SUPPLY CHAIN MANAGEMENT EXAM
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chapter4iyerppts.1.pptxManaging Supply Chains: Concepts, Tools, Applications Chapter 4: Capacity
These powerpoints are a companion to the book: Managing Supply Chains: Concepts, Tools and Applications by Ananth. V . Iyer, Hercher Publishing Inc., ISBN 978-1-939297-01-3
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Outline
Capacity – hardware and software
Choosing Capacity Buffers ahead of demand
Capacity given long lead times
Queuing and capacity impact
Parallel capacity – Split or Pool Capacity ?
Make-Buy decisions
Temporal Capacity adjustments
Summary
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Capacity – hardware and software
Capacity – Designed maximum flow over a period of time
Hardware decision
Examples: Classroom size, Truck volume, Machine production rate
Software decision
Class scheduling, Truck routing, Batch sizes
May need to be chosen under
Limited Information
Uncertain demand
Changing conditions
Long build time
Alternate capacity choices
Competing customers
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4.1 Capacity buffer given demand uncertainty
Demand uncertainty – see table 4.1
Cost per unit of capacity = $25,
Revenue per unit of demand satisfied = $100,
Salvage value per unit of capacity = $10
Choose capacity to maximize expected profit
Capacity has to buffer against demand uncertainty
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Calculating Expected profit
If 300 units of capacity are chosen then the expected profit =
This expected profit is the average profit across possible demand realizations
It is the best estimate of the profit after demand is realized (Minimize squared deviation of profits around the estimate)
It is the folded decision tree expected profit
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Optimal Capacity Choice
Optimal Capacity = 300 units
Verify that it is covers the critical fractile of 0.83
Expected Demand = 200
Expected Profit under perfect information = 15,000, so the cost of uncertainty = 15,000-11,500= 3,300
Capacity buffers against uncertainty may be profitable
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4.2 Capacity, lead time and demand uncertainty
Low Demand ~ U(1,5), High Demand ~ U(6,10)
Long lead times, so a 50% probability of Low or High Demand. So the demand is distributed as
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Capacity and Expected Profit
If r=200, c=100, s=20, g=200
Cs = 300, Ce = 80, Critical fractile =Cs/(Cs+Ce) = 78.9%
Optimal Capacity = 8 units
Calculate the expected profit as $236 (see spreadsheet)
Note that the expected demand = 5.5 units.
Since capacity is chosen in advance, a buffer is optimal to cover demand upside.
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Suppose capacity could be chosen after demand signal
If the demand type is known i.e., Low or High demand
Cost structures same
If Demand level is Low i.e., U(1,5), optimal capacity is 4 units, expected profit = $144
If Demand level is High i.e., U(6,10), optimal capacity is 9 units, expected profit = $644
Overall expected profit = (0.5*144)+(0.5*644)=$394
Overall expected capacity = (0.5*4)+(0.5*9)=6.5 units
How did profits increase and capacity decrease ? Better matching of capacity with demand
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4.3 Capacity and Queuing Models
Consider demand for make to order units that queue up to access capacity
Use the queuing template (spreadsheet provided) and parameters
Demand rate = λ
Service rate/server (unit of capacity) = µ
Numbers of units of capacity = m
Read off
1) Lead Time,
2) Utilization,
3) Number in the system,
4) Number in the Queue,
5) Lead time in the queue
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Single Unit of capacity
Example with arrival rate of orders of 4/hour, service rate of 6/hour.
Average time between orders = 15 minutes, average service time = 10 minutes
From the template with λ=4, µ=6, m=1 obtain
L=0.5 hours or 30 minutes, Lq = 20 minutes
N= 2 orders, Nq=1.33
Utilization = 0.67
Thus, the mean and variability in arrivals and processing as well as the sequential capacity access based on arrival time causes delays in providing capacity to satisfy demand
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The impact of the arrival rate
The table above shows that as the arrival rate increases, given a fixed capacity and processing rate, the lead time increases and the average orders-in-queue increase exponentially
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4.4.1 Capacity Pooling
Two locations, each with one unit of capacity, demand of 4.375 order/hour, processing rate of 5 orders/hour. From the template, obtain
L=1.6 hours, N= 7 orders per location or 14 orders across both locations
If you pool the two units of capacity, demand is 8.75 orders/hour, processing rate per unit of capacity remains 5 orders/hour, m = 2, obtain
L=0.853 hours, N = 7.46 orders
Lead time decreased and WIP decreased due to capacity pooling
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4.5 Capacity Splitting
If tasks pooled have different requirements, setup times may be incurred due to pooling, thus increasing processing times
Example:
Pooled: m=16 machines, λ=20 orders/hour, µ=60/(14.25+30) = 1.3559 customers/hour
L=1.132 hours from the template
Split: 4 groups of m=4 machines, each group: λ=5 orders/hour, µ=60/(3+30) = 1.818 orders per hour
L=0.773 hours from the template
Splitting Capacity based on customer characteristics increases processing rate, which may compensate for the decrease in capacity access across groups, and thus decrease lead time
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4.6 A chain of production stages
Consider MS stages of production, organized in series
The total lead time for the entire system is the sum of the individual lead times (assuming initial arrivals are Poisson and processing times are exponential)
Example: Three stages in a plant, λ=4 orders/hour
Stage 1: 1 machine, µ = 5 orders/hour
Stage 2: 3 machines in parallel, µ=1.4 orders/hour
Stage 3: 2 machines in parallel, µ =2.2 orders/hour
Use the queuing template to get L1=1,L2=5.27,L3=2.61, so the total lead time = 8.8 hours
Thus capacity of processing and the number of parallel units of capacity influence the overall lead time for a system
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4.7 Shared Facility Lead time, – the impact of batching
Consider a demand of D units/time per location
Batch size “Q”
Orders of “Q” units every Q/D units of time for a batch order rate per location of D/Q batches/unit time
W locations ordering from a single facility so λ = W D/Q
Setup time ts, per unit processing time tp so batch processing time of (ts+(tp Q)), so µ = 1/(ts+(tp Q))
The W locations interact through their shared facility. The setup time ts reflects differences between requirements across locations and could cause longer lead times, higher inventories at locations and greater costs associated with sharing the facility
See example in section 4.7
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4.9 Make-Buy Decisions
Consider an example where orders received from customers come with a fixed delivery lead time
The company has the option to use internal capacity (make) or subcontract
It is more expensive to subcontract, but that may be the best option in the short run to guarantee on-time delivery albeit with smaller margins
See example in Section 4.9
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Make-Buy Decisions
The example in 4.9 shows that
Capacity has a shadow price if it is fully used, else it is zero
The value of capacity reflects how it will be deployed to improve profits or decrease costs
The best deployment of capacity is based on the “bottleneck” resource (similar to the book “The Goal”)
The linear program identifies the bottlenecks and thus provides the logic for the best deployment of capacity to maximize profits
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4.11 Temporal Capacity Adjustments
Contexts where demand varies over time
Examples: Service systems, trucking etc
Shifts with varying costs based on working hours and their temporal contiguity
Goal: Allocate people to shifts to cover projected capacity requirements
Mathematical Programming to frame the problem (next page)
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Capacity Planning for Temporal Demands
Model:
Let the day be divided into N time periods (say half-hour intervals). Let di be the demand (in number of staff) required in time period, i (where i = 1, 2, ..., N). Let aij be equal to 1 if a person working on shift j is available in period i. Let cj be the cost for a person to work in shift j.
The problem is the following:
Minimize ΣjcjXj.
ΣjaijXj ≥ di for all i = 1, 2, ..., N
Xj are restricted to be integer values.
The solution allocates people to shifts in a way that allows us to provide adequate staff during each time period of the day.
See the details in the spreadsheet “Section 4.11 Example” for the example described in the book in section 4.11
Adjusting shift allocations may permit the capacity available to be better tailored to required capacity based on temporal demand variation while minimizing costs
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Capacity Chapter Summary
Capacity is the designed system throughput per unit time
Buffer capacity may be optimal to hedge against demand uncertainty
Longer procurement lead times may require larger capacity
Splitting or pooling capacity is a decision that requires a focus on task characteristics and thus lead time
Sharing facilities (capacity) requires planning designs to reduce setup times
Adjusting the make-buy decision to capacity usage may improve performance
Temporal capacity adjustments may require shift allocations to be matched to demand patterns
The Capacity “C” is a key decision that can impact supply chain performance metrics
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