INVENTORY_SIMULATION.xls

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Sheet: Introduction File: 186992628.xls.ms_office Page 1 of 58

sS.xls Version 1.4 03/22/02

[email protected]

Johnson Graduate School of Management

Cornell University

Ithaca NY 14853

This workbook is intended for teaching or research. You are welcome to use it in any manner,

and change it as you see fit. It comes without any guarantee whatsoever, and is distributed

free of charge. Changes are frequent, so check back f requently for a new version .

Most inventory control systems use a formula for lead-time demand to set safety stock levels.

Research has uncovered situations where that method leads to large and expensive errors.*

In particular, if replenishment orders might not arrive in the same order in which they are placed, then

the above method will leave you with too much inventory if your objective is a high level of protection,

and too little inventory if you are aiming to run out of stock frequently. That is, the variance of the

inventory level is smaller than the variance of lead-time demand.

*See Robinson, L.R, J.R. Bradley and L.J. Thomas, "Consequences of Order Crossover underOrder-up-to Inventory Policies."M&SOM Manufacturing and Service Operations Management,

Volume 3, No. 3 (2001), pp.175-188.

This workbook contains a macro, written in Visual Basic, that allows you to simulate the inventory control

system known variously as the Min-Max system, the (s,S) system, or the reorder-level, order-up-to system.

Two versions are available in the simulation:

> Periodic review: orders may be placed only at specific points of time, such as daily or weekly.

> Continuous review: orders are placed instantly, as soon as inventory reaches the reorder level.

In both cases, the state of the system is tracked at all times, so that accurate costs may be calculated.

The word "order" refers to an action taken to replenish the supply of an item that is stocked in inventory

and sold to customers. The word "demand" refers to a customer wanting to buy one unit of the item.

A "backorder" is an unsatisfied demand for which the customer will take delivery at a later time.

The simulation assumes that all customers are willing to wait if their demand is backordered.

The simulation allows orders to cross. It assumes that the lead time of one order is independent of

that for any other order, and therefore crossing occurs whenever the lead time for an order is longer

than the interval between orders plus the lead time for the next order.

Please note that the independence assumption is not true in some real circumstances. For example,

if both orders are shipped by rail, and if one freight car cannot pass another, the orders cannot cross.However, in that case lead times are also not independent, but rather are positively correlated, so

models that assume independence (i.e. most inventory models) are also incorrect.

Simulating Inventory Control with Orders that Cross during Lead Time


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Contents:These are the sheets in this workbook.

Introduction (this sheet), with the following sections:

where you set up the model and run the simulation.

where simulation results are displayed in detail for any run stored on the Data sheet.

where the first part of the most recent simulation run is shown in a table and a graph.

where the results of all simulation runs are stored, until you erase them.

Other sheets in this book, if any, may contain data and graphs from previous simulation experiments.

1. Measuring Inventory and Shortages at Time of Delivery:

sreorder level, or Min I nvOn-hand inventory

Sorder-up-to level, or Max BONumber of units backordered to customers

QS - s NetInv= Inv- BO (can be positive or negative)

L A value of lead time I nvPositionNetInv + Outstanding Orders

DA value of one-period demand DL Demand that occurs during lead timeL, VarL Average & Variance of L DL, VarDL Average & Variance of DLD, VarD Average & Variance of D

(a) Shortfall below Reorder Level at Delivery: Shortfall@Deliv

Protection against shortages focuses attention on inventory at the time a replenishment order

arrives. Safety stock governs the likelihood that backorders will exist at that instant.

In the simulation, @Deliv refers to events that happen just before replenishments occur.

However, rather than tracking inventory, which can be positive or negative, the simulation monitors

"Shortfall below sat delivery," defined as

1) Shortfall@Deliv= s-NetI nv@Delivat the time (just before) replenishment occurs.

This is a non-negative variable since net inventory is at or below the reorder level, s, whenever any

order is outstanding (i.e. not yet received.)

From Shortfall@Delivwe may compute certain performance measures:

2) NetInv@Deliv = s- Shortfall@Deliv3) I nv@Deliv = MAX(0, s- Shortfall@Deliv)

4) BO@Deliv= MAX(0, Shortfall@Deliv- s) = I nv@Deliv - s +Shortfall@Deliv

5) P(BO@Deliv>0) = P( Shortfall@Deliv> s)

The latter may also be expressed as a rate, although the meaning is a little confusing. It is NOT the

rate at which backorders occur, but rather "occurrences per unit time" of the joint event

"replenishment arrives, backorders exist," or "replenishment arrives too late to prevent backorders."

That event is denoted "BO@Deliv>0" and its occurrence rate is

6) Rate(BO@Deliv>0) = P( Shortfall@Deliv> s)(Replenishment Orders Per Uni t Time)

Trace

Data

4. Optimization

Simulate

Graphs

2. Inventory and Shortages at Any Time

1. Measuring Inventory and Shortages at Time of Delivery

3. Cost of Inventory, Backorders and Ordering:

(a) Shortfall below Order-up-to Level

(b) Distribution of Shortfall@Delivery if Orders do not Cross

(a) Shortfall below Reorder Level at Delivery: Shortfall@Deliv

(ii) Periodic Review

(i) Continuous Review

(b) Average Inventory and Shortages


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(b) Distribution of Shortfall@Delivery if Orders do not Cross

The following gives the classical argument for the distribution of shortfall, assuming that orders do

not cross, and also assuming that lead times are independent, two assumptions which are convenient

but contradictory. These numbers may be compared to the actual values from the simulation to see

how much is lost if the classical rules are used.

With no order crossing, when an order arrives, all prior replenishment orders have already arrived,

and no subsequent ones have. At the time that order was placed, Inventory Position included the prior

orders, so to compute inventory at delivery, we only have to account for the demand that occurs in the

lead time (or lag time) between placing and receiving the order. That is,

7) NetInv@Deliv= InvPosition@Ordering- DL and

8) Shortfall@Deliv= s- I nvPosition@Orderi ng+ DL if orders do not cross (substitute 7 into 1).

(i) Continuous Review

Under continuous review, an order is placed the instant that inventory position reaches the reorder

level. That is,

9) I nvPosition@Orderi ng= sfor continuous review, so

10) Shortfall@Deliv= DLfor continuous review if orders do not cross (substitute 9 into 8).

>> Shortfall@Delivequals lead-time demand for continuous review, if orders do not cross.

The probability that backorders occur before an order arrives is

11) P(BO@Deliv>0) = P( DL> s) (substitute 10 into 5).

The following formulas assume that Lead Times are independent and identically distributed, and that

the same is true for Demands, and that Lead Times are independent of Demands. They are, in fact, the

well-known formulas for the mean and variance of lead-time demand.

12) E[Shortfall@Deliv] = mD mLand

13) Var[Shortfall@Deliv] = mL VarD + mD2

VarL for continuous review if orders do not cross.

(ii) Periodic Review

Under periodic review, inventory position can reach the reorder point at a time t that is before the end

of the period, so inventory position will be at or below the reorder point when the order is placed.

If t is at the end of the period, the order is placed at the instant that the reorder level is reached.

If t is just after the beginning of the period, a one-period demand occurs before ordering.

This leads to the following inequality:

14) s - DI nvPosition@Orderi ngs

Substituting 14 into 8,

15) DLShortfall@DelivDL+ D = DL+1 for periodic review if orders do not cross.

>> Shortfall@Delivis between the demand during lead time and the demand during one period longer

than lead time, if orders do not cross. Also, because the probability above sis a nonincreasingfunction of s,

16) P(DL> s) P(Shortfall@Deliv>s) P( DL+ D' - 1> s) , and so

17) P(DL> s) P(BO@Deliv>0) P( DL+ D' - 1> s) (substitute 16 into 5).

The expected value of 15 yields

18) mDmLShortfall@DelivmD(1+mL)

The arguments leading to equation 15 also yield a lower limit for the variance:

19) Var[Shortfall@Deliv] mLVarD + mD2VarL

The upper limit in equation 15 also yields a variance estimate, but it is not necessarily an upper limit:


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20) Var[Shortfall@Deliv] (1 + mL) VarD + mD2VarL

2. Inventory and Shortages at Any Time

The simulation also measures the inventory level after every event. Inventory is constant between

events (by definition, since an event is defined as a change of state), so the distribution is

tabulated by accumulating the time that each state persists.

(a) Shortfall below Order-up-to Level

"Shortfall below S" is defined at every time in the simulation as

20) Shortf all = S - NetI nv.

Notice that Shortfalluses a different reference point than Shortfall@Delivery, namely Srather

than s. This is necessary to avoid negative values.

From Shortfall, we may compute more performance measures:

21) NetI nv = S - Shortf all.

22) I nv = MAX(0, S - Shortfall)

23) BO= MAX(0, Shortfall - S) = I nv-S+Shortf all

24) P(BO>0) = P( Shortfall> S)Since a demand is backordered if it arrives when inventory is zero, the average number of demands

backordered per unit time is

25) Rate(BO) = P( ShortfallS)(Demand Rate)

We can also calculate the average time that a backorder endures which, according to Little's Law,

is proportional to the average number of backorders waiting.

Average duration of a Backorder = (Average # Backordered)(Rate of Backorders Occuring)

26) Av(Wait per BO) = Av(BO){Av(DemandRate) P{ShortfallS)}

If you want to include in this average the fact that many customers have zero backorder time, then

27) Av(Wait per Demand) = Av(BO)Av(DemandRate) (includes zero-length backorders.)

(b) Average Inventory and Shortages

Average inventory is greater when computed over time than when computed just before a delivery.

Inventory just before delivery can never be above the reorder point, whereas it can at other times.

The average inventory over time will include the "sawtooth pattern" commonly seen in textbooks,

caused by cycle stock represented by the order quantity. Therefore the exact theoretical expression

for average inventory and backorders is elusive, and I will not try to include it here. However the

simulation results yield averages from the distribution of Shortfall, using equations 22 through 25.


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3. Cost of Inventory, Backorders and Ordering:

The simplest model has linear inventory and backorder costs. However, what constitutes backorder

cost? There may be a cost per unit time for backorders, and a fixed cost whenever a backorder

occurs. There also might be a fixed cost per unit time that accrues as long as there are any

backorders. If the gap between s and S is changed, the number of orders placed will change, which

changes the cost of ordering. A model that covers all of these costs is

28) Average Cost per Period = C1 Av(I nv) + C2 Av(BO) + C3 mD P(BO0)

+ C4 P(BO>0) + C5 Av(OrderRate)

4. Optimization

The value of Q(the gap between sand S) is held constant during a simulation. (In fact, it operates as

if the order-up-to level were S=0 with reorder level s= -Q.) However, the output may be used

to represent any (s,S) system that has S-s=Q. You can find the optimal value of samong all

systems that have the same Qas the one in your simulation, and then set S=s+Q.

On the Graphs sheet, an Excel Table calculates costs for a range of values of s. A graph shows the

results. You may input the first value of sand the interval between points. To home in on the

optimum, adjust the first value until the graph is U-shaped, and then lower the interval to 1.

However, the result is only optimal for the value of Qthat you simulated. To find an overall

optimum, you must repeat the simulation for a series of values of Q, and use the table to find the

best reorder level for each Q. Record those values and select the one with lowest cost.


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Sheet: Simulate File 186992628.xls.ms_office Page 6 of 58

Periodic Review. Q=30, D=10, varD=10

Gamma InterDemandTime: Mu= 0.1, Std=0.1. Discrete LT: Mu= 3, Std=1.41Change the design by entering numbers in the yellow boxes, and by checking or unchecking the selection boxes.

Theoretical Values Mean Var StDev

LTD 30.00 230.00 15.166

LT+1 Dem 40.00 240.00 15.492

LT 3.00 2.00 1.414mean 0.1 mean 3 Inter-Demand Time 0.1 0.01 0.100

StDev 0.1 StDev 1.41421356 Demand/period 10.00 10.00 3.162

Minimum Q = S-s 30 IDT f(IDT) LT f(LT) Conversion Formulas:

0 0.5 0 Mean Var StDev

0.033333333 1 0.2 Demand per Period: 10 10 3.162

0.066666667 2 0.2 Inter-demand Time: 0.1 0.01 0.100

0.1 3 0.2

Runin Periods 5,000 0.133333333 4 0.2 Inter-Demand Time 0.1 0.01 0.100

Run Periods 50,000 0.166666667 5 0.2 Demand/period 10 10 3.162

RNSeed 5235 0.2 0.5 6 0

mean 0.1 mean 3

StDev 0.1 StDev 1.41421356

Discrete LT

Gamma IDT

Discrete IDT (not in use)

Gamma LT (not in use)

Gamma IDT? TRUE

Periodic Review

Type of Review

Minimum Order Quantity

Run Controls

Click here to view simulation results.

Click here to view graphs of the distributions

Current Simulation Design:

Simulation of a Min-Max (s,S) Inventory System in Continuous Time: Discrete or Continuous Review

Inter-demand time (IDT) Lead Time (LT)

Gamma LT? FALSEPeriodic Review? TRUE

Simulate

Delete Old Data


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Sheet: Graphs File: 186992628.xls.ms_office Page 7 of 58

LinksEOQ = 32 Number of columns of data available: 8

Min order Qty, Q = S-s = 50 Use data in column number: 8 Choose your data set hereOrder-up-to level, S = 80 Reorder trigger level (to vary): s = 30 Set the Reorder Level here

Mean = 29.980 35.014 41.017 57.046Variance = 230.033 242.520 239.770 489.283

E[Inventory] = 6.476 4.293 2.138 24.736 1.00$ Inventory Cost per unit time

E[Backorders] = 6.456 9.307 12.156 1.783 9.00$ Backorder Cost per unit time

P[Backorders>0] = 0.478 0.577 0.697 0.158 -$ Cost whenever Backorders > 0

Backorder Rate = 0.087 0.105 0.127 1.684 -$ Cost per unit BackorderedDemands=500784, Orders=9100, Periods=50000, Orders/Period= 0.182 50.00$ Fixed Cost of Ordering

For s=30, S=80, Total Cost per Unit Time = 49.88$

Crossings=0 Crossings per Delivery = 0.000

Analysis of Service Level Accuracy. Target Probability of No Backorders: 0.95 This target's meaning:For "Shortfall",

it means "% of time during which

To achieve target probability, s= 55 61 66 44 there are some backorders."

S=s+Q: 105 111 116 94 For "Shorfall@Delivery",

Actual P(no BO@Deliv): 0.895 0.956 0.984 0.696 it means "% of orders for

Actual P(no BO, time av.): 0.989 0.997 0.999 0.952 which some backorders exist

Predicted by LTD 0.956 0.988 0.996 0.792 when the order arrives."

Predicted by LT+1 Dem 0.795 0.895 0.949 0.580

Search for Minimum Cost Reorder Level (s) holding constant S-s=50

Graph of Cost vs s, starting at

First value of s for the graph: 35 this value, and incrementing byInterval between values: 1 this amount.

Performance Statistics for

s=30, S=80Unit Costs

Shortfall

@Deliv.LTDem LT+1 Dem Shortfall

Minimum Cost = $47.83

at s =37, S =87

Using simulated distribution of: LTDemShortfall

@Deliv.LT+1 Dem

Make sure "Calculation" is set to "Automatic". If it is

not, then press F9 to recalculate the cost curve

whenever you change anything.

Shortfall

Periodic Review, Q=50. D=10 (Var=10). Discrete LT: Mu= 3, Std=1.41

View Graphs of Distributions

View Simulation Data

Go To Simulation Design

View Performance Summary

Gamma InterDemandTime: Mu= 0.1, Std=0.1 Crossings/Delivery=0

47484950515253

0 20 40 60

Cost

Reorder Level, s


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LinksPeriodic Review, Q=50. D=10 (Var=10). Discrete LT: Mu= 3, Std=1.41



View Performance SummaryGamma InterDemandTime: Mu= 0.1, Std=0.1 Crossings/Delivery=0

Change which simulation

is graphed by changing the

column number in cell G5.

Page Down for

cumulative

distributions

Graphs of Distributions for simulation run number 8

0.01 0.055 0.1 0.145 0.19 0.235 0.28

IDT: Mean = 0.1, CV = 1, Gamma

0 1 2 3 4 5 6

LT: Mean = 3, CV = 0.471, Discrete

0

0.005

0.01

0.015

0.02

0.025

0.03

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

LTDem

LT+1 Dem

Shortfall

0

0.005

0.01

0.015

0.02

0.025

0.03

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

LTDem

Shortfall @Deliv.

LT+1 Dem

Periodic Review, Q=50. D=10 (Var=10). Discrete LT: Mu= 3, Std=1.41Gamma InterDemandTime: Mu= 0.1, Std=0.1 Crossings/Delivery=0

0.00

0.20

0.40

0.600.80

1.00

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

Cumulative Distributions

LTDem

Shortfall @Deliv.

LT+1 Dem

Shortfall

Periodic Review, Q=50. D=10 (Var=10). Discrete LT: Mu= 3, Std=1.41



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LinksPeriodic Review, Q=50. D=10 (Var=10). Discrete LT: Mu= 3, Std=1.41



View Performance Summary


Description of Simulation Data being Viewed:

Inputs: Outputs:

Runin Periods 5,000 SimTime 50,000

Run Periods 50,000 Demands 500,784

Q = S-s 50 Orders 9,100

Exp. Demand 10 Deliver ies 9,100

Var. Dmd (approx) 10 Crossings 0RNSeed 5235 Cross/Deliv 0

Periodic Review? TRUE

Gamma LT? FALSE

Gamma IDT? TRUE

Exp. Inter-Demand Time 0.1 Shortfall, Avg. 57.046254

StDev Inter-Demand Time 0.1 Shortfall, var. 489.28271

Exp. LT 3 Shortfall@Deliv. Avg. 35.013956

StDev LT 1.41421356 Shortfall@Deliv. var. 242.52035

Exp LTD 30 LTD Avg. 29.98033

Var LTD 230 LTD var. 230.03291

Exp D(LT+1) 40 LT+1 Dem Avg 41.017363

Var D(LT+1) 240 LT+1 Dem Var 239.76981

Input Distributions: Below Output Distributions: Farther Below

Inter-Demand Time Distribution: Ignore Discrete. Gamma used. Distribution Actually Used:Gamma Parameters: 1.000 0.100 IDT: Mean = 0.1, CV = 1, Gamma

Discrete IDT F(IDT) f(IDT) Gamma IDT f(IDT) Gamma IDT f(IDT)

0.000 0.500 0.500 0.010 9.048 0.010 9.048

0.033 0.500 0.000 0.055 5.769 0.055 5.769

0.067 0.500 0.000 0.100 3.679 0.100 3.679

0.100 0.500 0.000 0.145 2.346 0.145 2.346

0.133 0.500 0.000 0.190 1.496 0.190 1.496

0.167 0.500 0.000 0.235 0.954 0.235 0.954

0.200 1.000 0.500 0.280 0.608 0.280 0.608

Will Gamma overflow? FALSE

Lead Time Distribution: Ignore Gamma. Discrete used. Distribution Actually Used:

Gamma Parameters: 4.500 0.667 T: Mean = 3, CV = 0.471, Discrete

Discrete LT iscrete F(LT) iscrete f(LT) Gamma LT amma f(LT) Discrete LT f(IDT)

0.000 0.000 0.000 0.300 0.005 0.000 0.000

1.000 0.200 0.200 1.650 0.259 1.000 0.200

2.000 0.400 0.200 3.000 0.277 2.000 0.200

3.000 0.600 0.200 4.350 0.134 3.000 0.200

4.000 0.800 0.200 5.700 0.046 4.000 0.200

5.000 1.000 0.200 7.050 0.013 5.000 0.200

6.000 1.000 0.000 8.400 0.003 6.000 0.000

Will Gamma overflow? FALSE


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Sheet: Trace File: 186992628.xls.ms_office

Order Crossing Simulation Partial Simulation Results Theory

(s, S) with S=0 demands 452 Shortfall Leadtime LeadtimeContinuous time! orders placed 14 Shortfall @ Delivery Demand Demand

Q = S-s 30 deliveries 13 Mean 43.35 60.62 26.69 30.00

Exp. Demand 10 Number of Crossings 1 Variance 248.71 153.59 226.90 230.00

Var. Dmd (approx) 10

RNSeed 5235

Periodic Review? TRUE Periodic Review. Q=30: D=10, var=10: L= 3, Std=1.41

Gamma LT? FALSE

Gamma IDT? TRUE

Exp. IDT 0.1

StDev IDT 0.1

Exp. LT 3

StDev LT 1.41421

Current Time 55.556

Arriving Inventory Order Lead Delivery - Leadtime Inv. before orders Order Pi

Period Dmd Orders On-Hand On-Order Position Quantity Time Period Demand Delivery crossed 1

5000 -27 0 -27

5000.047463 1 -28 0 -28

5000.118557 1 -29 0 -29

5000.11895 1 -30 0 -30

5000.453041 1 -31 0 -31

5000.509626 1 -32 0 -32

5000.76021 1 -33 0 -33

5001 -33 33 0 33 4 5005 0 5005

5001.154046 1 -34 33 -1

5001.264099 1 -35 33 -2

5001.318424 1 -36 33 -3

5001.330007 1 -37 33 -4

5001.431884 1 -38 33 -5

5001.708118 1 -39 33 -6

5001.746788 1 -40 33 -7

5001.82104 1 -41 33 -8

5001.85482 1 -42 33 -9

5001.938805 1 -43 33 -10

5002.244994 1 -44 33 -11

5002.280199 1 -45 33 -12

5002.303541 1 -46 33 -13

5002.344361 1 -47 33 -14

5002.381167 1 -48 33 -15

5002.453742 1 -49 33 -16

5002.753257 1 -50 33 -17

5002.770789 1 -51 33 -18

5003.033741 1 -52 33 -19

5003.129288 1 -53 33 -20

5003.131748 1 -54 33 -21

5003.139099 1 -55 33 -22

5003.144072 1 -56 33 -23

5003.445661 1 -57 33 -24

5003.464883 1 -58 33 -25

5003.515421 1 -59 33 -26

5003.959563 1 -60 33 -27

5004.059034 1 -61 33 -28

5004.282059 1 -62 33 -29

5004.308 1 -63 33 -30

5004.463619 1 -64 33 -31

5004.552588 1 -65 33 -32

5004.57251 1 -66 33 -33

5004.585094 1 -67 33 -34

5004.59645 1 -68 33 -35

5004.85119 1 -69 33 -36

5004.935838 1 -70 33 -37

5004.939203 1 -71 33 -385004.98294 1 -72 33 -39

5005 -72 72 0 39 2 5007 0 5005

5005 33 -39 39 0 -39 -72 5005

-80

-70

-60

-50

-40

-30

-20

-10

0

4995

5000

5005

5010

5015

5020

5025

5030

Periodic Review. Q=30: D=10, var=10: L= 3, Std=1.41


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5006.045509 1 -52 39 -13

5006.066182 1 -53 39 -14

5006.082214 1 -54 39 -15

5006.119373 1 -55 39 -16

5006.132403 1 -56 39 -17

5006.197546 1 -57 39 -18

5006.550895 1 -58 39 -195007 39 -19 0 -19 -19 -58

5007.128251 1 -20 0 -20

5007.317277 1 -21 0 -21

5007.338246 1 -22 0 -22

5007.39217 1 -23 0 -23

5007.41161 1 -24 0 -24

5007.412227 1 -25 0 -25

5007.622616 1 -26 0 -26

5007.63529 1 -27 0 -27

5007.636659 1 -28 0 -28

5007.882665 1 -29 0 -29

5007.898352 1 -30 0 -30

5007.987569 1 -31 0 -31

5007.99081 1 -32 0 -32

5008 -32 32 0 32 5 5013 0 50135008.159031 1 -33 32 -1

5008.254136 1 -34 32 -2

5008.542844 1 -35 32 -3

5008.590475 1 -36 32 -4

5008.656459 1 -37 32 -5

5008.871643 1 -38 32 -6

5009.002582 1 -39 32 -7

5009.068712 1 -40 32 -8

5009.071957 1 -41 32 -9

5009.298852 1 -42 32 -10

5009.629066 1 -43 32 -11

5009.653796 1 -44 32 -12

5009.801481 1 -45 32 -13

5009.810995 1 -46 32 -14

5009.860536 1 -47 32 -155009.877569 1 -48 32 -16

5009.957243 1 -49 32 -17

5009.984397 1 -50 32 -18

5010.127253 1 -51 32 -19

5010.327687 1 -52 32 -20

5010.352583 1 -53 32 -21

5010.361235 1 -54 32 -22

5010.59064 1 -55 32 -23

5010.703538 1 -56 32 -24

5010.747061 1 -57 32 -25

5010.77391 1 -58 32 -26

5010.778124 1 -59 32 -27

5010.898752 1 -60 32 -28

5010.918525 1 -61 32 -29

5010.955608 1 -62 32 -305011 -62 62 0 30 1 5012 1 5012

5011.007742 1 -63 62 -1

5011.169116 1 -64 62 -2

5011.207074 1 -65 62 -3

5011.209828 1 -66 62 -4

5011.292345 1 -67 62 -5

5011.394348 1 -68 62 -6

5011.429936 1 -69 62 -7

5011.606302 1 -70 62 -8

5011.622673 1 -71 62 -9

5011.63795 1 -72 62 -10

5011.664522 1 -73 62 -11

5011.974317 1 -74 62 -12

5012 30 -44 32 -12 -12 -74 5012

5012.001531 1 -45 32 -135012.13312 1 -46 32 -14

5012.150276 1 -47 32 -15

5012 193078 1 48 32 16


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5013.621019 1 -27 0 -27

5013.72919 1 -28 0 -28

5014.052806 1 -29 0 -29

5014.057097 1 -30 0 -30

5014.21525 1 -31 0 -31

5014.348423 1 -32 0 -32

5014.488077 1 -33 0 -335014.688973 1 -34 0 -34

5015 -34 34 0 34 3 5018 0 5018

5015.055203 1 -35 34 -1

5015.245878 1 -36 34 -2

5015.375231 1 -37 34 -3

5015.394512 1 -38 34 -4

5015.553738 1 -39 34 -5

5015.615365 1 -40 34 -6

5015.701141 1 -41 34 -7

5015.888689 1 -42 34 -8

5015.934368 1 -43 34 -9

5015.962724 1 -44 34 -10

5016.325344 1 -45 34 -11

5016.424787 1 -46 34 -12

5016.466211 1 -47 34 -135016.560876 1 -48 34 -14

5016.593837 1 -49 34 -15

5016.732494 1 -50 34 -16

5016.743301 1 -51 34 -17

5016.765898 1 -52 34 -18

5016.778627 1 -53 34 -19

5016.885058 1 -54 34 -20

5016.931916 1 -55 34 -21

5017.045089 1 -56 34 -22

5017.052655 1 -57 34 -23

5017.290737 1 -58 34 -24

5017.366025 1 -59 34 -25

5017.495418 1 -60 34 -26

5017.597363 1 -61 34 -27

5017.636664 1 -62 34 -285017.656176 1 -63 34 -29

5017.69609 1 -64 34 -30

5017.753189 1 -65 34 -31

5017.799449 1 -66 34 -32

5018 -66 66 0 32 2 5020 0 5018

5018 34 -32 32 0 -32 -66 5018

5018.289444 1 -33 32 -1

5018.393903 1 -34 32 -2

5018.551277 1 -35 32 -3

5018.707399 1 -36 32 -4

5018.992446 1 -37 32 -5

5019.127468 1 -38 32 -6

5019.200439 1 -39 32 -7

5019.393495 1 -40 32 -8

5019.425834 1 -41 32 -95019.477375 1 -42 32 -10

5019.633081 1 -43 32 -11

5019.70644 1 -44 32 -12

5019.716464 1 -45 32 -13

5019.856859 1 -46 32 -14

5019.938467 1 -47 32 -15

5020 32 -15 0 -15 -15 -47

5020.443185 1 -16 0 -16

5020.53125 1 -17 0 -17

5020.692152 1 -18 0 -18

5020.705346 1 -19 0 -19

5020.763168 1 -20 0 -20

5020.770471 1 -21 0 -21

5020.784454 1 -22 0 -22

5020.787054 1 -23 0 -235020.822942 1 -24 0 -24

5020.825711 1 -25 0 -25

5021 035497 1 26 0 26


13/58




5022.261045 1 -37 35 -2

5022.263916 1 -38 35 -3

5022.271804 1 -39 35 -4

5022.316076 1 -40 35 -5

5022.57658 1 -41 35 -6

5022.824805 1 -42 35 -7

5022.829559 1 -43 35 -85022.986078 1 -44 35 -9

5023 35 -9 0 -9 -9 -44

5023.170266 1 -10 0 -10

5023.319448 1 -11 0 -11

5023.556362 1 -12 0 -12

5023.57303 1 -13 0 -13

5023.592373 1 -14 0 -14

5023.733228 1 -15 0 -15

5023.763896 1 -16 0 -16

5023.820688 1 -17 0 -17

5023.895811 1 -18 0 -18

5023.942577 1 -19 0 -19

5024.043329 1 -20 0 -20

5024.270086 1 -21 0 -21

5024.378698 1 -22 0 -225024.483592 1 -23 0 -23

5024.485565 1 -24 0 -24

5024.529116 1 -25 0 -25

5024.653183 1 -26 0 -26

5024.722509 1 -27 0 -27

5024.854316 1 -28 0 -28

5024.966056 1 -29 0 -29

5025.064577 1 -30 0 -30

5025.111872 1 -31 0 -31

5025.17711 1 -32 0 -32

5025.257125 1 -33 0 -33

5025.475878 1 -34 0 -34

5025.493196 1 -35 0 -35

5025.608927 1 -36 0 -36

5025.68282 1 -37 0 -375025.742549 1 -38 0 -38

5025.777209 1 -39 0 -39

5025.78503 1 -40 0 -40

5025.811158 1 -41 0 -41

5026 -41 41 0 41 1 5027 0 5027

5026.10751 1 -42 41 -1

5026.176283 1 -43 41 -2

5026.453755 1 -44 41 -3

5026.470435 1 -45 41 -4

5026.648804 1 -46 41 -5

5026.649343 1 -47 41 -6

5026.684638 1 -48 41 -7

5026.796194 1 -49 41 -8

5026.928016 1 -50 41 -9

5026.948504 1 -51 41 -105026.993829 1 -52 41 -11

5027 41 -11 0 -11 -11 -52

5027.225137 1 -12 0 -12

5027.225765 1 -13 0 -13

5027.357827 1 -14 0 -14

5027.556581 1 -15 0 -15

5027.582707 1 -16 0 -16

5027.741786 1 -17 0 -17

5027.775092 1 -18 0 -18

5027.896066 1 -19 0 -19

5027.964415 1 -20 0 -20

5028.200946 1 -21 0 -21

5028.26773 1 -22 0 -22

5028.402307 1 -23 0 -23

5028.516994 1 -24 0 -245028.634542 1 -25 0 -25

5028.676194 1 -26 0 -26

5028 83791 1 27 0 27


14/58


15/58




5038.55365 1 -47 33 -14

5038.578496 1 -48 33 -15

5038.75299 1 -49 33 -16

5038.824419 1 -50 33 -17

5038.839401 1 -51 33 -18

5038.941159 1 -52 33 -19

5039.052493 1 -53 33 -205039.30073 1 -54 33 -21

5039.34189 1 -55 33 -22

5039.346488 1 -56 33 -23

5039.466435 1 -57 33 -24

5039.508918 1 -58 33 -25

5039.653927 1 -59 33 -26

5039.850323 1 -60 33 -27

5039.873611 1 -61 33 -28

5039.897019 1 -62 33 -29

5039.926865 1 -63 33 -30

5039.976452 1 -64 33 -31

5040 -64 64 0 31 5 5045 0 5041

5040.157764 1 -65 64 -1

5040.272391 1 -66 64 -2

5040.462255 1 -67 64 -35040.534409 1 -68 64 -4

5040.847826 1 -69 64 -5

5040.920234 1 -70 64 -6

5041 33 -37 31 -6 -37 -70 5041

5041.016447 1 -38 31 -7

5041.12444 1 -39 31 -8

5041.178727 1 -40 31 -9

5041.290514 1 -41 31 -10

5041.432829 1 -42 31 -11

5041.535971 1 -43 31 -12

5041.605302 1 -44 31 -13

5041.693973 1 -45 31 -14

5041.849468 1 -46 31 -15

5041.914911 1 -47 31 -16

5041.976849 1 -48 31 -175042.053916 1 -49 31 -18

5042.170456 1 -50 31 -19

5042.326573 1 -51 31 -20

5042.468459 1 -52 31 -21

5042.493427 1 -53 31 -22

5042.512026 1 -54 31 -23

5043.141543 1 -55 31 -24

5043.197075 1 -56 31 -25

5043.28622 1 -57 31 -26

5043.307647 1 -58 31 -27

5043.462904 1 -59 31 -28

5043.59267 1 -60 31 -29

5043.850839 1 -61 31 -30

5043.981739 1 -62 31 -31

5044 -62 62 0 31 1 5045 0 50455044.145907 1 -63 62 -1

5044.163523 1 -64 62 -2

5044.315559 1 -65 62 -3

5044.410533 1 -66 62 -4

5044.808169 1 -67 62 -5

5044.872432 1 -68 62 -6

5044.975082 1 -69 62 -7

5045 31 -38 31 -7 -38 -69 5045

5045 31 -7 0 -7 -7 -38

5045.193782 1 -8 0 -8

5045.377253 1 -9 0 -9

5045.387592 1 -10 0 -10

5045.441223 1 -11 0 -11

5045.653598 1 -12 0 -12

5045.672726 1 -13 0 -135045.72577 1 -14 0 -14

5045.877501 1 -15 0 -15

5045 889819 1 16 0 16


16/58




5046.782132 1 -28 0 -28

5046.829459 1 -29 0 -29

5046.888235 1 -30 0 -30

5047 -30 30 0 30 5 5052 0 5052

5047.029942 1 -31 30 -1

5047.231122 1 -32 30 -2

5047.389787 1 -33 30 -35047.458878 1 -34 30 -4

5047.551307 1 -35 30 -5

5047.638875 1 -36 30 -6

5047.939996 1 -37 30 -7

5047.984952 1 -38 30 -8

5048.017181 1 -39 30 -9

5048.020285 1 -40 30 -10


17/58

Runin Periods 5,000 5,000 5,000 5,000

Run Periods 50,000 50,000 50,000 50,000

Q = S-s 20 20 10 50

Exp. Demand 10 10 10 10

Var. Dmd (approx) 10 10 10 10

RNSeed 5235 5235 5235 5235Periodic Review? FALSE TRUE TRUE TRUE

Gamma LT? FALSE FALSE FALSE FALSE

Gamma IDT? TRUE TRUE TRUE TRUE

Exp. Inter-Demand Time 0.1 0.1 0.1 0.1

StDev Inter-Demand Time 0.1 0.1 0.1 0.1

Exp. LT 3 3 3 3

StDev LT 1.4142136 1.4142136 1.4142136 1.4142136

Exp LTD 30 30 30 30

Var LTD 230 230 230 230

Exp D(LT+1) 40 40 40 40

Var D(LT+1) 240 240 240 240

SimTime 50,000 50,000 50,000 50,000

Demands 501,009 500,940 501,008 500,784

Orders 25,050 20,110 34,155 9,100

Deliveries 25,050 20,112 34,154 9,100

Crossings 5,149 1,600 8,476 0

Cross/Deliv 0.2055489 0.0795545 0.2481701 0

LTD Avg. 30.051018 30.004177 29.979007 29.98033

LTD var. 229.0572 230.83888 231.78743 230.03291

"LT+1 Dem" or "LTD", Avg. 30.051018 41.033313 41.295251 41.017363

"LT+1 Dem" or "LTD", Var. 229.0572 240.86912 240.24175 239.76981S-Inv. (Time Av) Avg. 39.530602 42.216215 37.395718 57.046254S-Inv. (Time Av) var. 184.53422 241.16825 155.04833 489.28271

s-Inv @Deliv. Avg. 30.051018 34.982946 34.874451 35.013956

s-Inv @Deliv. var. 150.95101 194.4201 142.49282 242.52035

x x x x x

0 0 0 0

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4

5 5 5 56 6 6 6

7 7 7 7

8 8 8 8

9 9 9 9

10 10 10 10

11 11 11 11


18/58

12 12 12 12

13 13 13 13

14 14 14 14

15 15 15 15

16 16 16 16

17 17 17 1718 18 18 18

19 19 19 19

20 20 20 20

21 21 21 21

22 22 22 22

23 23 23 23

24 24 24 24

25 25 25 25

26 26 26 26

27 27 27 27

28 28 28 28

29 29 29 29

30 30 30 30

31 31 31 31

32 32 32 32

33 33 33 33

34 34 34 34

35 35 35 35

36 36 36 36

37 37 37 37

38 38 38 3839 39 39 39

40 40 40 40

41 41 41 41

42 42 42 42

43 43 43 43

44 44 44 44

45 45 45 45

46 46 46 46

47 47 47 47

48 48 48 48

49 49 49 4950 50 50 50

51 51 51 51

52 52 52 52

53 53 53 53

54 54 54 54

55 55 55 55


19/58

56 56 56 56

57 57 57 57

58 58 58 58

59 59 59 59

60 60 60 60

61 61 61 6162 62 62 62

63 63 63 63

64 64 64 64

65 65 65 65

66 66 66 66

67 67 67 67

68 68 68 68

69 69 69 69

70 70 70 70

71 71 71 71

72 72 72 72

73 73 73 73

74 74 74 74

75 75 75 75

76 76 76 76

77 77 77 77

78 78 78 78

79 79 79 79

80 80 80 80

81 81 81 81

82 82 82 8283 83 83 83

84 84 84 84

85 85 85 85

86 86 86 86

87 87 87 87

88 88 88 88

89 89 89 89

90 90 90 90

91 91 91 91

92 92 92 92

93 93 93 9394 94 94 94

95 95 95 95

96 96 96 96

97 97 97 97

98 98 98 98

99 99 99 99


20/58


21/58

144 144 144 144

145 145 145 145

146 146 146 146

147 147 147 147

148 148 148 148

149 149 149 149150 150 150 150

151 151 151 151

152 152 152 152

153 153 153 153

154 154 154 154

155 155 155 155

156 156 156 156

157 157 157 157

158 158 158 158

159 159 159 159

160 160 160 160

161 161 161 161

162 162 162 162

163 163 163 163

164 164 164 164

165 165 165 165

166 166 166 166

167 167 167 167

168 168 168 168

169 169 169 169

170 170 170 170-Inv -Inv -Inv -Inv -Inv

0 0 0 0

5.39E-06 7.195E-06 0 3.341E-05

2.805E-05 5.969E-05 6.067E-05 1.26E-05

7.196E-05 0.0001126 0.0001143 8.524E-05

0.0001714 0.0002473 9.026E-05 0.0001675

0.0003403 0.0004642 0.000274 0.0002705

0.0006986 0.0007244 0.0005325 0.0005051

0.0010466 0.0013021 0.0009539 0.0008976

0.0015789 0.0018973 0.001385 0.0011896

0.0022252 0.0023525 0.0021908 0.00147940.0028909 0.0031825 0.0028884 0.0021735

0.0037181 0.0038969 0.0036387 0.0026129

0.0043397 0.0046586 0.0045123 0.0030778

0.0051222 0.0054877 0.0052079 0.0034604

0.0060303 0.00611 0.0061619 0.0037958

0.0068243 0.0067537 0.0069439 0.0040066


22/58

0.0075703 0.007496 0.0080825 0.0045078

0.0085157 0.0081999 0.0090399 0.0046368

0.0095298 0.0091968 0.0101532 0.0051967

0.0106826 0.010057 0.0118148 0.0054742

0.0117124 0.0108426 0.0129255 0.0057886

0.0128015 0.0118055 0.0147945 0.00629420.0139101 0.0126107 0.0160542 0.0066731

0.0152132 0.013985 0.0178978 0.0069427

0.0160448 0.0148342 0.0195415 0.007189

0.0175499 0.0153575 0.0206708 0.0076418

0.018829 0.0162435 0.0223878 0.0082318

0.020107 0.0174993 0.0237914 0.0083975

0.0212398 0.0175913 0.0255667 0.0087557

0.0223756 0.0187152 0.0266633 0.0089793

0.0232978 0.0196702 0.0274485 0.0093796

0.0245302 0.0204681 0.0283579 0.0099374

0.0251058 0.0208848 0.0292479 0.0101457

0.0260062 0.021634 0.0296534 0.0106357

0.0266456 0.0223096 0.0310419 0.0111452

0.0273774 0.0226852 0.0306789 0.0113045

0.0276505 0.0228394 0.0308876 0.0116326

0.0276667 0.0233092 0.0311532 0.0119498

0.0281307 0.0241654 0.0310583 0.0123727

0.0279218 0.0235115 0.0303261 0.0125313

0.028144 0.0239649 0.0303144 0.013323

0.0280129 0.023801 0.0296497 0.0134063

0.0273256 0.0236371 0.0285475 0.01377040.026762 0.0236198 0.0273109 0.0144156

0.0267964 0.0242864 0.0272351 0.0143963

0.026598 0.0233058 0.0252623 0.0146179

0.0256303 0.023317 0.0242037 0.0150305

0.0246146 0.0230879 0.0228935 0.0153612

0.0236493 0.0224123 0.0213486 0.0155286

0.0221351 0.0223276 0.0199292 0.0160701

0.0209785 0.0215409 0.0182612 0.0163454

0.0197803 0.0213662 0.0168116 0.016465

0.0184825 0.0199791 0.0159913 0.0172905

0.0174697 0.0191008 0.0144275 0.01679180.0161256 0.0188137 0.0130015 0.0173585

0.0149942 0.0177741 0.0119868 0.0172673

0.0138515 0.0170216 0.0106302 0.0173441

0.0130034 0.0160853 0.0095251 0.0176212

0.0119771 0.0153084 0.0086748 0.0175408

0.0108276 0.0145535 0.0074396 0.0170605


23/58

0.0099974 0.013582 0.0066802 0.0172055

0.0090167 0.0128339 0.0058106 0.0172291

0.0083296 0.0117722 0.0050295 0.0165939

0.007303 0.0111094 0.0042297 0.0165851

0.0064457 0.0099746 0.0035132 0.0160283

0.0057306 0.0095069 0.0031474 0.01588730.0053497 0.0083934 0.0026669 0.0157737

0.0044251 0.0077963 0.0020666 0.0150993

0.0036904 0.0071211 0.0017544 0.0148333

0.0031929 0.006385 0.0014473 0.0142462

0.0027051 0.0058165 0.0012022 0.0141148

0.0021994 0.0051761 0.0009473 0.0137565

0.0018887 0.0046509 0.000822 0.0132967

0.0015219 0.0040251 0.0007043 0.0131786

0.0012046 0.0036514 0.0005803 0.0129615

0.0010102 0.0030677 0.0004689 0.0124334

0.0008216 0.0025786 0.0002766 0.0120802

0.0005845 0.002389 0.0002488 0.0115348

0.000424 0.0020313 0.0002089 0.0110938

0.0003478 0.0017799 0.0001697 0.011124

0.0002892 0.0014927 0.0001197 0.0105466

0.0002324 0.0012215 6.984E-05 0.0100465

0.0001826 0.0011029 5.367E-05 0.0098815

0.0001385 0.0008063 3.968E-05 0.0091364

9.73E-05 0.0007183 2.801E-05 0.0093107

6.748E-05 0.0005126 2.106E-05 0.0088438

4.291E-05 0.0004476 1.055E-05 0.0083783.047E-05 0.0003709 1.341E-05 0.0079701

2.668E-05 0.00029 6.939E-06 0.0076158

8.635E-06 0.0002134 6.087E-06 0.0071293

1.253E-05 0.0001595 6.327E-06 0.0069482

1.67E-06 0.0001069 4.957E-06 0.0065961

7.302E-06 0.0001178 1.518E-06 0.0062243

5.909E-06 6.746E-05 3.003E-06 0.0057947

9.314E-07 7.628E-05 2.698E-06 0.005551

2.263E-08 4.184E-05 0 0.0052786

7.916E-07 4.823E-05 0 0.0047339

0 3.236E-05 0 0.00449040 2.497E-05 0 0.0040532

0 1.013E-05 0 0.0036575

0 3.27E-06 0 0.0032626

0 3.417E-06 0 0.0031173

0 4.691E-06 0 0.0027299

0 2.351E-06 0 0.0024427


24/58

0 1.906E-06 0 0.0021407

0 1.46E-06 0 0.0019214

0 2.657E-06 0 0.0016252

0 1.8E-06 0 0.0014863

0 5.052E-06 0 0.0013282

0 0 0 0.00114540 0 0 0.0008808

0 0 0 0.0008689

0 0 0 0.0006779

0 0 0 0.0005182

0 0 0 0.0004595

0 0 0 0.0003402

0 0 0 0.0002479

0 0 0 0.0002348

0 0 0 0.0001817

0 0 0 0.0001534

0 0 0 0.0001289

0 0 0 7.318E-05

0 0 0 5.985E-05

0 0 0 6.286E-05

0 0 0 5.306E-05

0 0 0 2.576E-05

0 0 0 2.415E-05

0 0 0 2.214E-05

0 0 0 1.007E-05

0 0 0 4.035E-06

0 0 0 1.582E-060 0 0 1.888E-06

0 0 0 6.731E-07

0 0 0 3.045E-06

0 0 0 3.164E-06

0 0 0 1.382E-07

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


25/58

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

LTD LTD LTD LTD LTD

0 0 0 0

7.984E-05 9.944E-05 0.0001171 0.0003297

0.0006786 0.0004475 0.0007613 0.00010990.0015569 0.00179 0.0017275 0.0012088

0.0031138 0.0037788 0.0038356 0.0040659

0.006986 0.0077068 0.0072612 0.0068132

0.0124152 0.012679 0.0122972 0.0110989

0.0182435 0.0181981 0.0188558 0.0193407

0.0205988 0.0231702 0.0224571 0.0212088

0.0254291 0.0250099 0.0260584 0.0242857

0.0271058 0.0247116 0.0255607 0.0281319

0.0250299 0.0260044 0.0253265 0.0263736

0.0224351 0.0241647 0.0221936 0.0220879

0.0201597 0.0185959 0.020349 0.02087910.0178044 0.018397 0.0178603 0.0184615

0.0172854 0.0175517 0.0188265 0.0178022

0.0180838 0.0163087 0.0176846 0.0198901

0.0179242 0.0191428 0.0172454 0.016044

0.0188822 0.0202864 0.0194121 0.0198901

0.0203593 0.0225736 0.0204954 0.0212088


26/58

0.0214371 0.0202864 0.0218715 0.0224176

0.0209182 0.0205847 0.0216373 0.0213187

0.0230739 0.0215294 0.021813 0.0193407

0.0210778 0.0187947 0.0202904 0.0189011

0.020519 0.0174523 0.0196756 0.0189011

0.0192016 0.0185959 0.0195292 0.0239560.0187226 0.0203361 0.0195585 0.019011

0.019521 0.0215792 0.0182702 0.0191209

0.0209581 0.0181981 0.0191193 0.0194505

0.0198802 0.0192422 0.0199977 0.0206593

0.0202794 0.02143 0.0197049 0.0197802

0.0192016 0.01964 0.0211688 0.0198901

0.0207585 0.0207339 0.020349 0.0201099

0.020998 0.0206344 0.0200269 0.0213187

0.0215968 0.0207836 0.0203783 0.0201099

0.0188822 0.0214797 0.0209639 0.0198901

0.0207186 0.0185461 0.0201441 0.0196703

0.0183633 0.0198886 0.019617 0.0195604

0.0209182 0.0206842 0.0189729 0.0172527

0.018004 0.0200875 0.0194414 0.0194505

0.0199601 0.0200378 0.0191193 0.0198901

0.0203194 0.0184964 0.0198513 0.0197802

0.0192814 0.0185461 0.0188558 0.0172527

0.0182834 0.0192422 0.0188265 0.0181319

0.019002 0.0198886 0.0186215 0.0172527

0.0180838 0.0177009 0.0170112 0.019011

0.0175649 0.01785 0.0180067 0.01846150.0176447 0.0162092 0.0174211 0.0186813

0.0169261 0.0166567 0.016045 0.0184615

0.0149701 0.0143198 0.0160743 0.0176923

0.0149701 0.0153142 0.0153716 0.0162637

0.0151297 0.0147673 0.0144932 0.0145055

0.0130539 0.0124801 0.0129707 0.0134066

0.0105788 0.0122812 0.0112432 0.0108791

0.0106587 0.0105907 0.0093986 0.0092308

0.0094212 0.0086018 0.0089887 0.0074725

0.0078244 0.0084527 0.0084617 0.007033

0.0067864 0.0063644 0.0066756 0.00637360.0063473 0.0058174 0.0065 0.0045055

0.0045908 0.0057677 0.005036 0.0051648

0.0039122 0.0042761 0.0038356 0.0050549

0.0033932 0.00358 0.0033085 0.0040659

0.0027146 0.002685 0.0028401 0.0020879

0.0016367 0.0021877 0.0024302 0.0024176


27/58

0.0018363 0.0018894 0.0022252 0.0020879

0.0016766 0.0011933 0.0012883 0.0013187

0.001477 0.0009447 0.0011419 0.0005495

0.0006786 0.0009447 0.0007905 0.000989

0.0005988 0.0001989 0.0007027 0.0008791

0.000479 0.0004972 0.0006441 0.00043960.0002794 0.0002983 0.0002928 0.0006593

7.984E-05 0.0001989 0.000205 0.0003297

0.0003194 0.0002486 0.0002342 0

0.0001597 0.0001492 0.0001464 0.0002198

3.992E-05 0 0 0

7.984E-05 0 0 0

3.992E-05 4.972E-05 0 0.0001099

0 9.944E-05 0 0

0 0 0 0

0 0 5.856E-05 0

0 4.972E-05 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 2.928E-05 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


28/58

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


29/58

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

s-Inv @Deliv. -Inv @Deliv. -Inv @Deliv. -Inv @Deliv. -Inv @Deliv.

0 0 0 0

3.992E-05 0 0 0.0001099

0.0003194 4.972E-05 0 0

0.0005988 0.0001492 0.0001171 0.0001099

0.0015569 0.0002486 0.0002635 0.0006593

0.0034731 0.0010939 0.0005563 0.0013187

0.0059481 0.0015414 0.0012004 0.00186810.008503 0.0034805 0.0009955 0.0042857

0.0105389 0.0044749 0.0026937 0.0059341

0.014012 0.0064141 0.0032207 0.0086813

0.0152495 0.0076571 0.0046847 0.0123077

0.0148104 0.0101432 0.0054459 0.0134066

0.0137325 0.009099 0.0056216 0.0161538

0.0146108 0.0124304 0.0071441 0.0154945

0.0160878 0.0133254 0.0084617 0.0197802

0.0151297 0.0162092 0.009018 0.0175824

0.0169261 0.0165076 0.0098671 0.0194505

0.017525 0.0161595 0.0114481 0.02175820.0203992 0.0171539 0.0132927 0.0206593

0.0201198 0.0176014 0.0161621 0.019011

0.0229541 0.0175517 0.0162792 0.02

0.0228343 0.0187947 0.0180067 0.0226374

0.0245509 0.0200378 0.0206711 0.0212088

0.0242715 0.0197892 0.0224864 0.019011


30/58

0.0251497 0.0233691 0.0234233 0.0205495

0.0259082 0.0204356 0.0252093 0.0192308

0.0289421 0.0212808 0.025912 0.0205495

0.0342515 0.0220267 0.0279323 0.0205495

0.0358084 0.0249602 0.0275224 0.0193407

0.0353293 0.024463 0.0301575 0.02109890.0362475 0.0233691 0.0312116 0.0204396

0.0345709 0.0256563 0.0322071 0.0176923

0.0350898 0.0254077 0.0323242 0.0195604

0.0305389 0.0268994 0.0305089 0.0213187

0.0284232 0.0270485 0.0332611 0.0183516

0.0254691 0.0264021 0.0325877 0.0178022

0.0257485 0.0254077 0.0320314 0.0194505

0.0221956 0.0256066 0.0336417 0.0216484

0.0229541 0.0256066 0.0311237 0.0206593

0.0208383 0.0267502 0.0301282 0.0193407

0.0207186 0.0251094 0.0290742 0.019011

0.0205988 0.0236177 0.0276395 0.0204396

0.0198403 0.0250597 0.0260584 0.0201099

0.017006 0.0241647 0.0258828 0.0183516

0.0170459 0.0211814 0.0221058 0.0191209

0.0158882 0.0216289 0.0216373 0.0198901

0.0147705 0.0215294 0.0202026 0.0178022

0.0132136 0.0190931 0.0194414 0.0216484

0.012495 0.0173031 0.0183873 0.0175824

0.0112575 0.0160103 0.0164549 0.0189011

0.0110579 0.0152645 0.0149031 0.02010990.01002 0.0151154 0.0133806 0.0186813

0.0077445 0.0149662 0.0117117 0.0186813

0.0066667 0.0127784 0.0108626 0.0142857

0.0055888 0.0127287 0.0104819 0.0149451

0.0050699 0.0116846 0.0085202 0.0159341

0.0039521 0.0105907 0.0073198 0.0124176

0.0033533 0.0079057 0.007027 0.0120879

0.0027944 0.0078063 0.0052702 0.0112088

0.001996 0.0079057 0.0041869 0.0104396

0.0016367 0.0062152 0.0036013 0.0083516

0.0012375 0.0064141 0.0033378 0.00681320.0010379 0.0054694 0.0031329 0.0071429

0.0006786 0.0043258 0.0025766 0.0064835

0.0007186 0.0040772 0.001991 0.0053846

0.0006786 0.0036794 0.0018153 0.0045055

0.000519 0.0023369 0.0011419 0.0043956

0.0001198 0.002685 0.0009662 0.0034066


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0.0002395 0.0022375 0.0008784 0.0024176

0.0001597 0.0012928 0.0008784 0.001978

7.984E-05 0.0014419 0.0008491 0.0010989

3.992E-05 0.0006464 0.0003806 0.0015385

0 0.0008453 0.0002928 0.0014286

7.984E-05 0.0002486 0.0001464 0.00065930 0.0003978 0.0001464 0.000989

0 0.0003978 0.0001171 0.0006593

3.992E-05 0.0002486 0.0001464 0.0006593

0 0.0003978 5.856E-05 0.0006593

0 0.0001492 2.928E-05 0.0003297

0 0.0002486 2.928E-05 0.0001099

0 0 2.928E-05 0.0002198

0 4.972E-05 0 0

0 0 2.928E-05 0

0 0 0 0

0 4.972E-05 5.856E-05 0

0 0 0 0.0001099

0 0 0 0

0 4.972E-05 0 0

0 4.972E-05 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


32/58

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


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0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

LT+1 Dem LTDem LT+1 Dem LT+1 Dem LT+1 Dem

0 0 0 0

7.984E-05 0 0 0

0.0006786 0 0 0

0.0015569 0 0 0

0.0031138 0 0 0

0.006986 0 2.928E-05 0

0.0124152 0 0 0

0.0182435 4.972E-05 2.928E-05 0

0.0205988 0.0001989 0.0002342 0.0002198

0.0254291 0.0001989 0.0001757 0.0001099

0.0271058 0.0002983 0.0003513 0.00021980.0250299 0.001243 0.0008198 0.000989

0.0224351 0.002138 0.001464 0.0017582

0.0201597 0.0028341 0.0021374 0.0025275

0.0178044 0.0050716 0.0040698 0.0052747

0.0172854 0.0089499 0.0069099 0.0071429

0.0180838 0.0101432 0.0092815 0.0106593

0.0179242 0.0143198 0.0121216 0.0131868

0.0188822 0.0163584 0.0152544 0.0148352

0.0203593 0.0167064 0.0180067 0.0181319

0.0214371 0.0202864 0.0198805 0.0223077

0.0209182 0.0198886 0.021813 0.01912090.0230739 0.0217283 0.0214616 0.0214286

0.0210778 0.0213803 0.0215202 0.0207692

0.020519 0.0215294 0.0205832 0.0212088

0.0192016 0.0174025 0.0198513 0.0213187

0.0187226 0.0189439 0.0198513 0.0195604

0.019521 0.0198886 0.0202612 0.0194505


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0.0209581 0.020187 0.0190314 0.0205495

0.0198802 0.0200875 0.0186508 0.0201099

0.0202794 0.0187947 0.0195585 0.0220879

0.0192016 0.0210819 0.0213152 0.02

0.0207585 0.0211814 0.0211395 0.02

0.020998 0.0201372 0.0204954 0.02010990.0215968 0.0190931 0.0195585 0.0193407

0.0188822 0.0200378 0.0206125 0.0208791

0.0207186 0.0209825 0.0188558 0.0202198

0.0183633 0.0199383 0.0194414 0.0195604

0.0209182 0.017502 0.0208175 0.0189011

0.018004 0.0199383 0.0194999 0.0156044

0.0199601 0.0193417 0.0204076 0.0221978

0.0203194 0.0184964 0.0201733 0.0192308

0.0192814 0.0195903 0.0195292 0.0183516

0.0182834 0.0219769 0.0205247 0.0240659

0.019002 0.0198389 0.0189143 0.0184615

0.0180838 0.0220267 0.0212274 0.0202198

0.0175649 0.0204853 0.019822 0.0181319

0.0176447 0.0192422 0.0202319 0.0205495

0.0169261 0.0199881 0.0189143 0.0186813

0.0149701 0.0186456 0.0205832 0.0206593

0.0149701 0.020535 0.0197049 0.0215385

0.0151297 0.0192422 0.0195585 0.0192308

0.0130539 0.019292 0.0178017 0.0207692

0.0105788 0.018745 0.0184166 0.017033

0.0106587 0.0182975 0.0183287 0.01813190.0094212 0.0186456 0.0181824 0.0201099

0.0078244 0.018745 0.017099 0.0167033

0.0067864 0.0170048 0.0199684 0.0179121

0.0063473 0.0159606 0.0166013 0.0154945

0.0045908 0.0165076 0.0154008 0.0185714

0.0039122 0.0154634 0.0148152 0.0153846

0.0033932 0.014469 0.0157815 0.0159341

0.0027146 0.0146181 0.0143761 0.0132967

0.0016367 0.0127287 0.0129707 0.0127473

0.0018363 0.0118337 0.012268 0.0108791

0.0016766 0.0088007 0.0106576 0.00923080.001477 0.0095465 0.0091351 0.0082418

0.0006786 0.0085024 0.0084324 0.0075824

0.0005988 0.007508 0.0076126 0.006044

0.000479 0.0054196 0.0065585 0.006044

0.0002794 0.005718 0.0051824 0.0065934

7.984E-05 0.0053699 0.0047432 0.0046154


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0.0003194 0.0039777 0.0045675 0.0037363

0.0001597 0.00358 0.0032793 0.0027473

3.992E-05 0.0022872 0.002723 0.002967

7.984E-05 0.0020883 0.0021959 0.0017582

3.992E-05 0.0013425 0.0016689 0.0017582

0 0.0012928 0.0014347 0.00142860 0.0011436 0.0012297 0.0017582

0 0.0011436 0.0009955 0.0005495

0 0.0004475 0.0010833 0.000989

0 0.0002983 0.0004977 0.0004396

0 0.0003481 0.0003513 0.0003297

0 0.0002486 0.0001464 0.0003297

0 9.944E-05 0.000205 0.0005495

0 0.0001989 0.0001464 0

0 4.972E-05 0.000205 0.0002198

0 4.972E-05 8.784E-05 0.0001099

0 0 5.856E-05 0

0 4.972E-05 2.928E-05 0.0001099

0 9.944E-05 0 0

0 4.972E-05 0 0

0 4.972E-05 2.928E-05 0

0 0 0 0

0 4.972E-05 2.928E-05 0

0 0 0 0

0 0 0 0

0 0 2.928E-05 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


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0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


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0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

Discrete IDT Discrete IDT Discrete IDT Discrete IDT Discrete IDT

0 0 0 0

0.0333333 0.0333333 0.0333333 0.0333333

0.0666667 0.0666667 0.0666667 0.0666667

0.1 0.1 0.1 0.1

0.1333333 0.1333333 0.1333333 0.1333333

0.1666667 0.1666667 0.1666667 0.1666667

0.2 0.2 0.2 0.2

Discrete F(IDT) crete F(IDT) crete F(IDT) crete F(IDT) crete F(IDT)

0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5

1 1 1 1Discrete LT Discrete LT Discrete LT Discrete LT Discrete LT

0 0 0 0

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4

5 5 5 5

6 6 6 6

Discrete F(LT) iscrete F(LT) iscrete F(LT) iscrete F(LT) iscrete F(LT)

0 0 0 0

0.2 0.2 0.2 0.20.4 0.4 0.4 0.4

0.6 0.6 0.6 0.6

0.8 0.8 0.8 0.8

1 1 1 1

1 1 1 1


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5,000 5,000 5,000 5,000

50,000 50,000 50,000 50,000

50 50 50 50

10 10 10 10

1.6 1.6 10 10

5235 5235 5235 5235TRUE FALSE FALSE TRUE

FALSE FALSE FALSE FALSE

TRUE TRUE TRUE TRUE

0.1 0.1 0.1 0.1

0.04 0.04 0.1 0.1

3 3 3 3

1.4142136 1.4142136 1.4142136 1.4142136

30 30 30 30

204.8 204.8 230 230

40 40 40 40

206.4 206.4 240 240

50,000 50,000 50,000 50,000

500,285 500,203 500,771 500,784

9,205 10,004 10,015 9,100

9,205 10,004 10,015 9,100

0 0 32 0

0 0 0.0031952 0

30.322651 29.434026 30.02666 29.98033

205.12545 210.07711 232.50503 230.03291

40.574253 29.434026 30.02666 41.017363

206.88588 210.07711 232.50503 239.7698157.890613 54.706093 54.482139 57.046254

458.26579 419.01377 440.23707 489.28271

34.671157 29.434026 30.02666 35.013956

217.07481 210.07711 231.62635 242.52035

x x x x

0 0 0 0

1 1 1 1

2 2 2 2

3 3 3 3

4 4 4 4

5 5 5 56 6 6 6

7 7 7 7

8 8 8 8

9 9 9 9

10 10 10 10

11 11 11 11


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12 12 12 12

13 13 13 13

14 14 14 14

15 15 15 15

16 16 16 16

17 17 17 1718 18 18 18

19 19 19 19

20 20 20 20

21 21 21 21

22 22 22 22

23 23 23 23

24 24 24 24

25 25 25 25

26 26 26 26

27 27 27 27

28 28 28 28

29 29 29 29

30 30 30 30

31 31 31 31

32 32 32 32

33 33 33 33

34 34 34 34

35 35 35 35

36 36 36 36

37 37 37 37

38 38 38 3839 39 39 39

40 40 40 40

41 41 41 41

42 42 42 42

43 43 43 43

44 44 44 44

45 45 45 45

46 46 46 46

47 47 47 47

48 48 48 48

49 49 49 4950 50 50 50

51 51 51 51

52 52 52 52

53 53 53 53

54 54 54 54

55 55 55 55


40/58

56 56 56 56

57 57 57 57

58 58 58 58

59 59 59 59

60 60 60 60

61 61 61 6162 62 62 62

63 63 63 63

64 64 64 64

65 65 65 65

66 66 66 66

67 67 67 67

68 68 68 68

69 69 69 69

70 70 70 70

71 71 71 71

72 72 72 72

73 73 73 73

74 74 74 74

75 75 75 75

76 76 76 76

77 77 77 77

78 78 78 78

79 79 79 79

80 80 80 80

81 81 81 81

82 82 82 8283 83 83 83

84 84 84 84

85 85 85 85

86 86 86 86

87 87 87 87

88 88 88 88

89 89 89 89

90 90 90 90

91 91 91 91

92 92 92 92

93 93 93 9394 94 94 94

95 95 95 95

96 96 96 96

97 97 97 97

98 98 98 98

99 99 99 99


41/58

100 100 100 100

101 101 101 101

102 102 102 102

103 103 103 103

104 104 104 104

105 105 105 105106 106 106 106

107 107 107 107

108 108 108 108

109 109 109 109

110 110 110 110

111 111 111 111

112 112 112 112

113 113 113 113

114 114 114 114

115 115 115 115

116 116 116 116

117 117 117 117

118 118 118 118

119 119 119 119

120 120 120 120

121 121 121 121

122 122 122 122

123 123 123 123

124 124 124 124

125 125 125 125

126 126 126 126127 127 127 127

128 128 128 128

129 129 129 129

130 130 130 130

131 131 131 131

132 132 132 132

133 133 133 133

134 134 134 134

135 135 135 135

136 136 136 136

137 137 137 137138 138 138 138

139 139 139 139

140 140 140 140

141 141 141 141

142 142 142 142

143 143 143 143


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144 144 144 144

145 145 145 145

146 146 146 146

147 147 147 147

148 148 148 148

149 149 149 149150 150 150 150

151 151 151 151

152 152 152 152

153 153 153 153

154 154 154 154

155 155 155 155

156 156 156 156

157 157 157 157

158 158 158 158

159 159 159 159

160 160 160 160

161 161 161 161

162 162 162 162

163 163 163 163

164 164 164 164

165 165 165 165

166 166 166 166

167 167 167 167

168 168 168 168

169 169 169 169

170 170 170 170-Inv -Inv -Inv -Inv

0 0 0 0

0 0 1.494E-05 3.341E-05

0 0 2.651E-05 1.26E-05

0 0 7.946E-05 8.524E-05

0 0 0.0001832 0.0001675

0 0 0.0002769 0.0002705

5.41E-06 1.274E-05 0.0006138 0.0005051

6.858E-05 0.0001772 0.0009107 0.0008976

0.0003221 0.0005403 0.0013714 0.0011896

0.0007977 0.0012819 0.0017294 0.00147940.0014986 0.0021571 0.0023351 0.0021735

0.0022171 0.0031584 0.0029807 0.0026129

0.0029673 0.0037694 0.0033138 0.0030778

0.0033857 0.0041092 0.0037514 0.0034604

0.003497 0.0042022 0.0041895 0.0037958

0.0035626 0.0042344 0.0042563 0.0040066


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0.0037227 0.0042676 0.0049591 0.0045078

0.0039013 0.0046395 0.0050332 0.0046368

0.0040981 0.0049026 0.0057097 0.0051967

0.0047755 0.0055519 0.0059432 0.0054742

0.0051969 0.0062682 0.0066084 0.0057886

0.0056314 0.0069855 0.0067803 0.00629420.0063585 0.0075745 0.0073057 0.0066731

0.0066801 0.0079758 0.0074776 0.0069427

0.0071485 0.0081725 0.0082476 0.007189

0.007208 0.0081785 0.0083344 0.0076418

0.0074757 0.0083876 0.0089633 0.0082318

0.0078056 0.0087221 0.0091628 0.0083975

0.0080426 0.0089721 0.0096219 0.0087557

0.0084772 0.0094762 0.0101633 0.0089793

0.0087867 0.0101282 0.0104474 0.0093796

0.0094378 0.0106916 0.0107436 0.0099374

0.0098189 0.0112872 0.0112902 0.0101457

0.0100284 0.0117812 0.011633 0.0106357

0.0105418 0.0118338 0.0116918 0.0111452

0.0107534 0.0121516 0.0120839 0.0113045

0.0111211 0.0124728 0.0126102 0.0116326

0.0112604 0.0125568 0.0133272 0.0119498

0.0119238 0.0130987 0.0137409 0.0123727

0.0122151 0.0134413 0.01407 0.0125313

0.0125262 0.0141926 0.0145164 0.013323

0.0129686 0.0144382 0.015038 0.0134063

0.0134952 0.0151892 0.0151015 0.01377040.0137968 0.0154375 0.0155995 0.0144156

0.0140892 0.0158633 0.0157743 0.0143963

0.0145886 0.016073 0.0163068 0.0146179

0.0150238 0.0162939 0.0165279 0.0150305

0.0152636 0.0166225 0.0173991 0.0153612

0.0157277 0.0170551 0.0173817 0.0155286

0.0158568 0.0174587 0.0172491 0.0160701

0.0164053 0.0180052 0.0178794 0.0163454

0.0168378 0.0185253 0.018371 0.016465

0.0170838 0.0189861 0.0183541 0.0172905

0.0176013 0.0194166 0.0181321 0.01679180.0176275 0.0195895 0.0185445 0.0173585

0.0179724 0.019815 0.0184929 0.0172673

0.0185533 0.01981 0.0186464 0.0173441

0.0186034 0.019966 0.0185336 0.0176212

0.0186459 0.0196233 0.0181812 0.0175408

0.0182133 0.0190064 0.0178828 0.0170605


44/58

0.0181625 0.0175417 0.0175116 0.0172055

0.0177012 0.0165079 0.0168613 0.0172291

0.0172089 0.0159598 0.016419 0.0165939

0.0171109 0.0156787 0.0161042 0.0165851

0.0164836 0.0157156 0.0158032 0.0160283

0.0162114 0.0157507 0.0158615 0.01588730.0161613 0.0157103 0.0152213 0.0157737

0.015901 0.0157424 0.0148847 0.0150993

0.0156038 0.0153626 0.0144912 0.0148333

0.0150751 0.0144321 0.0135176 0.0142462

0.0148303 0.0137607 0.0134812 0.0141148

0.0141184 0.012913 0.0132191 0.0137565

0.0137094 0.0123117 0.0126915 0.0132967

0.0134346 0.0119525 0.0121874 0.0131786

0.0130292 0.0119234 0.0121468 0.0129615

0.0128513 0.0116331 0.0115597 0.0124334

0.0126425 0.0115726 0.0111195 0.0120802

0.012173 0.0114225 0.0105052 0.0115348

0.01196 0.0110938 0.0105779 0.0110938

0.0115263 0.0107004 0.009972 0.011124

0.0110232 0.0098339 0.009684 0.0105466

0.0105659 0.0091739 0.0091492 0.0100465

0.0101311 0.008553 0.008792 0.0098815

0.0097975 0.0083075 0.0083889 0.0091364

0.0094959 0.0080424 0.0081624 0.0093107

0.009108 0.0079662 0.0078752 0.0088438

0.0088615 0.0077538 0.0071352 0.0083780.008538 0.00751 0.0067203 0.0079701

0.0082729 0.0070868 0.0063323 0.0076158

0.0079091 0.0064289 0.0060877 0.0071293

0.0074739 0.0059003 0.0056185 0.0069482

0.00699 0.0053121 0.0053086 0.0065961

0.0065957 0.0048805 0.0048281 0.0062243

0.0063081 0.0044512 0.0045172 0.0057947

0.0058463 0.0042007 0.0040206 0.005551

0.0055363 0.0039733 0.0037065 0.0052786

0.0051419 0.0036776 0.003469 0.0047339

0.0047879 0.0034981 0.0029638 0.00449040.0044714 0.003066 0.0025486 0.0040532

0.0040431 0.0026147 0.0023841 0.0036575

0.0035685 0.0019711 0.002009 0.0032626

0.0031609 0.0014542 0.0018601 0.0031173

0.0028977 0.0009652 0.0015901 0.0027299

0.0024442 0.0005859 0.0013177 0.0024427


45/58

0.0022106 0.0003096 0.0011393 0.0021407

0.0018083 0.0001459 0.000993 0.0019214

0.0015015 7.449E-05 0.0008017 0.0016252

0.0011924 3.118E-05 0.0006016 0.0014863

0.0009468 1.092E-05 0.0005021 0.0013282

0.0007132 5.792E-06 0.0004031 0.00114540.0004899 1.398E-06 0.0002617 0.0008808

0.0002888 0 0.0002386 0.0008689

0.0001734 0 0.0001538 0.0006779

0.0001001 0 0.000118 0.0005182

5.357E-05 0 7.862E-05 0.0004595

3.267E-05 0 8.871E-05 0.0003402

9.491E-06 0 4.917E-05 0.0002479

2.245E-06 0 1.921E-05 0.0002348

0 0 1.553E-05 0.0001817

0 0 6.476E-06 0.0001534

0 0 1.1E-05 0.0001289

0 0 8.386E-06 7.318E-05

0 0 8.723E-06 5.985E-05

0 0 1.264E-06 6.286E-05

0 0 2.795E-07 5.306E-05

0 0 2.503E-06 2.576E-05

0 0 2.442E-06 2.415E-05

0 0 2.247E-06 2.214E-05

0 0 3.981E-07 1.007E-05

0 0 2.649E-09 4.035E-06

0 0 0 1.582E-060 0 0 1.888E-06

0 0 0 6.731E-07

0 0 0 3.045E-06

0 0 0 3.164E-06

0 0 0 1.382E-07

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


46/58

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

LTD LTD LTD LTD

0 0 0 0

0 0 0.0001997 0.0003297

0 0 0.0005991 0.00010990 0 0.0012981 0.0012088

0 0 0.0033949 0.0040659

0 0 0.0060909 0.0068132

0.0002173 0.0007997 0.0132801 0.0110989

0.0036936 0.0090964 0.0187718 0.0193407

0.0185769 0.0318872 0.0231653 0.0212088

0.0463878 0.0615754 0.0215676 0.0242857

0.057686 0.0592763 0.030654 0.0281319

0.0429115 0.0315874 0.0271593 0.0263736

0.0175991 0.0126949 0.0204693 0.0220879

0.0052146 0.002399 0.0215676 0.02087910.0014123 0.0010996 0.0203694 0.0184615

0.0003259 0.0019992 0.0161757 0.0178022

0.0029332 0.004898 0.0161757 0.0198901

0.0117328 0.0159936 0.0182726 0.016044

0.0267246 0.0319872 0.0218672 0.0198901

0.0379142 0.0420832 0.01997 0.0212088


47/58

0.0416078 0.0408836 0.0207688 0.0224176

0.0380228 0.0312875 0.0197703 0.0213187

0.0237914 0.0193922 0.0204693 0.0193407

0.0124932 0.0077969 0.0208687 0.0189011

0.0046714 0.0039984 0.0202696 0.0189011

0.0038023 0.0038984 0.0201697 0.0239560.0077132 0.0087965 0.0198702 0.019011

0.0142314 0.0178928 0.0171742 0.0191209

0.0231396 0.0268892 0.0181727 0.0194505

0.0305269 0.0288884 0.020669 0.0206593

0.0344378 0.0364854 0.0201697 0.0197802

0.0322651 0.0288884 0.0198702 0.0198901

0.0212928 0.0208916 0.0193709 0.0201099

0.01434 0.0112955 0.018672 0.0213187

0.0090168 0.0082967 0.0187718 0.0201099

0.0077132 0.0076969 0.0215676 0.0198901

0.00956 0.0114954 0.0208687 0.0196703

0.0158609 0.0185926 0.0211682 0.0195604

0.0249864 0.0291883 0.0204693 0.0172527

0.0310701 0.0288884 0.0172741 0.0194505

0.0333514 0.0287885 0.0184723 0.0198901

0.0321564 0.0257897 0.0204693 0.0197802

0.0228137 0.019892 0.0204693 0.0172527

0.0148832 0.0161935 0.0201697 0.0181319

0.0137968 0.010096 0.0202696 0.0172527

0.0117328 0.010096 0.0163754 0.019011

0.0130364 0.0131947 0.0181727 0.01846150.0181423 0.0182927 0.0168747 0.0186813

0.0216187 0.02509 0.0156765 0.0184615

0.0296578 0.0272891 0.015976 0.0176923

0.0285714 0.0290884 0.0143784 0.0162637

0.0239001 0.0259896 0.0123814 0.0145055

0.0225964 0.0188924 0.0127808 0.0134066

0.0183596 0.014994 0.012681 0.0108791

0.0103205 0.0088964 0.010684 0.0092308

0.005975 0.0045982 0.0096855 0.0074725

0.0031505 0.0022991 0.0083874 0.007033

0.0010864 0.0008996 0.0065901 0.00637360.0006518 0.0004998 0.0061907 0.0045055

0.0003259 0.0001999 0.0053919 0.0051648

0 9.996E-05 0.0042936 0.0050549

0 0 0.0037943 0.0040659

0 0 0.0024963 0.0020879

0 0 0.0024963 0.0024176


48/58

0 0 0.001997 0.0020879

0 0 0.0014978 0.0013187

0 0 0.0015976 0.0005495

0 0 0.000699 0.000989

0 0 0.0002996 0.0008791

0 0 0.0004993 0.00043960 0 0.0001997 0.0006593

0 0 0.0001997 0.0003297

0 0 0.0001997 0

0 0 0 0.0002198

0 0 0 0

0 0 0 0

0 0 9.985E-05 0.0001099

0 0 0 0

0 0 0 0

0 0 9.985E-05 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


49/58

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


50/58

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

-Inv @Deliv. -Inv @Deliv. -Inv @Deliv. -Inv @Deliv.

0 0 0 0

0 0 0.0001997 0.0001099

0 0 0.0005991 0

0 0 0.0012981 0.0001099

0 0 0.0033949 0.0006593

0 0 0.0060909 0.0013187

0.0001086 0.0007997 0.0130804 0.00186810.0006518 0.0090964 0.018672 0.0042857

0.0039109 0.0318872 0.0229656 0.0059341

0.0086909 0.0615754 0.0213679 0.0086813

0.0172732 0.0592763 0.0305542 0.0123077

0.0200978 0.0315874 0.0267599 0.0134066

0.0207496 0.0126949 0.020669 0.0161538

0.0199891 0.002399 0.0213679 0.0154945

0.0151005 0.0010996 0.0207688 0.0197802

0.0115155 0.0019992 0.0162756 0.0175824

0.0166214 0.004898 0.0161757 0.0194505

0.0181423 0.0159936 0.0185721 0.02175820.0196632 0.0319872 0.021967 0.0206593

0.0232482 0.0420832 0.0202696 0.019011

0.0239001 0.0408836 0.0207688 0.02

0.0234655 0.0312875 0.0197703 0.0226374

0.020315 0.0193922 0.0204693 0.0212088

0.0193373 0.0077969 0.0208687 0.019011


51/58

0.0174905 0.0039984 0.0202696 0.0205495

0.015535 0.0038984 0.0201697 0.0192308

0.0159696 0.0087965 0.0198702 0.0205495

0.0189028 0.0178928 0.0171742 0.0205495

0.021836 0.0268892 0.0181727 0.0193407

0.0237914 0.0288884 0.020669 0.02109890.023031 0.0364854 0.0201697 0.0204396

0.0217273 0.0288884 0.0198702 0.0176923

0.0217273 0.0208916 0.0193709 0.0195604

0.0181423 0.0112955 0.018672 0.0213187

0.0172732 0.0082967 0.0187718 0.0183516

0.018251 0.0076969 0.0215676 0.0178022

0.0166214 0.0114954 0.0208687 0.0194505

0.0153178 0.0185926 0.0211682 0.0216484

0.0200978 0.0291883 0.0204693 0.0206593

0.0221619 0.0288884 0.0172741 0.0193407

0.0216187 0.0287885 0.0184723 0.019011

0.0246605 0.0257897 0.0204693 0.0204396

0.0221619 0.019892 0.0204693 0.0201099

0.0190114 0.0161935 0.0201697 0.0183516

0.0180337 0.010096 0.0202696 0.0191209

0.0190114 0.010096 0.0163754 0.0198901

0.0200978 0.0131947 0.0181727 0.0178022

0.01912 0.0182927 0.0168747 0.0216484

0.0220532 0.02509 0.0156765 0.0175824

0.0231396 0.0272891 0.015976 0.0189011

0.0208582 0.0290884 0.0143784 0.02010990.0204237 0.0259896 0.0123814 0.0186813

0.020315 0.0188924 0.0127808 0.0186813

0.0183596 0.014994 0.012681 0.0142857

0.0192287 0.0088964 0.010684 0.0149451

0.0168387 0.0045982 0.0096855 0.0159341

0.01673 0.0022991 0.0085871 0.0124176

0.0142314 0.0008996 0.00669 0.0120879

0.0127105 0.0004998 0.0063904 0.0112088

0.0120587 0.0001999 0.0055916 0.0104396

0.0111896 9.996E-05 0.0043934 0.0083516

0.0074959 0 0.0041937 0.00681320.0041282 0 0.0022966 0.0071429

0.00239 0 0.002696 0.0064835

0.0014123 0 0.0015976 0.0053846

0.0013036 0 0.0013979 0.0045055

0.0006518 0 0.0015976 0.0043956

0.0001086 0 0.0003994 0.0034066


52/58

0 0 0.0001997 0.0024176

0 0 0.0001997 0.001978

0 0 0.0001997 0.0010989

0 0 0.0001997 0.0015385

0 0 0.0001997 0.0014286

0 0 0 0.00065930 0 0 0.000989

0 0 0 0.0006593

0 0 9.985E-05 0.0006593

0 0 0 0.0006593

0 0 0 0.0003297

0 0 9.985E-05 0.0001099

0 0 0 0.0002198

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0.0001099

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


53/58

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


54/58

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

LT+1 Dem LTDem LTDem LT+1 Dem

0 0 0 0

0 0 0.0001997 0

0 0 0.0005991 0

0 0 0.0012981 0

0 0 0.0033949 0

0 0 0.0060909 0

0 0.0007997 0.0132801 0

0 0.0090964 0.0187718 0

0 0.0318872 0.0231653 0.0002198

0 0.0615754 0.0215676 0.0001099

0 0.0592763 0.030654 0.00021980 0.0315874 0.0271593 0.000989

0 0.0126949 0.0204693 0.0017582

0 0.002399 0.0215676 0.0025275

0.0001086 0.0010996 0.0203694 0.0052747

0.0004345 0.0019992 0.0161757 0.0071429

0.0024986 0.004898 0.0161757 0.0106593

0.0099946 0.0159936 0.0182726 0.0131868

0.0202064 0.0319872 0.0218672 0.0148352

0.0326996 0.0420832 0.01997 0.0181319

0.0424769 0.0408836 0.0207688 0.0223077

0.0382401 0.0312875 0.0197703 0.01912090.0256382 0.0193922 0.0204693 0.0214286

0.0141228 0.0077969 0.0208687 0.0207692

0.0055405 0.0039984 0.0202696 0.0212088

0.0029332 0.0038984 0.0201697 0.0213187

0.0060837 0.0087965 0.0198702 0.0195604

0.0128191 0.0178928 0.0171742 0.0194505


55/58

0.0240087 0.0268892 0.0181727 0.0205495

0.0284628 0.0288884 0.020669 0.0201099

0.036176 0.0364854 0.0201697 0.0220879

0.0346551 0.0288884 0.0198702 0.02

0.0268332 0.0208916 0.0193709 0.02

0.0178164 0.0112955 0.018672 0.02010990.0091255 0.0082967 0.0187718 0.0193407

0.0077132 0.0076969 0.0215676 0.0208791

0.0101032 0.0114954 0.0208687 0.0202198

0.0127105 0.0185926 0.0211682 0.0195604

0.0171646 0.0291883 0.0204693 0.0189011

0.0299837 0.0288884 0.0172741 0.0156044

0.0286801 0.0287885 0.0184723 0.0221978

0.0270505 0.0257897 0.0204693 0.0192308

0.0257469 0.019892 0.0204693 0.0183516

0.0184682 0.0161935 0.0201697 0.0240659

0.0121673 0.010096 0.0202696 0.0184615

0.0114068 0.010096 0.0163754 0.0202198

0.0105378 0.0131947 0.0181727 0.0181319

0.0159696 0.0182927 0.0168747 0.0205495

0.0223791 0.02509 0.0156765 0.0186813

0.0258555 0.0272891 0.015976 0.0206593

0.0307442 0.0290884 0.0143784 0.0215385

0.0298751 0.0259896 0.0123814 0.0192308

0.025421 0.0188924 0.0127808 0.0207692

0.0175991 0.014994 0.012681 0.017033

0.0154264 0.0088964 0.010684 0.01813190.0126018 0.0045982 0.0096855 0.0201099

0.0170559 0.0022991 0.0083874 0.0167033

0.0184682 0.0008996 0.0065901 0.0179121

0.0222705 0.0004998 0.0061907 0.0154945

0.020641 0.0001999 0.0053919 0.0185714

0.026616 9.996E-05 0.0042936 0.0153846

0.0262901 0 0.0037943 0.0159341

0.0217273 0 0.0024963 0.0132967

0.0185769 0 0.0024963 0.0127473

0.0121673 0 0.001997 0.0108791

0.0082564 0 0.0014978 0.00923080.0052146 0 0.0015976 0.0082418

0.0024986 0 0.000699 0.0075824

0.001195 0 0.0002996 0.006044

0.0005432 0 0.0004993 0.006044

0 0 0.0001997 0.0065934

0 0 0.0001997 0.0046154


56/58

0 0 0.0001997 0.0037363

0 0 0 0.0027473

0 0 0 0.002967

0 0 0 0.0017582

0 0 9.985E-05 0.0017582

0 0 0 0.00142860 0 0 0.0017582

0 0 9.985E-05 0.0005495

0 0 0 0.000989

0 0 0 0.0004396

0 0 0 0.0003297

0 0 0 0.0003297

0 0 0 0.0005495

0 0 0 0

0 0 0 0.0002198

0 0 0 0.0001099

0 0 0 0

0 0 0 0.0001099

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0


57/58

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 00 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

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INVENTORY_SIMULATION.xls

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