# project sheet

```Bullwhip Effect
MAT 231 – Modelling – Fall 2015
Weeks: 11 – 12
Goal.
Understand that Supply Chain Management is hard(!) and attempt to model it.
Watch the short movie:
https://youtu.be/2nlmkTYZG5s
to understand a bit better about the bullwhip effect.
1
Bullwhip Effect
Near Beer Game (Novice).
MAT231 - Fall 2015
You own a (tiny) Beer Store.
your inventory and orders match the situation (so you don’t run low on inventory and you don’t accumulate
either).
From the second week, your customers start ordering 15 cases of beer instead.
It is you job to stabilize the whole supply chain as soon as possible.
Below is a screen from the “game”.
• New Orders from Customers: Number of beer cases your new customers want this week
• Cumulative Unfilled Orders: Number of beer cases that your old customers ordered and that you haven’t
filled
• Total Orders from Customers: Sum of the previous two values.
• Raw Material Orders: Order of Yeast (it takes one week for it to arrive)
• In Transit from Vendors: Yeast that will arrive next week
• Work in Process (Brewing): Beer is being made (it takes 1 week to finish)
• Finished Goods Inventory: Number of Cases of beer in stock ready to be sold
• Shipments to Customers: Number of Cases of beer sent to customers
• Unfilled Orders: Number of Cases of beer that can’t be filled (due to lack of cases in inventory)
2
Bullwhip Effect
MAT231 - Fall 2015
Go to
https://forio.com/simulate/mbean/near-beer-game/run/
The goal of the “game” is to try and stabilize the number of customer orders, your inventory, arriving orders,
and your order, so that you end up with the following situation
• Customer Orders: 15 cases every week (with no unfilled orders)
• Inventory: 15 cases
• Arriving Order: 15 cases
• Order 15 cases
1.
Play the “game” on Novice as a group and see how many weeks it takes to stabilize the situation.
Consider the following sequences:
• cn = number of beer cases ordered by customers
• un = number of cases ordered previously but not fulfilled yet
• in = number of cases in inventory
• on = number of cases ordered
• rn = number of cases of beer produced
where n is the number of weeks elapsed since the beginning of the “game”.
(a) What are the initial conditions (n = 0) ?
(b) What is the formula for cn ?
(c) What is the formula for rn ?
(d) What is in ?
(e) What is un ?
(f ) Decide on a strategy for ordering beer cases. Decide on a formula for on that can depend on n, cn ,
un , in , rn . Explain your choice.
(g) Run the “game” with your choice of on and confirm that your modelling is correct, that is, that your
variables follow the outcome of the game.
(h) What is the result of your strategy? Does it go “amuck” – bullwhip effect∗ ? Or does it control the
supply chain nicely?
∗ It’s
ok if it goes “amuck”! The goal is to see the Bullwhip Effect in action... Now try to fix it!
3
Bullwhip Effect
2.
MAT231 - Fall 2015
Play the “game” on Expert as a group and see how many weeks it takes to stabilize the situation.
Consider the same sequences as for 1.
The difference between Novice and Expert is that the customer orders go from 10 → 50 and every week
25% of unfilled orders are cancelled.
(a) What are the initial conditions (n = 0) ?
(b) What is the formula for cn ?
(c) What is the formula for rn ?
(d) What is in ?
(e) What is un ?
(f ) Decide on a strategy for ordering beer cases. Decide on a formula for on that can depend on n, cn ,
un , in , rn . Explain your choice.
(g) Run the “game” with your choice of on and confirm that your modelling is correct, that is, that your
variables follow the outcome of the game.
(h) What is the result of your strategy? Does it go “amuck” – bullwhip effect? Or does it control the
ordering nicely?
4
Bullwhip Effect
MAT231 - Fall 2015
Further Investigation.
1.
There is a more complex version of the game
https://beergame.pipechain.com/
which includes 1–4 players from 4 different stages of the supply chain. It takes 2 weeks for orders to arrive
to a different stage and it takes 2 weeks to fulfill a request.
(a) Play the game with 2 players† who do not communicate with each other, i.e., two-stage supply chain.
(b) Define the new sequences
• cn = number of beer cases ordered by customers
• on = number of cases ordered by the retailer
• sn = number of cases in the retailer’s stock
• pn = number of cases ordered by the producer
• qn = number of cases in the producer’s stock
(c) Make a similar study for this case. Observe that now you have to decide on the strategy for both on
and pn .
2.
Study the bullwhip effect and ways to avoid its effects.
† Create
a game and then use another computer to join the same game
5
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