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# 18

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## gilles coppens

on 6 May 2010

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#### Transcript of 18

Chapter 18: Capacity Management 18.1
The Capacity-Setting Problem 18.2
Modeling and analysis 18.3 Modifying Existing Production Lines
18.4 Designing New Production Lines 18.5
Capacity Allocation and Line Balancing 18.1 The Capacity-Setting Problem Strategic Capacity Planning
How much and when should capacity be added?
What type of capacity should be added?
18.2 Modelling and analysis Parameters: t_e: Mean effective process time for machine
c_e: Effective coefficient of variation
m: Number of machines
k: Cost per machine
A: Fixed cost of machine option Assumptions: A single Line
M workstations
Production of a single product
Each station: different technology options
No mixing of the machine type at the same station Compute: u(m) = utilization of station with m machines
CT(m) = cycle time at station with m machines
c_a = CV of arrivals to station
c_d = CV of departures from station Formulas: We can now find a starting point where we have a sufficient capacity:
CAPACITY FEASIBLE Example: A minimum cost, capacity-feasible (MCCF) line Target Four-station line
SCV arrival to the line equal to 1 Indice of performance of the line TH: the required throughput
CT: the maximum total cycle time Troughput: 2,5 jobs/hour
Cycle time: 16 hours Data: We obtain the number of machines needed to respect our TH target and obtain the minimum cost, capacity-feasible By using the formula u(m) CT target? We obtain 34 hours instead of the target of 16 hours Three possible improvements:
Modify the existing machine
Change the machine options
Add more machines We use: 18.3 Modifying existing production lines Heuristic procedure:
For determining a least-cost configuration
Meets:
- TH constraint
- CT constraint How does the heuristic work?
(Minimum Cost Capacity-Feasible)
Look for the changes that results in "biggest bang for the buck" with respect to cycle time improvements Illustration Recall the MCCF configuration: It does not satisfy the CT constraint!
34 hours (MCCF) >< 16 hours (desired) We have to bring the configuration into CT compliance in a cost-efficient way! Suppose:
we can add a machine at any worksation in order to reduce the cycle time.
At station 3, we can also reduce the variability of the machines So, we can modify the machines at station 3:
Cost: \$10 000/machine
Effects:
- shorter but more frequent outages
- assume t_e does not change
- reduce c^2_e from 3.14 to 1
How: Installing field replacement parts and/or doing more preventive maintenance => we can consider that variability reduction is an alternative to addinf machines How to know at which station we have to add a machine (or reduce variability)?
We compute changes in CT and changes in cost for each station.
Reasonable measure of effectiveness:
- Ratio change in cost/change in CT
=> "best single change" = that with lowest ratio
Compute ratio for each option No single change reduces total CT by enough to satisfy the CT constraint! (we need a reduction of 18 hours) Computation: 4.49 + 14.73 = 19.22 > 18 => CT has been reduced to 14.78 (34-19.22) Solution: Initial situation: Actual situation: The total cost (\$2,640,000) is \$185,000 higher thant the MCCF configuration Notice that the line isn't balanced NB: This approach works usually well, but it does not guarantee that it will bring us within the CT constraint at a minimum cost.

In any case it does yield a configuration that is throughput and CT feasible. Chapter 18: Capacity Management 18.4 Designing new production lines Traditional approach:
Basic size and shape of facility
Minimize cost of facility
Disposition of the workstations within the facility
Product flow
2 approaches x Tendency to linear layouts
x Problem : little consideration for the product flow
Factory Physics approach:
Customer determines the product
Product determines the processes
Processes determines the set of machines
Machines determines the facility needed
Facility determines the overall structure and size x Problem: Too costly facility
Solution: combine the two approaches
Settle on a basic layout
Choose the best singles changes Trade off between cost and performance Other facility design considerations:
Material handling
Physical plant layout
Storage and warehousing
Office planning
Facility services
Short-Term and Long-Term Capacity Setting
Traditional and Modern Views of Capacity Management
Production economies of scale Short-Term Intermediate-Term Long-Term Production diseconomies of scale If Plant is too big: Bureaucratization

Longer CT

Higher Risk Traditional view Feasible when utilization is lower than capacity

Infeasible Otherwise To define the best one, we use the satisficing technique
Problem is divided into a strategic problem that defines one or more tactical problems "For a fixed budget, design the 'best facility possible" Formulation of the capacity-planning problem: Lead time and WIP grow with utilization

Decreasing responsiveness when utilization grows Modern view Focus on optimality AND robustness Short Term Overtime

Subcontracting

... Adjust the number of shifts

Subcontracting

Change Plant

... Long-Term 18.5 Capacity allocation and Line Balancing Factory Physics procedures >> unbalenced line

WHY?

Easier to manage : Distinct bottleneck
Different cost of capacity related to differents stations
Capacity often available only in discrete-size increments

However, sometimes line balancing makes sense!
> Known as line-of-balance (LOB) problem.
> Applicable only on paced assemlby lines >< ≠flow lines !
what’s the difference ?
in a flow line:
- stations = independent
- bottleneck = the slowest station

in a paced assembly line:
- parts flow through the line on a belt or chain that moves at a constant speed Parts moves through zones that contain one or more operators.
The line is designed so that the operators will almost have the time to complete their task
=> if not, line is disrupted Paced Assembly lines
Illustration Therefore, in paced assembly line, the bottleneck is the line-mechanism itself!

Additionally, capacity increments are usually much smaller in paced assembly line

Another justification for a balanced assembly line is one of personnel managment. Balanced lines allow to avoid « jealousy » between workers. Example technique for solving the LOB problem Unbalancing Flow Lines
Previous reasons for unbalancing flow lines suggest that a process with small and inexpensive capacity increments should never be a bottleneck. Example: 2 different process centers in a circuit board plant: copper plate – manual inspect

Manual inspect occurs befor the copper plate operation

Copper plate utilizes a machine that involves a chemical bath along with enormous amouts of electricity

Each machine has a capacity of 2000 panels per day

Adding a new machine at copper plate costs more that \$2 million and requires a significant amout of floor space.

Each of the stations in maunal inspect requires one semiskilled operator, an illuminated magnifier, and a touch-up tool.

Each stations can inspect around 150 pannels per day

Adding a new stations costs not more than \$100 Which station should be the bottleneck ???
Any question? Vincent Bollen
Gilles Coppens
Amaury Deckers
Julien Libert
François Van Lede Chapter 18: Capacity Management Operations Management and Factory Physics
LSMS2032 - Philippe Chevalier 06.05.2010 reminder : the problem consisits in assigning tasks on a paced assembly line so that each station has nearly the same amount of work.

n taks to be performed on each piece
t_i the time to do the ith task
k workstations
t_0 time allowed for each station
r_b = 1/ t_0
c the conveyor time

Objective : or

We consider only precedence constraints
Problem very complex NP-Hard
Example of LOB heuristic algorithm in 7 steps Example technique for solving the LOB problem (cont'd) Example technique for solving the LOB problem (cont'd) N = current station number
T = set of the tasks assigned to the current station
A = the time available to be assigned to the current station
S = set of available taks to be assigned
has to be an integer

we might be able to achieve a perfectly balance line with either 1,2,3 or 4 stations

Conclusion In this chapter:

We applied the factory physics framework
to the design of new production lines
and we improved existing ones
with respect to capacity.
Main Points:

Capacity decisions have a strategic impact on the competitiveness of the manufacturing operation.

Factory physics formulas can provide the basis for line design and improvement procedures. Main Points: (cont'd) Capacity additions and equipment or procedure modifications can be viable alternatives and/or complements to one another. Flow lines should generally be unbalaned. Paced assembly lines should generally be balanced Lines designed using factory physics procedures are likely to be more expensive than lines designed using a traditional minimum cost, capacity-feasible approach.

BUT:
- more likely to do what they are designed to do.
- more likely to be much more profitable in the long run.
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