Frequently Asked Questions in Preparation for Exam 1.
On the Case Study:
Q: On slide 39 it says that Denver ships 2.5 times per year. What equation did you use to determine this? It also says that Indianapolis ships 1.6 times per year. How was this determined, and why do you calculate inventory by 500,000/3.2? Why are you dividing by 3.2 and how did you determine to divide by this number?
A: I illustrated this calculation for Green Bay on slide 37. I did not repeat it for Denver and Indianapolis as the technique is the same.
For, Denver, for example, a truckload has 1,000 Consoles and a DC sells 2,500 Consoles per year so Denver has to replenish 2.5 times per year.
Why 500,000/3.2? Remember, in the simultaneous shipments case, all the DCs are on the same "clock" they are replenished at the same time. Indianapolis sells 500,000 monitors each year (1 per Computer and 1 per TV) and ships out to all the DCs (under simultaneous shipments) 1.6 times per year. So, each shipment is roughly 500,000/1.6 monitors. The plant builds up that quantity and ships it and then repeats the process. So the average amount of inventory staged in shipping is half that or 500,000/3.2.
Q: On slide 41, how did you get approx. 6 days for when the
peaks occur?
A: I translated the annual demand at the stores into daily demand -- 100 DCs each selling 10 CPUs a day. That's 1,000 CPUs each Day. I assumed that's how fast we make them as well. A truck holds 6,000 CPUs, so it takes 6 days of production to fill it.
Q: On slide 53, why do you have 1,000 per day? Is this supposed to represent an average trip of 1,000 miles?
A: No.
It is 1,000 per day --- see my answer to the previous question.. 100 DCs each
selling 10 a day. That means we have to send 1,000 each day out of the Indianapolis
cross dock and so, I assume that's how many we have to send to the cross dock
each day. If it takes 2 days to get there, there will always be 2,000 CPUs (on
average) on the road to Indianapolis --- that's the pipeline inventory.
Q: How did you come up with $513,900 on slide 64 for the Inventory Costs at Plants under the Consolidation strategy?
A: That includes two components:
Add those all up and you get $514,080 (Frankly, I don't know what happened to the $180. Perhaps we took the shipping staff to lunch one day)
Q: The total costs don't always add up correctly.
A: Ok, Ok. So I'm lazy. Sometimes I (incorrectly) failed to include pipeline inventory. But I think you still get the point about the differences, no?
On the EOQ formulas
Q: Huh?
A: That's a good question. Let me try to answer it. We consider three (or even 4) different models in this analysis.
In the first model we typically view the distribution center in isolation. The supplier is a different company and we are not concerned about the inventory we create there. In this case, receiving shipments of Q creates average inventory of Q/2 at our DC and so that's the average inventory we consider.
In the second model, the supplier is part of our company and so we are concerned with the inventory at that plant. The case of shipments from the plants to the cross dock in Indianapolis fits this model perfectly. Shipments of size Q create average inventory of Q/2 both at the plant and at the cross dock so we use average inventory of Q/2 + Q/2 = Q.
In the third model, the supplier is part of our company and has far more capacity than our little DC needs. The case of direct shipments from a plant to a DC is a perfect example of this. The point of this model is that since the plant has so much capacity, our DC's little orders for Q create far less than Q/2 average inventory at the plant. Why is this? Well, let's adopt the notion that the plant fills our orders just-in-time, i.e., it dedicates all its capacity to filling our order for a short time before it ships that order.
The first question is how long will it take the plant to fill our order? Well, looking at slide 12 of the Frequency notes, if the plant produces at Production Rate it will take Q/Production Rate to build a quantity Q. The item-days of inventory created in the process will be the area of the triangle or Q²/(2*Production Rate) and the item-days per year at the plant from building shipments for this DC will simply be this quantity times the number of shipments per year to this DC or D/Q. So, the total item-days of inventory at the plant just for shipments to this one DC will be
Q²/(2*Production Rate)*D/Q = Q*D/(2*Production Rate)
So now we can figure out the total cost of making shipments of size Q to this DC:
This would probably have been clearer if we went on to consider model 4: Let's look at how the "optimal" shipment quantity to a DC depends on the distance between the DC and the plant. Till now, we have blithly assumed every DC was the average distance or 1,000 miles from the plant. Till now, that's been a pretty safe assumption because all the calculations involving distance have been linear -- using the average did not create any inaccuracy. But in calculating the optimal shipment quantity, A, the transportation cost that depends on the distance, is under the square root.
So, the optimal shipment quantity to the closest DC, which is only 60 miles from Green Bay is:
Q* = SQRT[2*A*D/hC]SQRT[P/(D+P)] = Q* = SQRT[2*60*2,500/0.15*300] SQRT[250,000/(2,500+250,000)] = 81
While the optimal shipment quantity to the most distant DC, which is 2,244 miles from Green Bay is
Q* = SQRT[2*A*D/hC]SQRT[P/(D+P)] = Q* = SQRT[2*2244*2,500/0.15*300]SQRT[250,000/(2,500+250,000)] = 497
Q: Ok, I got that sort of, but what's this about "item-days"? You talked about "item-days of inventory". What's that all about?
A: One of the main components of inventory carrying cost is the cost of the money tied up in inventory. Think of it as a loan. We borrow money to invest in inventory. How do we pay the interest on that loan? Well it's based on how much we borrow and how long we borrow the money for. That's the time value of money. Our inventory carrying cost of 15% is really $0.15/per dollar in inventory/year. So, to get the cost of holding inventory we need the "interest rate" h, the value of the items in inventory C and the item-years (ok, so I changed the units, but you get the picture) we had tied up in inventory -- how much, for how long. Got it? You pay the same inventory carrying cost whether you put 1,000 items in inventory for 2 years or you put 2,000 items in inventory for 1 year. They are both 2,000 item-years of inventory.
Q: On slide 13, you ask what making shipments of size Q to
DC#1 adds to the average inventory at the plant. Is the answer to this question
Q*Demand at DC/
(2*Production Rate) or is it less than Q/2?
A: Q*Demand at DC/(2*Production Rate), which, by the way, is a lot less than Q/2, but is also more specific.
Q: On slide 14, when you mention correct EOQ for Direct Shipments
are you referring to modifying the one plant to one DC EOQ formula to handle
one plant
to many DCs?
A: Yes, the following line shows the correct total avoidable cost formula, which includes inventory at the plant, at the DC and the transportation or ordering cost.
Q: On slide 17, inventory costs at plant is Q/2 and at DC
is Q/2 which leads to total inventory costs of 101*Q/2. How do you get this?
What does the 101
represent?
A: Turns out that if all the DCs place orders of size Q, the inventory at the plant (from filling all the orders) will be Q/2 so we will have 100 + 1 locations with average inventory Q/2, i.e., the 100 DCs and the plant.
Q: On slide 18, is the cost of Direct EOQ the sum of transportation
costs and inventory costs? On slide 22 is the total cost of consolidate and
EOQ the sum
of transportation, inventory, and pipeline inventory costs? (I could not get
the numbers to add up correctly.)
A: Apologies, these numbers may omit pipeline inventory costs. I got lazy. All three figures should include transportation costs, the inventory carrying costs at the plants, the DCs and the cross dock (if any).