Capacity analysis of complex materials handling systems

Relevant features Reducing effect by mechanical interlocking Turntable A Driven roller conveyors v unit load time ω turntable time A B C B C t cycle t cycle = t moving in + t turning right +t moving out + t turning left Capacity = 3600/t cycle [piece/hour]

Relevant features Reducing effect by presence of multiple unit loads Empty roller conveyor sections due to traffic control v i+2 th unit load i+1 th unit load i th unit load S follow Capacity = 3600*v/S follow [piece/hour] Traffic control’s principle: If the unit load reaches end of the i th section, close down the i-1 th section and free the i-2 th section

Relevant features Reducing effect by presence of branches A B1 Definition: Partial capacity limits for different relations: μ AB1 = 3600 / t AB1 μ AB2 = 3600 / t AB2 B2 If the actual material flows for different relations are: AB1 and AB2 then the following equation is valid: AB1 / μ AB1 + AB2 / μ AB2  1 AB1, μ AB1 AB2, μ AB2 μ AB1 μ AB2

Relevant features Partial capacity limit example – opening branch A B1 Transfer table for roller conveyor μ AB2 = 3600 / t AB2 B2 3 m2 m3 m 2,5 m v unit load time v transfer table time A t cycle t cycle = t moving in + t transfer t. down +t moving out + t transfer t. up Speed and acceleration data: v unit load : 0,3 m/s a unit load : 0,2 m/s 2 v transfer t. : 0,2 m/s a transfer t. : 0,1 m/s 2 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 services Requirements on price delivery time and reliability Flexible materials handling and logistic services Low stock amount and WIP rates Economical operation required

Objectives of production logistic

Throughput time’s effect on the final value of a product Production costs total raw material workforce amortization techn. time throughput time wait time value production cost logistic cost profit value function production cost function modified throughput time loss value total production cost

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 models Characteristics: 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 server 3. 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 models M/M/1 queuing model: arrivals (unlimited length) Server Calculation of optimal service rate: Cost components

Queuing models M/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 A = Material flow related parameters: Material flow intensity vector: µ [piece/time unit] Nodal material flow intensity vector: µ n [piece/time unit] Relationship between µ and µ n : µ n = A µ Example: roller conveyor system for unit loads having different traveling order.

Petri net models Petri net: special bipartite graph for the description of discrete distributed systems. Components of a Petri net: Places Transitions Input functions Output functions Tokens Rule of operation: A transition in a Petri net may fire if there is at least one token at the end of each corresponding input places. By firing a transition one token is subtracted from each input place and one added to each output place.

Petri net models 1. Petri net example: Load handling of two different products by two robots 2. Petri net example: Closing branch

Simulation models Characteristics: modeling of static topology, state changes. Widespread visual, analytic and optimization features. Application of specialized simulation software, e.g: Arena, AutoMod, Enterprise Dynamics, Plant Simulation, Simul8, Witness, Promodel...)

Simulation: Modeling of real processes, where realness of the different aspects correspond to the modeling goals. Goals of simulation: To construct a certain copy of the reality for analyzing purposes, before any costly modification would be implemented in the system. Ancestors of simulation: graphs, Petri nets, Monte-Carlo methods Application fields of simulation: - There are no analytical methods for the problem’s solution, or they application would be too complicated. - Normal operation processes obstacle experiments. - Experiments on the real system would be too dangerous. - Experiments on the real system would take too much time. - The system is too complex to overview. - The system’s operation is probabilistic. - The result cannot be sensed. - There is only a single system. Simulation models

Main objects of production logistic systems: Modeling time in simulation software: - event controlled - time step controlled Simulation model’s components for manufacturing/ and material handling systems: - objects (manufacturing and materials handling machines, tools, unit loads, workforce...) - activities (warehousing strategies, manufacturing processes...) - events (internal and external events) - queues (inter manufacturing stocks) - features (number of work pieces / unit load) - settings (number of analyzed time interval Simulation models Static structure of machines Dynamically appearing and disappearing workpieces, goods etc.

1. System structure and input data analysis (25%) 2. Modell building (35%) 3. Result’s analyse (40%) Project goal determination Components of the necessary output Setting data structure Constructing and initial model Modell’s improvement and correction Model’s evaluation using former data Planning and setting experiments Results’ evaluation Documentation Simulation models Steps of a simulation project:

Simul8 overview

Simul8 object types Work entry pointStorage bin Resource

Simul8 object types Work center

Simul8 object types Conveyor

Simul8 object types Tanks and pipes

Simul8 object types Work exit points Groups Components

Application of simulation software for modeling assembly systems Manufacturing of prod 1. Assembly (1+1) Manufacturing of prod 2. Branch