Machine Simulation

Impact of Buffer Size on Throughput

Introduction

The workbook MACHSIM1.XLS allows the user to simulate the impact of changing the buffer size on the throughput from a system with two machines, one feeding the other. The workbook is written using Microsoft Excel Version 5.0. The system being simulated is as follows. There are two machines in series with the first machine feeding a buffer that feeds the second. It is implicitly assumed that the first machine always has access to raw material.

M/C 1 M/C 2

Raw Material Buffer

The simulation proceeds period by period. In each period there is a probability p that machine 1 will produce a usable part. Similarly there is a probability p that machine 2 will produce a usable part. In order for machine 2 to produce however, there must be material available in the buffer between machines 1 and 2. The user is allowed to specify a maximum buffer size. This in any period, if the buffer is full and machine 2 does not draw any part from the buffer, then machine 1 is not allowed to produce. Thus in each period, machine 1 produces a part with probability p if the buffer is not full or machine 2 draws a part. Machine 2 produces a part with probability p as long as the buffer is not empty.

The user is allowed to simulate the process for a specified number of periods and record the statistics for later use. The input area is located on sheet1 while the statistics are store on sheet3. The simulation itself is performed on sheet2 which is currently hidden. Students interested in seeing the simulation can unhide sheet2.

Buttons

There are five buttons in the input area that represent automated tasks which simplify the users job. The buttons are described as follows:

Simulate: Clicking on the simulate button will set the simulation in motion given the input parameters. The system is simulated for the specified number of periods and some results displayed. Before clicking on the simulate button make sure that the input parameters in Cells F21, F23, F25 are set as desired, and the old simulation has been cleared using clear simulation.

Clear Simulation: The clear simulation button should be clicked on before a new simulation is run. This clears up the simulation area for a new simulation. After clicking on the clear simulation button, enter the input parameters and then simulate.

Statistics: Clicking on the statistics button saves the input and output statistics of the current simulation as a row on a table. The statistics are saved on sheet3.

Clear Statistics: Clicking on the clear statistics button clears away all the old statistics from the table in sheet3.

Print Statistics: Clicking on the print statistics button prints the table of statistics collected so far.

WARNING: PLEASE DO NOT ATTEMPT TO ALTER EITHER SHEET2 OR SHEET3. ALWAYS CLICK ON RESTORE AND RESTORE STATISTICS WHEN STARTING FRESH. THIS WILL INITIALIZE ALL SHEETS.

Details of the inputs and outputs are described below:

Inputs

The inputs entered by the user are as follows:

Probability of production in a given period (p) (Cell F21): Given available raw material, p represents the probability that a machine will produce in a given period. The model assumes the probability to be the same for each of the two machines. However the realization of production for the two machines is independent

Maximum size of buffer (Cell F23): Here the user enters the maximum permissible size of the buffer. If the buffer is full, and machine 2 does not produce in the period (i.e., no material is drawn from the buffer), then machine 1 is not allowed to produce either. The simulation assumes that the buffer has one unit to start with.

Number of periods to simulate (Cell F25): The user enters the number of periods for which simulation is to be performed.

Each of the above inputs must be in place before simulate can be called.

Results

The results on sheet1 are as follows:

Production rate per shift (Cell F29): This cell gives the production rate (or throughput) per shift (480 periods) over the course of the simulation.

Average inventory in buffer (Cell F30): This cell contains the average inventory in the buffer over the course of the simulation.

Proportion of periods that buffer is empty (Cell F31): This cell contains the proportion of periods in the simulation that the buffer is empty.
Proportion of periods that buffer is full (Cell F32): This cell contains the proportion of periods in the simulation that the buffer is full.

The statistics are saved each in sheet3 time the statistics button is clicked on. These are the statistics that result for the given simulation. The statistics saved are: p, Maximum buffer size, Throughput, Average inventory, Probability (buffer is empty), Probability (buffer is full), and Simulation length. The chartsheet chart1 contains a plot of the quantity in buffer over time.

How to simulate and store statistics

Assume that you want to run several simulations for p = 0.7 and buffer sizes varying between 2 and 7 and store these statistics. Assume that you want to run the simulations for 480 periods each.

  1. Click on the clear simulation and clear statistics buttons. Set I = 7.
  1. Enter 0.7 in Cell F21, I in Cell F23.
  1. Enter 480 in Cell F25 and click on the simulate button.
  1. Click on the statistics button. The statistics for the current parameter values are saved on sheet3.
  1. Set I = I -1. If I 2 enter I in Cell F23 and go to 4, else stop.

The above sequence of steps will provide the user with statistics for buffer sizes ranging from 2 to 7 for a single simulation. To run another simulation click on clear simulation, set I = 7, and go to step 2. To change the parameters, click on clear simulation, set new parameter values, and repeat steps 2 to 5. When you have a sufficient number of statistics, click on print statistics to get a print out. Do not click on clear statistics at an intermediate stage, else the old statistics will be lost.

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