Inventory Control

Transcription

Inventory Control

Fifth session :
"Inventory Control"
Objectifs : Comprendre les techniques de gestion des stocks et les paramètres qui
s’y rapportent.
Contenu : - Exercice préliminaire à réaliser en salle d'
info avant la séance
d'
exercice (pages 2 à 10). Attention, cet exercice contient certaines
notions qui ne seront plus revues dans les autres exercices ;
-Correction de l’exercice préliminaire réalisé en salle d’info (pages 12
à 14);
- Enoncés des exercices (pages 15 à 17);
- Solutions des exercices (pages 18 à 21).
T.P. :
- Exercice à réaliser impérativement par deux en salle d’informatique;
- Plage horaire et locaux (voir annonce aux valves);
- Démarrage: Double-cliquez sur “p:\prod2100\level1.xls”.
Site WEB : - Il est possible de se procurer le fichier level1.xls sur la page WEB
suivante :
http://www.prod.ucl.ac.be/enseignement/notes/prod2100.html
Fifth session : Inventory Control
1
Computer Laboratory : Inventory Control
Problem Description
This game aims at getting familiar with the inventory control policies. The problem is
simple : one warehouse, one retailer and one product. The items flow from the
warehouse to the retailers where they are sold. The average demand at the retailers is
0.5 item per day (half a kilo for example).
You are the retailer and have to decide when and how many items should be ordered
from the warehouse. Your goal is to maximise the profit over a period of time.
Costs are due : -for placing orders at the warehouse (order cost);
-for holding items as soon as they are ordered (pipeline and holding cost).
Revenues are generated by selling items.
Software Description
You should get a similar screen to the following one.
CON T R OL
Warehouse ->
R e se t va lue s
S imula te 1 da y
S imula te 1 ye a r
Supply lead time (days)
Demand Distrib. (U, N, C)
Review period (days)
Initial inventory
Reorder point
Order quantity
Order up to level
7.0
0
<- order
transit(-4)
transit(-3)
transit(-2)
transit(-1)
for tomorrow
<- inventory
demand
sales
IAG 1997
S ta tistics on da y:
#sales
0
#demands
0
fill rate
0
#stockouts
0
#cycles
Retailer -> 0
stockout freq
today's 1
pipeline cost
today's 0
holding cost
Lt = 4
order cost
Type = u
total profit
Rp = 10 1 year = (days)
Io = 2 New random list(True,Fal.)
R=
Unit Profit ($/item)
Q=
Unit Holding cost ($/item/day)
Qmax = 6 Unit Order cost ($/order)
Inventory Control : Description
5.0
100
46
53
0.87
3
10
0.30
7.04
8.16
10
1354.8
100
FALSE
30
0.04
1
IAG/93-94
This3.0
game aims at getting familiar with the inventory control policies.
The1.0
problem is simple : one warehouse and one retailer.
The-1.0
items flow from the warehouse to the retailers where they are sold.
The average daily demand is 0.5. The distribution is either Constant (0.5) or Uniform (either 0 or 1).
The screen is divided into 5 different parts: the control part (top left), the daily status
(top center), the global statistics (top right), the data (middle) and a chart (bottom).
These different parts are detailed in the following four pages. If you want, you can
immediately move to the cases and refer to those explanations when needed only.
2
Help page 1: Data ( middle - green on the screen )
Meaning
The lead time is the number of days you will have to wait before
getting your order. It should remain in [0, 5] days. A lead time of
0 means that the order placed on the evening comes for the next
day morning. If your lead time is 1, your order will arrive one
day later. So, if you order on Monday evening, your order will
arrive on Wednesday morning.
Demand Distribution C = constant (the daily demand is 0,5);
(U, N, C)
U = uniform (the daily demand is variable and equals 0 or 1 with
Type=
probability 1/2);
N = normal (the daily demand is variable and distributed as a
normal function with a daily average demand of 0,5).
Review period (days) Number of days between two checks of the inventory level. An
Rp=
order can be placed only at the end of a review period.
If review period = 0, this is equivalent to a permanent review.
If review period > 0, then you are in a periodic review. In this
case, you check your inventory every (integer) Rp days.
Initial inventory
The initial inventory is the inventory you have at day zero and
Io=
that you can use at the beginning of the game. It allows you to
avoid problem at the start of the simulation, before your policy is
effective, otherwise you could miss some sales before your first
order is delivered.
Reorder Point
Used when your are in permanent review. The order point is the
R=
level of your inventory position at which an order of size Q is
automatically placed (when simulating a whole year).
Order Quantity
Used when you are in permanent review. The order quantity is
Q=
the quantity which is ordered when the reorder point is reached.
Order up to level
Used when you are in periodic review. Every review period, an
order is placed. The size of the order is the difference between
Qmax=
Qmax and the current inventory position. This difference is
calculated for you in the soft. You only have to choose Qmax.
1 Year (days)
The period of time during which your inventory control policy
will be simulated. A normal (but modifiable) value is 100 days.
New random list
If true, then a new random sequence is generated for the run.
(true or false)
Otherwise, a same pre-computed random sequence will be used.
Unit profit ($/item) The difference between the selling price and the purchase cost
gives the profit you make when selling 1 unit. Set to 30 $/item.
Unit Holding cost
Cost generated by holding one item one day in your inventory or
($/item/day)
in the pipeline (truck). Set here to 0.04 $ / day / item.
Order cost ($/order) Cost generated by each order you place at the warehouse. Set
here to 1 $ / order.
On your screen, the light green part (on the left) corresponds to the data (Lt, Type, Rp)
you have to enter according to your assignments and to the inventory control policy
you want to simulate (Io, R, Q, Qmax).
The dark green data are the simulation parameters and the cost data. These parameters
should normally not be modified.
DATA
Supply lead time
(days)
Lt=
3
Help page 2: Control, daily status and Statistics (Top of screen)
Click control buttons (top left - grey)
Reset values
The simulation restarts at zero, all the former statistics are erased. The
retailer inventory is set to Io.
Simulate 1 day The program simulates the demand for 1 day, determines the daily
sales and the new inventory position, and updates all the statistics.
Simulate 1 year The program simulates your strategy for one year (100 days).
Every day, it determines the demand, the sales and the new inventory
position. According to your policy, an order is possibly placed.
All the statistics are recorded.
Warehouse
Order
Transit from
warehouse to
retailer
Retailer
Inventory
Demand
Sales
Daily Status (top center; white and red)
is the quantity you order at the warehouse. You only have to type in
your order when you work day by day.
describes the transit of the order when you work day by day.
Enter for example a lead time of 5 days and a warehouse order of 2
items and click several times on ""Simulate 1 day"". Look at the
transit: the ordered items will go from "transit 4" to "for tomorrow"
before being in your stock.
shows what you have in your inventory (on the evening of the current
day). It is used to serve the demand and is replenished by your orders.
shows the retailer demand of the current day.
show the retailer sales of the current day.
Statistics (top right ; yellow)
Statistics on day Number of days you already simulated. All the statistics correspond
to the period from day 0 evening up that day, on the evening.
# sales
Number of sales made (up to the current evening).
# demands
Number of demands placed (up to the current evening).
fill rates
The fill rate observed over this period: = # sales / # demands.
# stockouts
Number of cycles where a stockout has been observed.
# cycles
Number of cycles observed in the simulated period. A cycle is
counted each time an order is received.
stockout fr.
The percentage of cycles with stockout: = # stockouts / # cycles.
Pipeline cost
Cost generated up to now by all the ordered items when they are "in
(Pc)
transit". Per day, it is equal to (# units in transit that day × 0.04).
Holding cost
Cost generated up to now by the items that remained in your
(Hc)
inventory.
Per day, it is equal to (average # of items in inventory that day ×
0.04). The average is taken between the morning and the evening.
Order cost
Cost generated by the orders you placed at the warehouse. Per day, it
(Oc)
equals 1 if an order is placed, 0 otherwise.
Total Profit
= (unit profit) * # Sales - Order cost - Holding cost - Pipeline cost.
4
Help page 3: Enter the Data
First you reset the data by clicking the corresponding button. Then you set the values
for the parameters: • supply lead time (Lt)
• demand distribution (Type)
Then you can decide to play either manually (day by day) or to let the computer
simulates your strategy for a whole "year".
How to Play: manually
Every day, you must decide how much to order and enter that quantity as a Warehouse
order (top center). Then, you click on "SIMULATE 1 DAY".
The program simulates the demand for 1 day and updates all the statistics.
You then repeat this process day by day.
Here below is an example where 4 units were ordered on day 0 evening, and 3 more
units on day 6 evening. The data here were (zero lead time, and constant demand =
1/2 per day).
W arehouse ->
CO N T R O L
R e se t va lue s
S imula te 1 d a y
S imula te 1 ye a r
Initial inventory
Reorder point
Order quantity
Order up to level
0
<- order
S ta tistics o n d a y:
transit(-4)
#sales
transit(-3)
#demands
transit(-2)
fill rate
transit(-1)
#stockouts
0 for tomorrow
#cycles
Retailer -> 3.5 <- inventory
stockout freq
today's 0.5 demand
pipeline cost
today's 0.5 sales
holding cost
Lt = 0
IAG 1997
order cost
T ype = c
total profit
Rp =
1 year = (days)
Io =
New random list(T rue,Fal.)
R=
Unit Profit ($/item)
Q=
Unit Holding cost ($/item/day)
Qmax =
Unit Order cost ($/order)
4.0
3.0
2.0
T his game aims at getting familiar with the inventory control policies.
1.0
T he0.0
T he-1.0
7
3.5
3.5
1.00
0
2
0.00
0
0.75
2
102.25
100
FALSE
30
0.04
1
IAG/93-94
T he average daily demand is 0.5. T he distribution is either Constant (0.5) or Uniform (either 0 or 1).
Order curve
Inventory
curve
Lost sales
Help: CHART (bottom)
The set of black (positive) columns correspond to your orders.
The green columns (positive, grey on the figure) indicate the evening
inventory positions
The red columns (negative, grey on the figure) show when sales are
missed.
For this example, all the statistics are quite obvious, except for the costs. Two orders
were placed and this explains the order cost. To determine the holding cost, you
should compute the average inventories on each day. They amount to 3.75 for day 1,
3.25 for day 2, and so on. All together, 18.75 unit day. This explains the holding cost.
The profit is obtained by subtracting the costs from the sales revenues.
5
Help page 4: How to Play automatically
First, you have to set the review period Rp.
A. * If you want to simulate a whole year with permanent review (Rp=0), you have to
choose and enter the reorder point R and the order quantity Q.
* Then, you click on "SIMULATE 1 YEAR".
The program simulates your strategy for a whole year: an order of size Q is
generated each time the inventory position hits the order point (R). Only integer
values are allowed for R and Q.
Here below is an example of results for the indicated data. The graph on the bottom
shows the orders that were automatically placed for you. Also, below the horizontal
axis are indicated the sales you missed. Try now to understand the statistics related to
the service performances (observed fill rate and stockout frequency).
Warehouse ->
CON T R OL
R e se t va lue s
S imula te 1 da y
S imula te 1 ye a r
Initial inventory
Reorder point
Order quantity
Order up to level
7.0
0
<- order
transit(-4)
transit(-3)
transit(-2)
transit(-1)
for tomorrow
<- inventory
demand
sales
IAG 1997
S ta tistics on da y:
#sales
0
#demands
6
fill rate
0
#stockouts
0
#cycles
Retailer -> 0
stockout freq
today's 1
pipeline cost
today's 1
holding cost
Lt = 4
order cost
Type = u
total profit
Rp = 0 1 year = (days)
Io = 3 New random list(True,Fal.)
R = 1 Unit Profit ($/item)
Q = 6 Unit Holding cost ($/item/day)
Qmax =
Unit Order cost ($/order)
100
45
53
0.85
6
7
0.86
7.2
10.82
8
1323.98
100
FALSE
30
0.04
1
IAG/93-94
5.0
This3.0
game aims at getting familiar with the inventory control policies.
The1.0
The-1.0
The average daily demand is 0.5. The distribution is either Constant (0.5) or Uniform (either 0 or 1).
Order curve
Inventory
curve
Lost sales
Help: CHART (bottom)
The set of black (positive) columns correspond to your orders.
The green columns (positive, grey on the figure) indicate the evening
inventory positions
The red columns (negative, grey on the figure) show when sales are
missed.
B. * If you want to simulate a whole year with periodic review (Rp>0), you have to
choose and enter the "order up to level" Qmax.
* Then, you click on "SIMULATE 1 YEAR".
the program simulates your strategy for a whole year: an order of size : ( Qmax current inventory position ) is generated at each review period.
An example of results was given with the software description (page 2).
6
Cases 0 and 1
If you do not understand some variables, some performance or some manipulation,
please refer to the former three help pages.
Case 0 : Manual simulation : understanding the game
* Set the inital inventory Io to 0 and reset by clicking on the "reset-restart" button. It's
now day 0, evening.
* Enter the following data : Constant demand (distribution = C), lead time = 1.
* Enter an order of size 10 (as a warehouse order) and click on "Simulate 1 day". It's
now day 1, evening.
Explain :
0.1. why your order did not arrive;
0.2. the demand of this day;
0.3. the sales of this day and the inventory position on the evening ;
0.4. all the statistics values;
* Click on "Simulate 1 day". It is now day 2, evening (see the day count). Explain
again :
0.5. the demand and sales of this day, the inventory on this evening;
0.6. all the statistics from day 0 up to day 2
(a holding cost is charged for the average inventory during this day. In the
morning, you had 10 units; in the evening, 9,5 units are left. This means an
average of 9,75 units);
* Click several more times on ""Simulate 1 day"" and each time, be sure you
understand all the figures. If you missed something, restart the case 0 completely
and refer systematically to the help pages. Leave the case 0 only when you are sure
you understood everything.
Case 1 : EOQ with zero lead time
Constant demand (distribution = C), lead time = 0, review period = 0 (permanent
review). With those assumptions:
1.1. Which are the best reorder point (R) and order quantity (Q) ? Determine those
values mathematically. Perform an automate simulation.
With these parameters, explain all the performance.
1.2. Once you've found the optimal values, record your results, then observe what you
obtain when you add or substract 1 to Q [look at the statistics].
1.3. At the optimum, how are the holding and order costs related ?
1.4. If you increase the reorder point by 1 (set R to 1), what do you gain, what do you
loose ? Check with the software.
Note : If you do not understand what happens, examine attentively the chart at the
bottom of the screen.
7
Cases 2 and 3
Case 2 : EOQ with lead time
Constant demand, lead time = 4 days, review period = 0 (permanent review).
With those assumptions :
2.1. Which are the optimal order point and order quantity ?
2.2. Don' t you think an initial inventory is necessary to avoid stockouts at the
beginning ? If yes, which one should be the best one ?
2.3. Compute the pipeline cost (still on a one year basis) mathematically and check
with the soft.
Case 3 : Safety stock with permanent review
Variable demand (distribution = U), lead time = 4 days, review period = 0.
With those assumptions:
3.1. Explain the demand distribution
3.2. Simulate one year with the same R, Q and Io you used in case 2. Examine the
chart. What do you observe in terms of number of sales ? Explain the fill rate and
the stockout frequency.
3.3. The reorder point R is normally defined as R = Dd*Lt + SS where Dd is the
evening daily demand, Lt the lead time and SS the safety stock. Which SS did
you use in case 2 ?
3.4. Set the safety stock to 2, what is then R ? Is there any risk of loosing sales in this
case ? What about the risk when R equals 3?
3.5. Check with the soft and record for each R value the observed fill rate and
stockout frequencies.
3.6. Check again with the soft (with R = 3) when working with a year length of 200
days. Don't you loose some sales in this case ? Why ?
3.7. A good exercise at home, consists in comparing the gains and losses when the
order point changes. In the computer room, just perform a simulation with R
equals to 2, 3 and 4 and each time, record all the statistics.
Here are indications on how to compare the solution R=2, R=3, R=4. The basic
question is:
"Is it worthwhile to increase R, for example, from R to R + 1 ?"
By increasing R by one unit, we increase the average inventory by one unit. How
much does this cost per year ? This money represents my "loss".
On the other hand, by increasing R by one unit, we could hope to save 1 sales
(one lost sales less). My gain is here :
= Prob (saving 1 sales in a cycle) * number of cycles per year * profit per sales
= Prob (DLt > R) * number of cycles per year * profit per sale
We give you this probability distribution :
Prob [demand during the lead time = 4] = 1/16
(Try also to understand where these values come from).
8
Decide finally (after having filled the next table), which R value is the best one,
economically. Did you find the same result with the simulation ?
2 ------------> 3
3 ------------> 4
4 ------------> 5
Loss
Gain
3.8. At home, for R = 2, 3 and 4; try to calculate the corresponding stockout
probability and fill rate. Remember that the fill rate is given by backorder model:
Q − n( R)
Q
R=2
R=3
R=4
SS
Stockout Probability
(per cycle) = X =
P( DLt > R)
Number of cycles in
100 days = Y
Number of stokouts in
100 days = X*Y
Time between 2
stockouts =
100 days/(X*Y)
n(R) =
P( DLt = X )( X − R)
X >R
fill rate = 1 −
n( R )
Q
Again, compare the mathematical results with the simulation results.
9
Case 4
Case 4 Safety stock with periodic review
Variable demand (distribution = U), lead time = 4, review period of 10 days.
With those assumptions:
4.1. Set Qmax = 8 and an initial inventory of 4. Simulate one year (100 days).
4.2. Examine the chart. Note when an order was placed and how much was ordered.
4.3. Did we loose some sales ?
4.4.The vulnerability period is the period of time during which we cannot interact on
the inventory. If we do not order now, we will have to wait for the next review
period (10 days), then order and wait for the lead time (4 days). How long is the
vulnerability period here ?
4.5. What is the maximal demand during the vulnerability period ?
4.6. Set Qmax to this value and simulate for one year (think at the initial inventory).
Can we loose sales ?
4.7. Decrease several times Qmax by 1 until you observe some lost sales.
4.8. Which Qmax gives the best profit ? Try several values and record all the
performances.
4.9. Again, as in case 3, you can try to calculate at home the different probabilities of
having a demand of 10, 11, 12, 13 and 14 items during the vulnerability period. You
can estimate it using a normal distribution (see case 3 / at the end of the page)
average daily demand is 0,5 item and that your vulnerability period lasts 14 days,
what is the average demand during this period ? Knowing that the daily standard
deviation is of 0,5 item, what is your standard deviation during the vulnerability
period ? Once you have those two variables, you can calculate the different
probabilities asked here above.
10
ANSWERS
COMPUTER LABORATORY:
Case 0:
0.1. because the lead time is 1 day. The order placed on day 0 evening will arrive on
day 2 morning.
0.2. The demand of the day is 0,5.
0.3. There is no sale at day 0. The inventory position is at zero but, there are 10 units
in the pipeline.
0.4. demands = 0,5
sales = 0
pipeline cost = 0,4 = 0,04 * 10 * 1
holding cost = 0
order cost = 1
profit = -1,4
0.5. demands = 0,5
sales = 0,5
0.6. demands = 1 = 0,5 + 0,5
sales = 0,5
pipeline cost = 0,4
holding cost = 0,39 = 9,75 * 0,04
order cost = 1
profit = 13,21 = 15 - 0,4 - 0,39 - 1
Case 1:
2 * 1 * 50
;
0,04 * 100
R = 0 (because the lead time is zero).
1.1. Q = 5 =
1.2.
4
5
6
Holding cost
8,16
10
12,32
Order cost
13
10
9
Total cost
21,16
20
21,32
Hc (R = 5) = 0,04 * 100 * 5/2 = 10;
Oc (R = 5) = 1 * 10 (indeed, number of cycles on one year = D/Q = 50/5 = 10).
1.3. at the optimum, Oc = Hc = 10.
1.4. Increasing R aims at reducing the number of lost sales. Here we do not loose any
sales (lead time being 0), so, we cannot gain anything. It would just cost us the
holding cost of 1 unit during 1 day.
11
Case 2:
2 * 1 * 50
;
0,04 * 100
R = 0,5 * 4 + 0 = 2
2.2. Yes, an initial inventory Io is necessary . Io = 2, Lt being of four days and the
demand of 0,5 per day;
2.3. pipeline costs = 8 = 50 * 4 * 0,04 (= yearly demand(items in transit) * Lt * Hc).
2.1. Q = 5 =
Case 3:
3.1. Prob[Dj = 0] = 0.5; Prob[Dj = 1] = 0,5;
3.2. Number of demands = 53
Number of sales = 49
4 lost sales
3.3. SS = 0 (case 2) because the daily demand was constant (C);
3.4. R = 4 = 0,5 * 4 + 2;
no risk of loosing sales in this case.
If R = 3, there is 1/16 chances to loose sales. Sales will be lost if (D > R) during
the lead time, i.e. prob (DLt>3) = Prob (DLt = 4) = 1/2 * 1/2 * 1/2 *1/2 = 1/16.
On a year length of 100 days, we will run 10 (Q = 5, year = 100 days, Dday = 0,5
=> 10 orders a year) times the risk to loose a sale with probabilité 1/16.
With the soft, no sales are lost, the probability of loosing sales being too small for
a year length of 100 days (number of demands = 53 = number of sales).
1 lost sale
3.7.
2 ------------> 3
3 ------------> 4
4 ------------> 5
Loss(1)
0,04 * 100 * 1 = 4
0,04 * 100 * 1 = 4
0,04 * 100 * 1 = 4
Gain
5/16 * 10 * 30
1/16 * 10 * 30
0
= 93,75
= 18,75
(1) on néglige le fait que cette unité supplémentaire quittera quelque fois le stock.
3.8.
R=2
SS
0 (= 2 - 0,5 * 4)
Stockout Probability 5/16
per cycle
(=1/16 + 4/16)
Number of cycles in 10
100 days
Number of stockouts 5/16 * 10 = 3,125
in 100 days
Time
between
2 100/3,125 = 32
stockouts (days)
R=3
1 (= 3 - 0,5 * 4)
1/16
R=4
2 (= 4 - 0,5 * 4)
0
10
10
10/16 = 0,625
0
100/0,625 = 160
100/0 = ∞
12
n(R) = average units
which are
backordered during a
cycle
fill rate
1*Prob (Dlt = 3) + 1*Prob (Dlt = 4)
2*Prob (Dlt = 4)
= 1/16
= 1*4/16 + 2*1/16
= 6/16
1 - 6/80 = 0,925
1 - 1/80 = 0,9875
0
1-0=1
Case 4:
4.2. One order every 10 days with a Qi = Qmax- Ii.
1 lost sale.
4.4. Vulnerability Period = 14 days.
4.5. Dmax = 14 units (1 unit per day).
4.6. With Qmax = 14, no lost sales.
4.7. First lost sale with Qmax = 8.
4.8. Best profit with Qmax = 9.
4.9. µ = 14 * 0,5 = 7
σ = 14 * 0,52 = 1,87
=> N(7; 1,87)
Prob (D≥8)
Prob (D≥9)
Prob (D≥10)
Prob (D≥11)
Prob (D≥12)
Prob (D≥13)
Prob (D≥14)
= Prob (D>6,5) = Prob (Z>(6,5-7)/1,87) = Prob(Z>-0,26)
= 1 - Prob(Z>0,26) = 1 - 0,39 = 0,61
= Prob(Z>0,5/1,87) = Prob(Z>0,26) = 0,39
= Prob(Z>1,5/1,87) = Prob(Z>0,80) = 0,21
= Prob(Z>2,5/1,87) = Prob(Z>1,33) = 0,09
= Prob(Z>3,5/1,87) = Prob(Z>1.87) = 0,03
= Prob(Z>4,5/1,87) = Prob(Z>2,40) = 0,008
= Prob(Z>5,5/1,87) = Prob(Z>2,94) = 0,0016
= Prob(Z>6,5/1,87) = Prob(Z>3,47) = 0,00026
Prob (D=7)
Prob (D=8)
Prob (D=9)
Prob (D=10)
Prob (D=11)
Prob (D=12)
Prob (D=13)
Prob (D=14)
= Prob (D≥7) - Prob (D≥8) = 0,22
= Prob (D≥8) - Prob (D≥9) = 0,18
= Prob (D≥9) - Prob (D≥10) = 0,12
= Prob (D≥10) - Prob (D≥11) = 0,06
= Prob (D≥11) - Prob (D≥12) = 0,022
= Prob (D≥12) - Prob (D≥13) = 0,0064
= Prob (D≥13) - Prob (D≥14) = 0,000134
infime...
Prob (D≥7)
13
QUESTIONS
Les questions 2 à 5 sont relativement courtes et importantes. La question 1 est
relativement longue mais vous permet de manipuler les techniques de calcul de
stock.
QUESTION 1
The BELGIAN DRUGS COMPANY manufactures pharmaceutical products in
Europe. This company is one of the most important subsidiary of the Drugs Company.
The corporate office is located in Dallas. The B.D.C. produces 600 products using
more than 100 different raw materials.
1. GENERAL DATA
Promoted “general manager” of the planning department, Mr Kozari was
commissioned to set up the best possible inventory management systems. The first
term spent in the company, allowed him to gather the needed information to set up an
effective inventory policy for one family of products. Here are the data :
• B.D.C. works 5 days a week, 48 weeks a year (1 month = 4 weeks).
• According to the accounting manager, the annual holding rate of raw materials is
of 20 % of the purchasing price. The order cost is estimated at 650 francs.
2. LIST OF THE PRODUCTS, OF THEIR PURCHASING PRICES AND OF
THE SUPPLIERS' LEAD TIMES
The following table only lists the most important products. The list was determined by
an ABC classification of all the raw materials.
Products
Denatured alcohol
Ammonic chloride
Acetone
Impalpable sugar
Chocolate flavour
Paraffin
Glycol propylene
Glycerine
Sodic glumitate
Coconut oil
Soja flour
Sodic citrate
Suppliers
Monsanto
Hoffman
Merck
Merck
Rhône-Poulenc
Merck
RIT
Capsulit
Rhône-Poulenc
Merck
Rexolin
Monsanto
Yearly average
consumption
(in KGs)
3500
16080
13500
8500
85
5500
18240
5500
32640
5000
2000
28080
Lead time
Unitary
(working days)
Price
(FRS/kg)
40
3
672
2
20
4
36
2
6500
5
49
4
70
var.
76
2
110
1
60
5
16
4
94
5
14
3. QUESTIONS
1) Establish an ABC classification on annual value criteria.
Annual Value =
annual consumption * unitary price
Products
Ammonic chloride
Sodic glumitate
Sodic citrate
Glycol propylene
Chocolate flavour
Glycerine
Impalpable sugar
Coconut oil
Acetone
Paraffin
Denatured alcohol
Soja flour
2)
Annual
Value
?
3.590.400
2.639.520
1.276.800
552.500
418.000
306.000
300.000
270.000
269.500
140.000
32.000
20.600.480
% of annual cumulated % of Class
value
annual value
?
?
?
17.43
69.88
12.81
82.69
6.2
88.89
2.68
91.57
2.03
93.60
1.48
95.08
1.45
96.53
1.31
97.84
1.31
99.15
0.68
99.83
0.17
100
100%
?
?
Assume the daily demand of the ammonic chloride is deterministic and constant,
when and how many KGs of ammonic chloride would you order ? What is the total
cost of this policy ?
3) Consider now that the daily demand follows a normal distribution with a weekly
variance of 180 kg2.
3.1.) Because of a frequent use of ammonic chloride, Mr Kozari believes it is
unacceptable to be out of stock more than once every five years. When and how
many KGs of ammonic chloride would you order in this case ? What is the total
3.2.) Mr Kozari assumes now a 99 % fill rate is needed. He would like to adopt
quickly a stock up policy to reduce the annoyances provoked by this product.
Once more, determine when and how many KGs of ammonic chloride you
would you order in this case ? What is the total cost of this policy ?
4.1.) Till now, we considered Mr Kozari had no or very low inventory control costs.
Time has changed and these turn out to be far more expensive. Mr Kozari
cannot bear it anymore, he thus decides to check the level of his inventory at
some fixed instants. When do you advice him to check his inventory level ?
Knowing that he doesn't want to be out of stock more than once every five year
(case 3.1), what security stock would you build up ? Is this policy more or less
expensive than the one chosen in case 3.1. ? Why ?
15
4.2.) Mr Hoffman changes once more its agreement with Mr Kozari and compels him
now to place one order exactly every month. Determine when and how many
KGs of ammonic chloride you would you order in this case ? What is the total
QUESTION 2
Votre firme utilise des plateaux garnis au rythme de 10 unités par jour, 360 jours par
an. Chaque plateau garni est composé d'un plateau et de quatre tasses.
Le fournisseur FA fournit vous facture: 10 FB par plateau, 20 FB par tasse et 450 FB
pour le transport (indépendamment de la composition et des quantités commandées).
Le fournisseur FB ne fabrique pas de plateau mais peut vous fournir des tasses au prix
de 20,25 FB sans aucun frais de livraison. Vous ne pouvez néanmoins commander
moins de 500 tasses à la fois. Vous estimez un coût de détention équivalent à 40%
l’an de la valeur stockée. Chez qui vous fournissez-vous, de combien et pourquoi?
QUESTION 3
Vous achetez des quotidiens au prix de 20 francs et les vendez au prix de 30 francs.
Les journaux invendus sont à jeter. La demande journalière est distribuée selon une
normale de moyenne 100 et d'écart type 20. Combien de journaux commanderez-vous
chaque jour?
QUESTION 4
Votre firme dessert ses clients à partir de 4 dépôts régionaux. Chacun de ces dépôts
traite approximativement le même volume. Votre firme envisage maintenant de
regrouper ses 4 dépôts en un seul. Peut-elle s'attendre à une économie en terme de
stock de sécurité?
QUESTION 5
Vous avez constitué un stock de sécurité afin de garantir en moyenne une rupture tous
les 5 ans. Vous décidez maintenant pour des raisons économiques d'augmenter les
quantités de commandes (Q) tout en gardant le même point de commande (R). Cela at-il une incidence sur le nombre moyen de ruptures par an?
16
Réponses
QUESTION 1
1)
Products
Ammonic chloride
Sodic glumitate
Sodic citrate
Glycol propylene
Chocolate flavour
Glycerine
Impalpable sugar
Coconut oil
Acetone
Paraffin
Denatured alcohol
Soja flour
Annual
Value
10.805.760
3.590.400
2.639.520
1.276.800
552.500
418.000
306.000
300.000
270.000
269.500
140.000
32.000
20.600.480
% of annual cumulated % of Class
value
annual value
52.45
52.45
A
17.43
69.88
A
12.81
82.69
B
6.2
88.89
B
2.68
91.57
C
2.03
93.60
C
1.48
95.08
C
1.45
96.53
C
1.31
97.84
C
1.31
99.15
C
0.68
99.83
C
0.17
100
C
100%
2)
When to order? R = 134 kg
How many to order? Q* = 395 kg
Total cost? TC = 10858764.7 frs
3)
3.1.)
Permanent review
When to order?
Vulnerability period = 2
σ2 days = 8.48 kg
P(z) = 0.00491 => z = 2.6
SS = 22 kg
R = 156 kg
How much to order?
Q* = 395 kg
Total cost? TC = 10.861.721 frs
3.2.)
Permanent review
When to order?
Vulnerability period = 2
E(z) = 0.46 => z= - 0.1
SS = 0
17
R = 134 kg
How much to order?
Q* = 395 kg
Total cost? TC = 10858764.7 frs
4.1.)
Periodic review
When to order?
T* = 0.024 year => ± 6 days
F* = 40 orders / year
How much to order? Qmax - Current inventory
Vulnerability period = 2 + 6 = 8 days
σ 8 days = 16.97 kg
z = 2.6
SS = 45 kg
Qmax = 581 kg
Total cost? TC = 10.864.822 frs (more than 3.1)
4.2. ) Periodic review
When to order?
T* = 1 month
F* = 12 orders / year
How much to order? Qmax - Current inventory
Vulnerability period = 2 + 20 = 22 days
σ 22 days = 28.14
P(z) = 0.0166 => z = 2.1
SS = 60 kg
Qmax = 1534 kg
Total cost? TC = 10911672 frs
QUESTION 2
18
FA uniquement: (on fait une commande groupée c-à-d des plateaux garnis):
calcul de Q optimal: (D = 3600; Oc = 450; Hc= 0.4*90 = 36)
Coûts associés:
détention :
36 * 300 / 2 =
commande
450 * 3600/300 =
Total
Q=300
5400
5400
10800
FA et FB:
Chez FA: Q optimal pour les plateaux: (D= 3600; Oc= 450; Hc= 0.4*10= 4) Q=900
Coûts associés:
détention :
0,4 *10* 900 / 2 =
1800
commande
450 * 3600/900 =
1800
Chez FB: aucun coût de commande
on commande le plus souvent possible Q = 500
Coûts associés:
détention :
0.4*20.25 * 500 / 2 =
Supplément de coût pour l’achat des tasses 3600*4*0.25 =
Total
2025
3600
9225
NB : 0,25 = 20.25F(coût des tasses chez FB) - 20F(coût d’achat chez FA)
On choisit donc la solution FA(plateaux par 900) + FB (tasses par 500)
QUESTION 3
Nous effectuons un raisonnemnt marginal. Ce raisonnement est par ailleurs plus
important que la calcul numérique qui s’en suit.
Supposons que l’on commande Q journaux et que l’on se pose la question : “est-il
intéressant de commander Q + 1 journaux ?”
Gain
Perte
Q -------------------------------> Q + 1
si je vends le journal supplémentaire
=> 10 francs de gain
si je ne vends pas le journal supplémentaire => 20 francs de perte
gain : Prob (D > Q) * 10
perte : Prob (D ≤ Q) * 20
J’augmente Q tant que le gain est > à la perte et je m’arrête aux environs de l’égalité :
Prob (D > Q) * 10 = Prob (D ≤ Q) * 20
<=> Prob (D > Q) * 10 = (1 - Prob (D > Q)) * 20
<=> Prob (D > Q) = 20 / 30 = 0,66 => Z = - 0,44 (cfr. table normale réduite).
Autrement dit, le dernier journal que j’achète doit être vendu avec une probabilité de
2/3 (et perdu avec un probabilité de 1/3) pour qu’en moyenne, ni je n’y gagne, ni je
n’y perde.
Si la demande est distribuée selon N(100, 20), alors je commanderai une 91 journaux.
Q−µ
En effet, Z = - 0,44 =
σ
19
<=> Q = - 0,44 * 20 + 100 = 91
QUESTION 4
Oui, car l’écart-type global sera inférieur à la somme des écarts-types individuels :
• si 4 dépots séparés : La demande dans chaque dépôt est de (µ, σ). Ainsi, dans
chaque dépôts on aura un SS = k * σ. Au total, cela donnera : SS = 4 * kσ
• si regroupement des 4 dépôts : La demande globale pour les 4 dépôts est de
moyenne : µ + µ + µ + µ = 4 µ et d'écart type σ = σ 2 + σ 2 + σ 2 + σ 2 = 2σ. Le
SS commun aux 4 dépôts sera donc de k * 2σ pour le même service, inférieur à la
somme des SS des 4 dépôts pris de manière séparée.
QUESTION 5
La probabilité de rupture par cycle ne changera pas car celle-ci ne dépend pas du
point de commande R qui ne change pas.
Par contre, le nombre de cycles par an va diminuer puisque l'on commande par plus
grande quantité. Le nombre moyen de ruptures par an va donc diminuer.
20

Inventory Control

Transcription

Documents pareils

Letter of recommendation from the European Commission

Inventory Troubleshooting Tips

Inventory Management in Dealer-Oriented Industries

Why Do Educated Mothers Matter? A Model of Parental Help

Optimizing Drug Dispensaries in a University Hospital: Pilot Study of

Medical Coverage Policy Psychological and Neuropsychological

Introduction Figure 2 Push Production Line Set

Case Study – Automotive Service Center A leading automotive quick

How much nano do we buy?