Inventory Management Homework Problems Graph

OPMG-UB.0001.01Operations ManagementFall 2016Homework 6Solutions1. B&H is deciding how to manage the inventory of cameras that it sells. The demand for camerasat B&H is 200 cameras per week. Each time that B&H places an order for a new shipment ofcameras it must pay $80 in fixed processing fees. A camera costs B&H $60 to purchase. The costfor B&H to hold a camera in its store for one week is $4.00. Assume that the leadtime for thedelivery of a camera is 0 weeks.a. Suppose that B&H places orders for cameras in quantities of 50 cameras at a time and places anew order for cameras each time that it runs out. Draw a graph showing the number of camerasthat B&H has on-hand in inventory at each point in time up until the time when it places its fourthorder. Label the points in time at which B&H places a new order, showing the time at which eachorder is placed. Assume that B&H places its first order for 50 cameras on day 0.The demand rate for cameras at B&H isD= 200 cameras per week. Therefore, if B&H or-dersQ= 50 cameras at a time, then they will place an order everyQ/D= 50/200 = 0.25 weeks.See below for a graph of B&H’s inventory levels as a function of time.Figure 1: Inventory levels for B&H in Problem 1.ab. Suppose again that B&H places orders for 50 cameras at a time. What will be B&H’s averageholding costs per week? What will be B&H’s average fixed ordering costs per week?.If B&H places orders in sizes ofQ= 50 cameras, then their average inventory level will beQAV G=Q/2 = 50/2 = 25 cameras. Holding costs for a camera areH= $4.00 /camera/weekand therefore average weekly holding costs will beH×QAV G= $4.00×25 = $100.

So why are some operations more productive than others?

Why are some operations more responsive than others?

To answer these questions we have to go inside the business processes that

make up for the operations.

This is the purpose of this module, process analysis.

In this module, we're going to introduce the three most important performance

measures of an operation, which are called flow rate,

also known as the throughput, inventory, and flow time.

To motivate these three performance measures and

get some intuition on how process analysis works, I would like you to join me

once again over to our local subway restaurant, and just see what's going on.

We'll make ourselves outside, comfortable outside the restaurant and we'll

just spend a couple of hours observing how people come in and out of the restaurant.

Now we're here to learn not to eat, and so I will not let you get inside

the restaurant, instead I will give you an assignment.

of the customers that have arrived.

That means if the first customer arrived after two minutes and

30 seconds, you're going to draw the first point here.

If the next customer came in a minute later, at three minutes 30,

the second person has arrived and

you're going to plot another data point over here.

So, step-by-step, you're going to draw the times of which customers arrive

The horizontal difference between our lines

is the amount of time the customer spent in the restroom.

We saw this was the first customer who arrived after roughly

30 seconds of observation time and then left after two minutes.

And then we see later on that some customers have a little longer wait.

So for example if you look here at the seventh customer, this person came in

around here and it took until here, until this person was leaving.

This suggests that there was beyond the activity times in the process potentially

a fair bit of waiting going on.

Now before we can do any process analysis we first have to define

what we want to analyze.

We defined the flow unit of the process as the atomic unit of analysis.

In this case we want to analyze the flow of customers.

Note that we could also analyze other things in the process, for example,

the flow of cheese, the flow of money, the flow of sandwiches, or other things.

The flow rate is the incoming and, or the graduating class, so

simply the number of students going through the process per year.

The processing time at least here at Wharton, it's a two year program, so

that's the time that the student spends at school.

The inventory time is the total number of students on campus in the first year and

in the second year.

And the flow rate is the amount of cars sold every year.

So flow time is the time from the beginning of the production to the time

that the vehicle is finally sold, and the inventory of the cars and the system.

Notice that only in the second and fourth case here,

my definition of inventory will be similar to the world of financial accounting.

In this case here, and in this case here or the service settings, these

are flow units that I would never show up on the balance sheet of an organization.

So inventory, the number of flow units in the system.

Flow rate, the number of flow units going through the system per unit of time.

And flow time, the amount of time it takes a flow unit to go

from the beginning of the process to the end.

I said at the beginning of this session that those are the most important

performance measures in any operations.

But why?

Who cares about inventory?

Now let me give you some reasons to care about inventory.

In the US economy alone, in a typical year,

we have about $1 trillion of inventory.

And that is just the manufacturing sector, because this is accounting inventory.

Now my colleagues in Economics Department,

they kind of like to ignore the supply-demand mismatches.

They take comfort in the notion of markets and

that prices will adjust once we have a mismatch between supply and demand.

However, if you are sick, and

you're sitting in an emergency department prices were not source of problem.

If you're hungry waiting for your lunch, this is not a matter of prices.

For this reason I argue that understanding inventory, flow rate, and

flow time are indeed the most important issues,

not just what we do in operations, what we do in management in general.

So, keep those three measures in mind when, next time,

you go through a process, be it as a tourist, as a person going for

lunch or when you have a chance to tour a factory.

And always look for the three things, flow rate, inventory, and flow time.

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