ASSEMKIT.MOD

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Contents

Description

ASSEMKIT.MOD models a simple assembly operation (several different parts are put together to form a single unit called a "kit"). In this model, one part from Operation 1 (OPRN1) is joined with P parts from Operation 2 (OPRN2) to form a kit for assembly Operation 3 (OPRN3). A more generalized assembly operation for N parts can be modeled using vertex parameters.

State Variables

State Variables in ASSEMKIT.MOD
Variable Name Abbreviation Variable Description Size Type
QUEUE Q[i] Number of parts in queue i 4 Integer
SERVER S Status if assembly machine (IDLE/BUSY) = (1/0) 1 Integer
P P Number of type 2 parts needed for each assembly 1,1 Real

Vertices

Vertices in ASSEMKIT.MOD
Vertex Name Vertex Description State Changes
RUN The simulation is started None
OPRN1 Production in operation number 1 Q[1]=Q[1]+1
OPRN2 Production in operation number 2 Q[2]=Q[2]+1
KIT Kit arrival Q[1]=Q[1]-1, Q[2]=Q[2]-P, Q[3]=Q[3]+1
OPRN3 Beginning of assembly operation S=0
PACK End of assembly operation S=1, Q[3]=Q[3]-1

Initialization Conditions

Initialization Conditions in ASSEMKIT.MOD
Variable Description
P Initial number of type 2 parts needed for each assembly

Event Relationship Graph

ASSEMKIT.MOD
ASSEMKIT.MOD

English Translation

An English translation is a verbal description of a model, automatically generated by SIGMA.

The SIGMA Model, ASSEMKIT.MOD, is a discrete event simulation. It models AN ASSEMBLY OPERATION.
I. STATE VARIABLE DEFINITIONS.
For this simulation, the following state variables are defined:

Q[i]: NUMBER OF PARTS IN QUEUE I   (integer valued)
S: STATUS OF ASSEMBLY MACHINE (IDLE/BUSY) = (1/0)   (integer valued)
P: NUMBER OF TYPE 2 PARTS NEEDED FOR EACH ASSEMBLY  (real valued)
II. EVENT DEFINITIONS.
 Simulation state changes are represented by event vertices (nodes or balls) in a SIGMA graph.  
 Event vertex parameters, if any, are given in parentheses.
 Logical and dynamic relationships between pairs of events are represented in a SIGMA graph 
 by edges (arrows) between event vertices.  
 Unless otherwise stated, vertex execution priorities, to break time ties, are equal to 5.
1. The RUN(P) event occurs when INITIALIZATION OF THE MODEL.
   Initial values for, P, are needed for each run.
   This event causes the following state change(s):
   S=1
   After every occurrence of the RUN event:
   Unconditionally, START OPERATION 1; 
   that is, schedule the OPRN1() event to occur without delay.
   Unconditionally, START OPERATION 2;
   that is, schedule the OPRN2() event to occur without delay.
2. The OPRN1() event occurs when PRODUCTION IN OPERATION NUMBER 1.
   This event causes the following state change(s):
   Q[1]=Q[1]+1
   After every occurrence of the OPRN1 event:
   Unconditionally, SCHEDULE THE NEXT MACHINE 1 CYCLE;
   that is, schedule the OPRN1() event to occur in 2*ERL{1} time units.
   (Time ties are broken by an execution priority of 6.)
   If (Q[2]>=P), then PLACE THE PART IN A KIT;
   that is, schedule the KIT() event to occur without delay.
3. The OPRN2() event occurs when PRODUCTION IN OPERATION NUMBER 2.
   This event causes the following state change(s):
   Q[2]=Q[2]+1
   After every occurrence of the OPRN2 event:
   Unconditionally, SCHEDULE THE NEXT MACHINE 2 CYCLE;
   that is, schedule the OPRN2() event to occur in ERL{1} time units.
   (Time ties are broken by an execution priority of 6.)
   If (Q[2]>=P) and (Q[1]>0), then PLACE THE PART IN A KIT;
   that is, schedule the KIT() event to occur without delay.
4. The KIT() event occurs when KIT ARRIVAL.
   This event causes the following state change(s):
   Q[1]=Q[1]-1
   Q[2]=Q[2]-P
   Q[3]=Q[3]+1
   After every occurrence of the KIT event:
   If S>0, then BEGIN KIT ASSEMBLY;
   that is, schedule the OPRN3() event to occur without delay.
5. The OPRN3() event occurs when BEGINNING OF ASSEMBLY OPERATION.
   This event causes the following state change(s):
   S=0
   After every occurrence of the OPRN3 event:
   Unconditionally, PACK THE PART AFTER ASSEMBLY;
   that is, schedule the PACK() event to occur in 1.5*ERL{1} time units.
   (Time ties are broken by an execution priority of 6.)
6. The PACK() event occurs when END OF ASSEMBLY OPERATION.
   This event causes the following state change(s):
   S=1
   Q[3]=Q[3]-1
   After every occurrence of the PACK event:
   If Q[3]>0, then START ASSEMBLY ON THE NEXT KIT;
   that is, schedule the OPRN3() event to occur without delay.

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