Capacity analysis of complex materials handling

systems

Capacity calculation of a single conveyor sectionCapacity

The capacity of a material handling machine can be calculated from the

follow distance of two incoming unit loads (L) and the speed of the

moving unit load (v).

v

LQ = v / L

[piece/sec]

Relevant features

Reducing effect by mechanical interlockingTurntable

ADriven roller conveyors

vunit load

time

ω turntable

time

A

B C

B C

tcycle

tcycle = tmoving in + tturning right +tmoving out + tturning left

Capacity = 3600/tcycle [piece/hour]

Relevant features

Reducing effect by presence of multiple unit loads

Empty roller conveyor sections due to traffic control

vi+2th unit load

i+1th unit load

ith unit load

Sfollow

Capacity = 3600*v/Sfollow [piece/hour]

Traffic control’s principle:

If the unit load reaches end of the ith section, close down the i-1th section and free the i-2th section

Relevant features

Reducing effect by presence of branches

A

B1

Definition: Partial capacity limits for

different relations:

μAB1 = 3600 / tAB1

μAB2 = 3600 / tAB2

B2

If the actual material flows for

different relations are: AB1 and AB2

then the following equation is valid:

AB1 / μAB1 + AB2 / μAB2 1

AB1 , μAB1

AB2 , μAB2

μAB1

μAB2

Relevant features

Partial capacity limit example – opening branch

A

B1Transfer table for roller conveyor

μAB2 = 3600 / tAB2

B2

3

m

2

m

3

m

2,5

m

vunit load

time

v transfer table

time

A

tcycle

tcycle = tmoving in + ttransfer t. down +tmoving out + ttransfer t. up

Speed and acceleration data:

vunit load : 0,3 m/s aunit load : 0,2 m/s2

vtransfer t. : 0,2 m/s atransfer t.: 0,1 m/s2

4,6/0,3+0,3/0,2

2,5/0,2+0,2/0,1

3,4/0,3+0,3/(2*0,2)

2,5/0,2+0,2/0,1

Fundamentals of Production Logistic systems

Relation of materials handling and production logistics

Materials handling

Provision of materials’ transport services

Production logistic

Requirements on timing and relations

Operational characteristics of a production company

Operation in increasing market competition

Decreasing product life cycles

Continuous adaptive behavior required

Increasing product diversity

Flexible manufacturing systems

Necessity of continuously improving products and servicesRequirements on price

delivery time and reliability

Flexible materials handling and logistic services

Low stock amount and WIP ratesEconomical operation

required

Objectives of production logistic

Objectives of production logistic

Throughput time’s effect on the final value of a product

Production

coststotal

raw

material

workforce

amortizatio

n

techn.

time

techn.

time

throughput

time

wait time

wait time

value

production

cost

logistic

cost

profit

value function

production cost function

modified throughput

time

loss

value

total production

cost

Effect of stock amount on the production costs

Delivery cost Storage cost

n

NkK 11 nT

n

NkK

2

122

Total cost

nTn

Nk

n

NkK

2

121

Optimal delivered amount:

2

12

k

kNnopt

Representation of logistic objectives in throughput diagrams

Modelling possibilities of complex materials handling

systems

Model types

1. Logistic operation function models

2. Queuing models

3. Graph models

4. Petri net models

5. Simulation models

Characteristics: examination of production related logistic features such as WIP, throughput time, using throughput diagrams

Characteristics: examination of equipment related features such as length of the waiting queue, average waiting time, statistical distribution of the incoming arrivals, necessary number of servers.

Characteristics: modeling of static topology and examination of material flow related parameters.

Characteristics: modeling and visualizing of actual states and state changes

Characteristics: modeling of static topology, state changes. Widespread visual, analytic and optimization features.

Logistic operation function modelsCharacteristics: examination of production related logistic features such as WIP, throughput time, using throughput diagrams

Queuing models

Construction of queuing models:

Characteristics: examination of equipment related features such as length of the waiting queue, average waiting time, statistical distribution of the incoming arrivals, necessary number of servers.

arrivals (unlimited or limited length)

Server 1

Server N

.:

Model types:

1. Queuing model with unlimited arrivals and a single server

2. Queuing model with limited arrivals and a single server3. Queuing model with unlimited arrivals and multiple servers

4. Queuing model with limited arrivals and multiple servers

Applicability of explicite equations:

Arrival rate – Poisson distribution Service time – Exponential distribution(Markov model)

Queuing modelsM/M/1 queuing model: arrivals (unlimited length) Server

Calculation of optimal service rate:

Cost components

Queuing modelsM/M/S queuing model:

arrivals (unlimited length)

Calculation of the number of optimal servers:

Server 1

Server N

.:

Graph models

Directed graphs – for modelling continuously operating materials handling machines

Undirected graphs – for modelling non-continuously operating materials handling machines

Graphs: set of objects, where some pairs are connected by links.

Characteristics: modeling of static topology and examination of material flow related parameters.

Graph models

Mathematical representation of graphs using adjacency matrix.

5

2

3

4

6

1A =

12

5

3

4

1 2 3 4 5 6

1 -1 12 1 -1 13 -1 -1 -14 1 -15 1 1

Material flow related parameters:Material flow intensity vector: µ [piece/time unit] Nodal material flow intensity vector: µn [piece/time unit]

Relationship between µ and µn: µn = A µ

Example: roller conveyor system for unit loads having different traveling order.