spending
 Sufficient demand for full working capacity
 No capacity cushion
 High impact of startup problems
 Insufficient capacity to meet demand
 No risk of overcapacity
 Capital spending is delayed
 Inventory is built when over capacity
 Used up when under capacity
Outline the 4 possible options for mediumterm capacity planning

Level capacity plan
 Processing capacity is set at a uniform level throughout the planning period, regardless of the fluctuations in forecast demand

Chase demand plan
 Attempts to match capacity closely to the varying levels of forecast demand

Optimal capacity plan
 Balances the costs of levelling and varying the capacity

Demand management
 Change demand to suit capacity
 Processing capacity is set at a uniform level throughout the planning period, regardless of the fluctuations in forecast demand
 Attempts to match capacity closely to the varying levels of forecast demand
 Balances the costs of levelling and varying the capacity
 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 nonperishable goods
Advantages
 Stable employment patterns
 High process utilisation
 High productivity with low unit costs
Disadvantages:
 Considerable inventory costs
 Decisionmaking: 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
 Calculate cumulative net demand (A)
 Adjust for existing inventory, and the inventory needed at the end of the forecast period
 Calculate the cumulative no. of units each worker is able to produce (B)
 Calculate the ratio A/B > number of workers needed

Hire the maximum needed number of workers
 Calculate cumulative production
 Calculate the ending inventory for each period
 Use the above to calculate the total cost:
 Coast of hiring + cost of storing inventory
 Adjust for existing inventory, and the inventory needed at the end of the forecast period
 Coast of hiring + cost of storing inventory
Steps in calculating the total cost of a chase demand plan, given demand forecasts
 Calculate the forecasted net demand (A)
 Adjust for existing inventory and the inventory required at the end of the period
 Calculate the no. of units each worker is able to produce (B)
 Calculate the ratio A/B > number of workers needed

Hire the exact number needed for each month, and fire them when no longer needed
 Calculate cumulative production
 Calculate the ending inventory for each period
 Use the above to calculate the total cost:
 Coast of hiring/firing + cost of storing inventory
 Adjust for existing inventory and the inventory required at the end of the period
 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 shortterm capacity planning
 Manage order mix
 Schedule downtime appropriately

Overtime planning
 Outsourcing
List 4 key considerations in the analysis of queues
 The average time a customer/order spends:
 In the system
 In the queue
 The average length of the queue
 The average resource utilisation
 When it is justified to increase resources
 In the system
 In the queue
Describe how a queueserver system can be modelled as a discrete system.
Derive the formulae for average number of customers in the system, N, and average queue length, N_{q}
 Arrival rate = λ
 Service rate = μ
 Assume λ/μ
 Arrival rate < service rate, so the queue is decreasing
Then:
 Let ρ = λ/µ
 Let p_{i }= probability of i orders being in the system after reaching equilibrium
At equilibrium, when p_{i} 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: µp_{1}= λp_{0 }→ p_{1} = ρp_{0}
 Node 1 → p_{2} = ρp_{1} = ρ^{2}p_{0}
 etc.
Generalise the above:
 p_{N+1} = ρp^{N} = ρ^{N+1}p_{0}
Noting that [p_{0} + p_{1 }+ p_{2} + … + p_{i} + … ] = 1
→ p_{0} [1 + ρ + ρ^{2} + ρ^{3} + … + ρ^{i}]= 1
→p_{0}/(1 ρ) = 1 (geometric series, assuming i → ∞)
Hence, we have:
 p_{0} = 1 – ρ
 p_{i} = ρ^{i}(1 ρ)
Average number of customers in the sysem, N:
= Sum (i=0 to i=∞)[ip_{i}],
i.e. sum[(no. of items in the queue)*(probability of there being that many items)
= Sum (i=0 to i=∞)[iρ^{i}(1 ρ)]
= ρ/(1 – ρ) [why?]
Average queue length, N_{q}
= Sum (i=0 to i=∞)[(i1)p_{i}]
= (ρ/(1 – ρ))  (1  p_{0})
= (ρ/(1 – ρ))  ρ
= (ρ^{2}/(1  ρ))
List three other cases which the basic queuing model (Little's Law) can be used to analyse
 Multiple queues, multiple server channels
 Single queue, multiple server channels
 Single queue, multiple stages
Give the formula for Little's Law
Derive expressions for average time spent in the system, W, average waiting time, W_{q}_{,} 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/(1ρ)
 Giving W = λ/((λ/μ)/(1λ/μ))
= 1/(μ(1ρ))
W_{q} = W  1/μ
 (average time spent in system, minus time spent being served)
= ρ/(μ(1ρ))
Outline 3 key trade offs in capacity planning
 Inventory cost vs. the cost of changing capacity
 Flexibility vs. quality
 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.
Advantages:
 Objective
 Quantitative
 Useful for searching for sites
Limitations:
 Depends on the actual transportation distance
 Local infrastructure and incentives
 Access to ports
 Location relative to transportation networks

Financial/regulatory considerations:
 Financial: exchange tariffs, taxes, shipping costs
 Regulatory: employment, environmental, safety/construction

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

Onedimensional
 Assumes transportation costs are a function of distance and number of units transported only
 May not be suitable sites close to the CoG
Describe the loaddistance method for determining location. Give the advantages and disadvantages of this method.
Used to choose the best location among available choices:
 Plot locations and destinations on a xy grid map
 Calculate load for each destination
 E.g. tons of good transported per month
 Calculate distance from each potential location
 E.g. Euclidean, rectilinear etc.
 Calculate weighted (load * distance) sum for each location
 Choose the location with the lowest load*distance
Advantages:
 Objective
 Quantitative
 Useful for evaluating candidate sites
Limitations:
 One dimensional
 Need target sites to already have been identified
Depends on the actual transportation distance  Local infrastructure and incentives
 Access to ports
 Location relative to transportation networks
 Financial/regulatory considerations:
 Financial: exchange tariffs, taxes, shipping costs
 Regulatory: employment, environmental, safety/construction
 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 (commonsense)
 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
 Simulation
 Optimisation
 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
 Associated costs
 Supply and demand constraints