Operations management using System Dynamics

Part II

Learning Objective

After this class the students should be able to:

Model and simulate a simple model for management operation using STELLA, a software based on System Dynamics, and

Understand how to model time as dependent variable.

Time management

The expected time to deliver this module is 50

minutes. 15 minutes are reserved for team

practices and exercises, 15 to practice “what-if”

and 20 minutes for lecture.

The problem from part I

Consider a store where people:

• people enter,

• receive some service, then

• move to the cash register and

• have to wait in a checkout line before they can pay

and leave.

The problem form part I Only one person can be served at a time, and initially

one person is already at the service center being served. It takes 5 minutes to be served and 1 minute to get from the service center to the checkout line.

There are already 8 people waiting in the checkout that last 2 minutes, and one person is currently being served. One customer arrives every 4 minutes and the first customer arrives in the third minute after we began the analysis

Exercise

The teams are invited to preset the diagram of model developed in the last class (part I), and then they are asked to try to figure out the possible behavior of the service line, the checkout line, and of the shopping time. (20 minutes)

Time

Che

ckou

t lin

e

Ser

vice

t lin

e

Sho

ppin

g tim

e

Reservoir

The STELLA software uses stocks to represent state

variables. Its default stock type is the Reservoir. A

Reservoir passively accumulates its inflows, minus its

outflows at each DT.

Conveyor, Queues and Ovens

In reality, many stocks receive inflows and result in outflows only at particular periods of time, depending of the process that is being modeled. All of this situation can be modeled using Reservoir, but it can be simplified by using the other versions of stocks offered in STELLA Conveyor, Queue, and Oven.

Conveyor

Think of a Conveyor as a conveyor belt. Material gets on the Conveyor, rides for a period of time (each DT) and then gets off.

Queue

Similar to Conveyor, think of a Queue as a line of items awaiting entry into some process or activity (e.g., grocery store checkout line, airport ticket counter line). Queues are FIFO (first in - first out) in their operation. Stuff enters the queue, and remains in line, waiting its turn to exit the Queue.

Oven

Think ovens as batch production system like the a bakery process. It opens its doors; fills (either to capacity or until it is time to close the door); bakes its contents for a time (as defined by its outflow logic); then unloads them in an instant.

Modeling

So far on, we will build together, step by step,

the model using the software Stella. Then,

we will practice “What-if”.

Modeling people arriving

The inflow of people into the store can be modeled, as before, with a unidirectional flow. Let us call it ENTER and specify it later.

?

ENTER

People going to be served

Upon arrival, people wait in line, the SERVICE QUEUE, to be served at the SERVICE CENTER. Place two stocks in your STELLA diagram, one called SERVICE QUEUE and one called SERVICE CENTER. Connect both with a flow called GET SERVICE.

People going to be served

Upon arrival, people wait in line, the SERVICE QUEUE, to be served at the SERVICE CENTER. Place two stocks in your STELLA diagram, one called SERVICE QUEUE and one called SERVICE CENTER. Connect both with a flow called GET SERVICE.

?

ENTER

?

GET SERVICE

?

SERVICE QUEUE

?

SERVICE CENTER

People going to checkout line Next, place a stock on the diagram, call it TRANSFER,

and connect it with a flow to the SERVICE CENTER. Choose another stock for the CHECKOUT LINE, with inflow, called MOVE TO CHECKOUT, from TRANSFER.

People going to checkout line Next, place a stock on the diagram, call it TRANSFER, and

connect it with a flow to the SERVICE CENTER. Choose another stock for the CHECKOUT LINE, with inflow, called MOVE TO CHECKOUT, from TRANSFER.

?

ENTER

?

GET SERVICE

?

SERVICE QUEUE

?

LEAVE SERVICE CENTER

?

SERVICE CENTER

?

MOVE TO CHECKOUT

?

TRANSFER

?

CHECKOUT LINE

People going to Cash Register The final stock, is the CASH REGISTER, capturing the people

currently paying. The final stock, is the CASH REGISTER, capturing the people currently paying. Connect the stock TRANSFER to CASH REGISTER with a flow called PAY, and an outflow into a cloud to represent the people leaving the store.

?

ENTER

?

GET SERVICE

?

SERVICE QUEUE

?

LEAVE SERVICE CENTER

?

SERVICE CENTER

?

MOVE TO CHECKOUT

?

TRANSFER

?

CHECKOUT LINE

PAY

?

LEAVE

?

CASH REGISTER

Complete diagram The final stock, is the CASH REGISTER, capturing the people

currently paying. The final stock, is the CASH REGISTER, capturing the people currently paying. Connect the stock TRANSFER to CASH REGISTER with a flow called PAY, and an outflow into a cloud to represent the people leaving the store.

Inputting parameters

Now that we have laid out the model, let us specify the stocks and flows. Open the SERVICE QUEUE stock and specify it as a queue with an initial value of 2, assuming two people are already waiting to be served.

Recognize that once you click on OK, the question mark will disappear, not only in the stock icon but also in the GET SERVICE flow. STELLA recognizes that the outflow from an oven is determined by its cook time.

Inputting parameters Next, open the SERVICE CENTER stock and specify it as

an oven with an initial value of 1, for the person already being served, and a "cook time" of 5. The cook time of 5 minutes defines the duration of items in the oven.

Similarly, specify the TRANSFER stock as a conveyor, set its initial value to 0, assuming no people are currently on their way from the service center to the checkout line, and the transit time as 1, corresponding to the 1 minute it takes to walk to the checkout line. Click on OK, and the question mark in MOVE TO CHECKOUT will disappear.

Inputting parameters

Now specify the state variable CHECKOUT LINE as a queue, with a initial value of 8, for the eight people waiting in line. When you click OK, the question mark in the outflow PAY will disappear. People coming out of the checkout line are assumed to pay at the CASH REGISTER before they can leave the store. The CASH REGISTER is specified as an oven with a cook time of 2 minutes, and we assume that currently one person is being served.

Model almost ready Our model should now look like the one below:

?

ENTER GET SERVICE

SERVICE QUEUE

LEAVE SERVICE CENTER

SERVICE CENTER

MOVE TO CHECKOUT TRANSFER

CHECKOUT LINE

PAYLEAVE

CASH REGISTER

Modeling people arriving Now, we are going to specify the rate of arrival of

customers into the store. One customer arrives every 4 minutes and the first arrives in the third minute after we began to run the model.

The PULSE built‑in function is designed to model such a case. We specify

Volume of the pulse

length of the interval

initial occurrence

ENTER = PULSE(1, 3, 4)

Modeling people arriving

Additionally, we time‑stamp the in flow into the store and the outflows from the store. This is done by checking the Time‑stamp check box in the upper right‑hand corner of the ENTER flow diagram:

Cycle time To calculate the shopping time, We will use the built‑in

function Cycletime with people leaving the bakery as argument.

This built‑in function requires for its specification, as its first input, a flow whose cycle time is calculated and, as a second input, a weight. When no weight is specified, Cycletime will return the per batch cycle time independent of volume.

When the weight is set to 1, it will return the per‑unit volume cycle time. The latter specification is chosen in our model:

SHOPPING TIME = CYCLETIME(LEAVE)

MEAN SHOPPING TIME = CTMEAN(LEAVE,1)

The complete model

ENTER GET SERVICE

SERVICE QUEUE

LEAVE SERVICE CENTER

SERVICE CENTER

MOVE TO CHECKOUT TRANSFER

SHOPPING

TIME CHECKOUT LINE

PAYLEAVE

CASH REGISTER

MEAN

SHOPPING TIME

Checkout line & Service Queue

Shopping time behavior

Practicing What-if

Each is invited to suggest alteration in the model or parameters, and figure out the possible results. Then, compare what was figure out by the students and the new output. (15 minutes)

Homework Assume you are the manager of a store of this type, but

you are lucky to have two service centers and two cash registers. There are three employees in your store, each of whom is qualified to work at the SERVICE CENTER and at the CASH REGISTER. An employee can be at only one place at one point in time. It is your task to decide when to have both service centers open and when to have both cash registers open. Find a work schedule that minimizes the mean shopping time over the course of an 8 hour workday. Then, assume that you need to give your employees a set of breaks from their work; for example, two 15 minute breaks each in the morning and afternoon, and a 1 hour lunch break. How does this influence the "optimum" work schedule?

Reference

Modeling Dynamic Economic System.

Ruth, M. & Hannon, B. Springer, 1997,

Chapter 4