Inventory Simulation Control Model

Sheet: Introduction File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Page 1 of 57 Simulating Inventory Control with Orders that Cross during Lead Time sS.xls Version 1.4 03/22/02 John.O.McClain@cornell.edu 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 frequently 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 under Order-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. Sheet: Introduction File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Page 2 of 57 Contents: These are the sheets in this workbook. Introduction (this sheet), with the following sections: 1. Measuring Inventory and Shortages at Time of Delivery (a) Shortfall below Reorder Level at Delivery: Shortfall@Deliv (b) Distribution of Shortfall@Delivery if Orders do not Cross (i) Continuous Review (ii) Periodic Review 2. Inventory and Shortages at Any Time (a) Shortfall below Order-up-to Level (b) Average Inventory and Shortages 3. Cost of Inventory, Backorders and Ordering: 4. Optimization Simulate where you set up the model and run the simulation. Graphs where simulation results are displayed in detail for any run stored on the Data sheet. Trace where the first part of the most recent simulation run is shown in a table and a graph. Data 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: s S Q L D mL, VarL mD, VarD reorder level, or Min Inv On-hand inventory order-up-to level, or Max BO Number of units backordered to customers S-s NetInv = Inv - BO (can be positive or negative) A value of lead time InvPosition NetInv + Outstanding Orders A value of one-period demand DL Demand that occurs during lead time Average & Variance of L mDL, VarDL Average & Variance of DL 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 s at delivery," defined as 1) Shortfall@Deliv = s - NetInv@Deliv at 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@Deliv we may compute certain performance measures: 2) NetInv@Deliv = s - Shortfall@Deliv 3) Inv@Deliv = MAX(0, s - Shortfall@Deliv ) 4) BO@Deliv = MAX(0, Shortfall@Deliv - s ) = Inv@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 Unit Time ) Sheet: Introduction File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Page 3 of 57 (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 - InvPosition@Ordering + 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) InvPosition@Ordering = s for continuous review, so 10) Shortfall@Deliv = DL for continuous review if orders do not cross (substitute 9 into 8). Shortfall@Deliv equals 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 mL and 2 13) Var[Shortfall@Deliv ] = mL VarD + mD 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 - D ≤ InvPosition@Ordering ≤ s Substituting 14 into 8, 15) DL ≤ Shortfall@Deliv ≤ DL + D = DL+1 for periodic review if orders do not cross. >> Shortfall@Deliv is 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 s is a nonincreasing function 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) mD mL ≤ Shortfall@Deliv ≤ mD (1+mL) The arguments leading to equation 15 also yield a lower limit for the variance: 2 19) Var[Shortfall@Deliv ] ≤ mL VarD + mD VarL The upper limit in equation 15 also yields a variance estimate, but it is not necessarily an upper limit: Sheet: Introduction File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Page 4 of 57 2 20) Var[Shortfall@Deliv ] ≈ (1 + mL) VarD + mD VarL 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) Shortfall = S - NetInv. Notice that Shortfall uses a different reference point than Shortfall@Delivery, namely S rather than s . This is necessary to avoid negative values. From Shortfall , we may compute more performance measures: 21) NetInv = S - Shortfall. 22) Inv = MAX(0, S - Shortfall ) 23) BO = MAX(0, Shortfall - S ) = Inv - S + Shortfall 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( Shortfall ≥ S )×(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{Shortfall ≥S )} 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. Sheet: Introduction File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Page 5 of 57 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(Inv ) + C2 × Av(BO ) + C3 × mD × P(BO ≥ 0) + C4 × P(BO >0) + C5 × Av(OrderRate) 4. Optimization The value of Q (the gap between s and 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 s among all systems that have the same Q as 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 s and 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 Q that 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. Sheet: Simulate File 259338ac-bf28-47ba-a39f-63577a468d95.xls Page 6 of 57 Simulation of a Min-Max (s,S) Inventory System in Continuous Time: Discrete or Continuous Review Periodic Review. Q=30, D=10, varD=10 Gamma InterDemandTime: Mu= 0.1, Std=0.1. Discrete LT: Mu= 3, Std=1.41 Change the design by entering numbers in the yellow boxes, and by checking or unchecking the selection boxes. Current Simulation Design: Type of Review Periodic Review? TRUE Inter-demand time (IDT) Gamma IDT? TRUE Lead Time (LT) Gamma LT? FALSE Theoretical Values LTD LT+1 Dem LT Inter-Demand Time Demand/period Conversion Formulas: Demand per Period: Inter-demand Time: Inter-Demand Time Demand/period Mean 10 0.1 0.1 10 Var StDev 10 3.162 0.01 0.100 0.01 10 0.100 3.162 Mean 30.00 40.00 3.00 0.1 10.00 Var StDev 230.00 15.166 240.00 15.492 2.00 1.414 0.01 0.100 10.00 3.162 Periodic Review Gamma IDT mean 0.1 StDev 0.1 Discrete IDT (not in use) IDT f(IDT) 0 0.5 0.033333333 0.066666667 0.1 0.133333333 0.166666667 0.2 0.5 mean 0.1 StDev 0.1 Gamma LT (not in use) mean 3 StDev 1.41421356 Discrete LT LT f(LT) 0 1 0.2 2 0.2 3 0.2 4 0.2 5 0.2 6 0 mean 3 StDev 1.41421356 Minimum Order Quantity Minimum Q = S-s 30 Run Controls Runin Periods 5,000 Run Periods 50,000 RNSeed 5235 Simulate Delete Old Data Click here to view simulation results. Click here to view graphs of the distributions Sheet: Graphs File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Page 7 of 57 View Performance Summary View Graphs of Distributions View Simulation Data Go To Simulation Design Choose your data set here Set the Reorder Level here Periodic Review, Q=50. D=10 (Var=10). Discrete LT: Mu= 3, Std=1.41 Gamma InterDemandTime: Mu= 0.1, Std=0.1 Crossings/Delivery=0 EOQ = 32 Min order Qty, Q = S-s = 50 Order-up-to level, S = 80 Number of columns of data available: Use data in column number: Reorder trigger level (to vary): s = Links  8 8 30 Performance Statistics for Shortfall LTDem LT+1 Dem Shortfall Unit Costs s=30, S=80 @Deliv. Mean = 29.980 35.014 41.017 57.046 Variance = 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 Backordered Demands=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. Using simulated distribution of: To achieve target probability, s= S=s+Q: Actual P(no BO@Deliv): Actual P(no BO, time av.): Predicted by LTD Predicted by LT+1 Dem LTDem 55 105 0.895 0.989 0.956 0.795 Target Probability of No Backorders: Shortfall LT+1 Dem Shortfall @Deliv. 61 66 44 111 116 94 0.956 0.984 0.696 0.997 0.999 0.952 0.988 0.996 0.792 0.895 0.949 0.580 0.95 This target's meaning: For "Shortfall", it means "% of time during which there are some backorders." For "Shorfall@Delivery", it means "% of orders for which some backorders exist when the order arrives." Search for Minimum Cost Reorder Level (s) holding constant S-s=50 53 52 51 50 49 48 47 0 20 40 Reorder Level, s 60 Make sure "Calculation" is set to "Automatic". If it is not, then press F9 to recalculate the cost curve whenever you change anything. First value of s for the graph: Interval between values: Minimum Cost = $47.83 at s =37, S =87 35 1 Cost Graph of Cost vs s , starting at this value, and incrementing by this amount. Sheet: Graphs File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Page 8 of 57 View Performance Summary View Graphs of Distributions View Simulation Data Go To Simulation Design Change which simulation is graphed by changing the column number in cell G5. Periodic Review, Q=50. D=10 (Var=10). Discrete LT: Mu= 3, Std=1.41 Gamma InterDemandTime: Mu= 0.1, Std=0.1 Crossings/Delivery=0 Links  Periodic Review, Q=50. D=10 (Var=10). Discrete LT: Mu= 3, Std=1.41 Gamma InterDemandTime: Mu= 0.1, Std=0.1 Crossings/Delivery=0 0.03 0.025 0.02 0.015 0.01 0.005 0 Graphs of Distributions for simulation run number 8 LTDem Shortfall @Deliv. LT+1 Dem 0 0.03 0.025 0.02 0.015 0.01 0.005 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 LTDem LT+1 Dem Shortfall Page Down for cumulative distributions  10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 IDT: Mean = 0.1, CV = 1, Gamma LT: Mean = 3, CV = 0.471, Discrete 0 1 2 3 4 5 6 0.01 0.055 0.1 0.145 0.19 0.235 0.28 LTDem Shortfall @Deliv. LT+1 Dem Shortfall Periodic Review, Q=50. D=10 (Var=10). Discrete LT: Mu= 3, Std=1.41 Gamma InterDemandTime: Mu= 0.1, Std=0.1 Crossings/Delivery=0 1.00 0.80 0.60 0.40 0.20 0.00 0 10 20 30 40 50 60 70 80 Cumulative Distributions 90 100 110 120 130 140 150 160 170 Sheet: Graphs File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Page 9 of 57 View Performance Summary View Graphs of Distributions View Simulation Data Go To Simulation Design Periodic Review, Q=50. D=10 (Var=10). Discrete LT: Mu= 3, Std=1.41 Gamma InterDemandTime: Mu= 0.1, Std=0.1 Crossings/Delivery=0 Links  Description of Simulation Data being Viewed: Inputs: Runin Periods 5,000 Run Periods 50,000 50 Q = S-s 10 Exp. Demand 10 Var. Dmd (approx) 5235 RNSeed TRUE Periodic Review? FALSE Gamma LT? TRUE Gamma IDT? 0.1 Exp. Inter-Demand Time 0.1 StDev Inter-Demand Time 3 Exp. LT StDev LT 1.41421356 30 Exp LTD 230 Var LTD 40 Exp D(LT+1) 240 Var D(LT+1) Input Distributions: Below Outputs: SimTime Demands Orders Deliveries Crossings Cross/Deliv 50,000 500,784 9,100 9,100 0 0 Shortfall, Avg. 57.046254 Shortfall, var. 489.28271 Shortfall@Deliv. Avg. 35.013956 Shortfall@Deliv. var. 242.52035 29.98033 LTD Avg. LTD var. 230.03291 LT+1 Dem Avg 41.017363 LT+1 Dem Var 239.76981 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 Gamma IDT f(IDT) Gamma IDT Discrete IDT F(IDT) f(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 LT: Mean = 3, CV = 0.471, Discrete Gamma LT Gamma f(LT) Discrete LT Discrete LT Discrete F(LT)Discrete f(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 Sheet: Trace File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Partial Simulation Results demands orders placed deliveries Number of Crossings 452 14 13 1 Theory Page 10 of 57 Order Crossing Simulation (s, S) with S=0 Continuous time! Q = S-s Exp. Demand Var. Dmd (approx) RNSeed Periodic Review? Gamma LT? Gamma IDT? Exp. IDT StDev IDT Exp. LT StDev LT 30 10 10 5235 Periodic Review. Q=30: D=10, var=10: L= 3, Std=1.41 TRUE Periodic Review. Q=30: D=10, var=10: L= 3, Std=1.41 FALSE 0 TRUE -10 0.1 -20 0.1 3 -30 1.41421 -40 4995 5000 5005 5010 5015 5020 -50 -60 -70 Shortfall Leadtime Leadtime Shortfall @ Delivery Demand Demand Mean 43.35 60.62 26.69 30.00 Variance 248.71 153.59 226.90 230.00 5025 5030 Current Time 55.556 -80 Period 5000 5000.047463 5000.118557 5000.11895 5000.453041 5000.509626 5000.76021 5001 5001.154046 5001.264099 5001.318424 5001.330007 5001.431884 5001.708118 5001.746788 5001.82104 5001.85482 5001.938805 5002.244994 5002.280199 5002.303541 5002.344361 5002.381167 5002.453742 5002.753257 5002.770789 5003.033741 5003.129288 5003.131748 5003.139099 5003.144072 5003.445661 5003.464883 5003.515421 5003.959563 5004.059034 5004.282059 5004.308 5004.463619 5004.552588 5004.57251 5004.585094 5004.59645 5004.85119 5004.935838 5004.939203 5004.98294 5005 5005 5005.043927 5005.125637 5005.134688 5005.222926 5005.254597 5005.297737 5005.401858 5005.444106 5005.70614 5005.88964 5005.895316 5006.028288 5006.045509 5006.066182 5006.082214 5006.119373 Dmd 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Arriving Inventory Order Orders On-Hand On-Order Position Quantity -27 0 -27 -28 0 -28 -29 0 -29 -30 0 -30 -31 0 -31 -32 0 -32 -33 0 -33 -33 33 0 33 -34 33 -1 -35 33 -2 -36 33 -3 -37 33 -4 -38 33 -5 -39 33 -6 -40 33 -7 -41 33 -8 -42 33 -9 -43 33 -10 -44 33 -11 -45 33 -12 -46 33 -13 -47 33 -14 -48 33 -15 -49 33 -16 -50 33 -17 -51 33 -18 -52 33 -19 -53 33 -20 -54 33 -21 -55 33 -22 -56 33 -23 -57 33 -24 -58 33 -25 -59 33 -26 -60 33 -27 -61 33 -28 -62 33 -29 -63 33 -30 -64 33 -31 -65 33 -32 -66 33 -33 -67 33 -34 -68 33 -35 -69 33 -36 -70 33 -37 -71 33 -38 -72 33 -39 -72 72 0 39 33 -39 39 0 -40 39 -1 -41 39 -2 -42 39 -3 -43 39 -4 -44 39 -5 -45 39 -6 -46 39 -7 -47 39 -8 -48 39 -9 -49 39 -10 -50 39 -11 -51 39 -12 -52 39 -13 -53 39 -14 -54 39 -15 -55 39 -16 Lead Time Delivery Period - Leadtime Inv. before orders Order Pipeline, Arrival Times Demand Delivery crossed 1 2 3 4 5 4 5005 0 5005 2 5007 -39 -72 0 5005 5005 5007 5035 Sheet: Trace File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Arriving Inventory Order Orders On-Hand On-Order Position Quantity -56 39 -17 -57 39 -18 -58 39 -19 39 -19 0 -19 -20 0 -20 -21 0 -21 -22 0 -22 -23 0 -23 -24 0 -24 -25 0 -25 -26 0 -26 -27 0 -27 -28 0 -28 -29 0 -29 -30 0 -30 -31 0 -31 -32 0 -32 -32 32 0 32 -33 32 -1 -34 32 -2 -35 32 -3 -36 32 -4 -37 32 -5 -38 32 -6 -39 32 -7 -40 32 -8 -41 32 -9 -42 32 -10 -43 32 -11 -44 32 -12 -45 32 -13 -46 32 -14 -47 32 -15 -48 32 -16 -49 32 -17 -50 32 -18 -51 32 -19 -52 32 -20 -53 32 -21 -54 32 -22 -55 32 -23 -56 32 -24 -57 32 -25 -58 32 -26 -59 32 -27 -60 32 -28 -61 32 -29 -62 32 -30 -62 62 0 30 -63 62 -1 -64 62 -2 -65 62 -3 -66 62 -4 -67 62 -5 -68 62 -6 -69 62 -7 -70 62 -8 -71 62 -9 -72 62 -10 -73 62 -11 -74 62 -12 30 -44 32 -12 -45 32 -13 -46 32 -14 -47 32 -15 -48 32 -16 -49 32 -17 -50 32 -18 -51 32 -19 -52 32 -20 -53 32 -21 -54 32 -22 -55 32 -23 32 -23 0 -23 -24 0 -24 -25 0 -25 -26 0 -26 -27 0 -27 -28 0 -28 -29 0 -29 -30 0 -30 -31 0 -31 -32 0 -32 -33 0 -33 -34 0 -34 Lead Time Delivery Period Page 11 of 57 Period 5006.132403 5006.197546 5006.550895 5007 5007.128251 5007.317277 5007.338246 5007.39217 5007.41161 5007.412227 5007.622616 5007.63529 5007.636659 5007.882665 5007.898352 5007.987569 5007.99081 5008 5008.159031 5008.254136 5008.542844 5008.590475 5008.656459 5008.871643 5009.002582 5009.068712 5009.071957 5009.298852 5009.629066 5009.653796 5009.801481 5009.810995 5009.860536 5009.877569 5009.957243 5009.984397 5010.127253 5010.327687 5010.352583 5010.361235 5010.59064 5010.703538 5010.747061 5010.77391 5010.778124 5010.898752 5010.918525 5010.955608 5011 5011.007742 5011.169116 5011.207074 5011.209828 5011.292345 5011.394348 5011.429936 5011.606302 5011.622673 5011.63795 5011.664522 5011.974317 5012 5012.001531 5012.13312 5012.150276 5012.193078 5012.358864 5012.360324 5012.44483 5012.530815 5012.890531 5012.916463 5012.923564 5013 5013.167599 5013.296098 5013.593854 5013.621019 5013.72919 5014.052806 5014.057097 5014.21525 5014.348423 5014.488077 5014.688973 Dmd 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - Leadtime Inv. before orders Order Pipeline, Arrival Times Demand Delivery crossed 1 2 3 4 5 -19 -58 5 5013 0 5013 1 5012 1 5012 5013 -12 -74 5012 -53 -55 Sheet: Trace File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Arriving Inventory Order Orders On-Hand On-Order Position Quantity -34 34 0 34 -35 34 -1 -36 34 -2 -37 34 -3 -38 34 -4 -39 34 -5 -40 34 -6 -41 34 -7 -42 34 -8 -43 34 -9 -44 34 -10 -45 34 -11 -46 34 -12 -47 34 -13 -48 34 -14 -49 34 -15 -50 34 -16 -51 34 -17 -52 34 -18 -53 34 -19 -54 34 -20 -55 34 -21 -56 34 -22 -57 34 -23 -58 34 -24 -59 34 -25 -60 34 -26 -61 34 -27 -62 34 -28 -63 34 -29 -64 34 -30 -65 34 -31 -66 34 -32 -66 66 0 32 34 -32 32 0 -33 32 -1 -34 32 -2 -35 32 -3 -36 32 -4 -37 32 -5 -38 32 -6 -39 32 -7 -40 32 -8 -41 32 -9 -42 32 -10 -43 32 -11 -44 32 -12 -45 32 -13 -46 32 -14 -47 32 -15 32 -15 0 -15 -16 0 -16 -17 0 -17 -18 0 -18 -19 0 -19 -20 0 -20 -21 0 -21 -22 0 -22 -23 0 -23 -24 0 -24 -25 0 -25 -26 0 -26 -27 0 -27 -28 0 -28 -29 0 -29 -30 0 -30 -31 0 -31 -32 0 -32 -33 0 -33 -34 0 -34 -35 0 -35 -35 35 0 35 -36 35 -1 -37 35 -2 -38 35 -3 -39 35 -4 -40 35 -5 -41 35 -6 -42 35 -7 -43 35 -8 -44 35 -9 35 -9 0 -9 -10 0 -10 -11 0 -11 -12 0 -12 Lead Time 3 Page 12 of 57 Period 5015 5015.055203 5015.245878 5015.375231 5015.394512 5015.553738 5015.615365 5015.701141 5015.888689 5015.934368 5015.962724 5016.325344 5016.424787 5016.466211 5016.560876 5016.593837 5016.732494 5016.743301 5016.765898 5016.778627 5016.885058 5016.931916 5017.045089 5017.052655 5017.290737 5017.366025 5017.495418 5017.597363 5017.636664 5017.656176 5017.69609 5017.753189 5017.799449 5018 5018 5018.289444 5018.393903 5018.551277 5018.707399 5018.992446 5019.127468 5019.200439 5019.393495 5019.425834 5019.477375 5019.633081 5019.70644 5019.716464 5019.856859 5019.938467 5020 5020.443185 5020.53125 5020.692152 5020.705346 5020.763168 5020.770471 5020.784454 5020.787054 5020.822942 5020.825711 5021.035497 5021.055711 5021.273183 5021.316599 5021.562636 5021.596209 5021.616976 5021.825483 5021.863034 5021.91974 5022 5022.256681 5022.261045 5022.263916 5022.271804 5022.316076 5022.57658 5022.824805 5022.829559 5022.986078 5023 5023.170266 5023.319448 5023.556362 Dmd 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Delivery - Leadtime Inv. before orders Order Pipeline, Arrival Times Period Demand Delivery crossed 1 2 3 4 5 5018 0 5018 2 5020 -32 -66 0 5018 5018 5020 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -15 -47 1 5023 0 5023 -9 -44 Sheet: Trace File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Arriving Inventory Order Orders On-Hand On-Order Position Quantity -13 0 -13 -14 0 -14 -15 0 -15 -16 0 -16 -17 0 -17 -18 0 -18 -19 0 -19 -20 0 -20 -21 0 -21 -22 0 -22 -23 0 -23 -24 0 -24 -25 0 -25 -26 0 -26 -27 0 -27 -28 0 -28 -29 0 -29 -30 0 -30 -31 0 -31 -32 0 -32 -33 0 -33 -34 0 -34 -35 0 -35 -36 0 -36 -37 0 -37 -38 0 -38 -39 0 -39 -40 0 -40 -41 0 -41 -41 41 0 41 -42 41 -1 -43 41 -2 -44 41 -3 -45 41 -4 -46 41 -5 -47 41 -6 -48 41 -7 -49 41 -8 -50 41 -9 -51 41 -10 -52 41 -11 41 -11 0 -11 -12 0 -12 -13 0 -13 -14 0 -14 -15 0 -15 -16 0 -16 -17 0 -17 -18 0 -18 -19 0 -19 -20 0 -20 -21 0 -21 -22 0 -22 -23 0 -23 -24 0 -24 -25 0 -25 -26 0 -26 -27 0 -27 -28 0 -28 -29 0 -29 -30 0 -30 -31 0 -31 -32 0 -32 -33 0 -33 -34 0 -34 -34 34 0 34 -35 34 -1 -36 34 -2 -37 34 -3 -38 34 -4 -39 34 -5 -40 34 -6 -41 34 -7 -42 34 -8 -43 34 -9 -44 34 -10 -45 34 -11 -46 34 -12 -47 34 -13 -48 34 -14 -49 34 -15 -50 34 -16 -51 34 -17 -52 34 -18 -53 34 -19 Lead Time Delivery Period Page 13 of 57 Period 5023.57303 5023.592373 5023.733228 5023.763896 5023.820688 5023.895811 5023.942577 5024.043329 5024.270086 5024.378698 5024.483592 5024.485565 5024.529116 5024.653183 5024.722509 5024.854316 5024.966056 5025.064577 5025.111872 5025.17711 5025.257125 5025.475878 5025.493196 5025.608927 5025.68282 5025.742549 5025.777209 5025.78503 5025.811158 5026 5026.10751 5026.176283 5026.453755 5026.470435 5026.648804 5026.649343 5026.684638 5026.796194 5026.928016 5026.948504 5026.993829 5027 5027.225137 5027.225765 5027.357827 5027.556581 5027.582707 5027.741786 5027.775092 5027.896066 5027.964415 5028.200946 5028.26773 5028.402307 5028.516994 5028.634542 5028.676194 5028.83791 5029.049764 5029.072065 5029.215814 5029.503296 5029.568933 5029.651647 5029.706527 5030 5030.054073 5030.154665 5030.325675 5030.347236 5030.694311 5030.909284 5031.00317 5031.065266 5031.134427 5031.210778 5031.231001 5031.284301 5031.494828 5031.804843 5031.873472 5032.37739 5032.551595 5032.587516 5032.603276 Dmd 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - Leadtime Inv. before orders Order Pipeline, Arrival Times Demand Delivery crossed 1 2 3 4 5 1 5027 0 5027 -11 -52 4 5034 0 5034 Sheet: Trace File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Arriving Inventory Order Orders On-Hand On-Order Position Quantity -54 34 -20 -55 34 -21 -56 34 -22 -57 34 -23 -58 34 -24 -59 34 -25 -60 34 -26 -61 34 -27 -62 34 -28 -63 34 -29 -64 34 -30 -65 34 -31 -66 34 -32 -67 34 -33 -68 34 -34 -68 68 0 34 34 -34 34 0 -35 34 -1 -36 34 -2 -37 34 -3 -38 34 -4 -39 34 -5 -40 34 -6 -41 34 -7 -42 34 -8 -43 34 -9 -44 34 -10 -45 34 -11 -46 34 -12 -47 34 -13 -48 34 -14 -49 34 -15 -50 34 -16 -51 34 -17 -52 34 -18 -53 34 -19 -54 34 -20 -55 34 -21 -56 34 -22 -57 34 -23 -58 34 -24 -59 34 -25 -60 34 -26 -61 34 -27 -62 34 -28 -63 34 -29 -64 34 -30 -65 34 -31 -66 34 -32 -67 34 -33 -67 67 0 33 -68 67 -1 -69 67 -2 -70 67 -3 -71 67 -4 -72 67 -5 -73 67 -6 -74 67 -7 -75 67 -8 34 -41 33 -8 -42 33 -9 -43 33 -10 -44 33 -11 -45 33 -12 -46 33 -13 -47 33 -14 -48 33 -15 -49 33 -16 -50 33 -17 -51 33 -18 -52 33 -19 -53 33 -20 -54 33 -21 -55 33 -22 -56 33 -23 -57 33 -24 -58 33 -25 -59 33 -26 -60 33 -27 -61 33 -28 -62 33 -29 -63 33 -30 -64 33 -31 -64 64 0 31 -65 64 -1 Lead Time Delivery Period Page 14 of 57 Period 5032.628982 5032.807748 5032.859922 5032.979348 5033.005025 5033.018108 5033.269005 5033.299715 5033.361913 5033.549289 5033.668252 5033.709487 5033.742204 5033.819765 5033.878407 5034 5034 5034.076231 5034.250177 5034.343843 5034.426428 5034.451541 5034.496684 5034.568854 5034.643506 5034.720052 5034.726437 5034.868104 5034.870989 5034.957622 5035.031428 5035.217971 5035.312471 5035.390787 5035.527393 5035.536364 5035.589322 5035.765561 5035.774386 5035.905474 5036.039154 5036.077696 5036.137509 5036.182616 5036.413066 5036.642166 5036.784987 5036.862945 5036.897086 5036.920594 5037 5037.024143 5037.144921 5037.257073 5037.308064 5037.333919 5037.583959 5037.726413 5037.747136 5038 5038.167452 5038.244063 5038.31158 5038.379458 5038.549572 5038.55365 5038.578496 5038.75299 5038.824419 5038.839401 5038.941159 5039.052493 5039.30073 5039.34189 5039.346488 5039.466435 5039.508918 5039.653927 5039.850323 5039.873611 5039.897019 5039.926865 5039.976452 5040 5040.157764 Dmd 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - Leadtime Inv. before orders Order Pipeline, Arrival Times Demand Delivery crossed 1 2 3 4 5 4 5038 -34 -68 0 5034 5034 5038 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 5041 0 5038 5041 -41 -75 5038 5 5045 0 5041 5045 Sheet: Trace File: 259338ac-bf28-47ba-a39f-63577a468d95.xls Arriving Inventory Order Orders On-Hand On-Order Position Quantity -66 64 -2 -67 64 -3 -68 64 -4 -69 64 -5 -70 64 -6 33 -37 31 -6 -38 31 -7 -39 31 -8 -40 31 -9 -41 31 -10 -42 31 -11 -43 31 -12 -44 31 -13 -45 31 -14 -46 31 -15 -47 31 -16 -48 31 -17 -49 31 -18 -50 31 -19 -51 31 -20 -52 31 -21 -53 31 -22 -54 31 -23 -55 31 -24 -56 31 -25 -57 31 -26 -58 31 -27 -59 31 -28 -60 31 -29 -61 31 -30 -62 31 -31 -62 62 0 31 -63 62 -1 -64 62 -2 -65 62 -3 -66 62 -4 -67 62 -5 -68 62 -6 -69 62 -7 31 -38 31 -7 31 -7 0 -7 -8 0 -8 -9 0 -9 -10 0 -10 -11 0 -11 -12 0 -12 -13 0 -13 -14 0 -14 -15 0 -15 -16 0 -16 -17 0 -17 -18 0 -18 -19 0 -19 -20 0 -20 -21 0 -21 -22 0 -22 -23 0 -23 -24 0 -24 -25 0 -25 -26 0 -26 -27 0 -27 -28 0 -28 -29 0 -29 -30 0 -30 -30 30 0 30 -31 30 -1 -32 30 -2 -33 30 -3 -34 30 -4 -35 30 -5 -36 30 -6 -37 30 -7 -38 30 -8 -39 30 -9 -40 30 -10 Lead Time Delivery Period Page 15 of 57 Period 5040.272391 5040.462255 5040.534409 5040.847826 5040.920234 5041 5041.016447 5041.12444 5041.178727 5041.290514 5041.432829 5041.535971 5041.605302 5041.693973 5041.849468 5041.914911 5041.976849 5042.053916 5042.170456 5042.326573 5042.468459 5042.493427 5042.512026 5043.141543 5043.197075 5043.28622 5043.307647 5043.462904 5043.59267 5043.850839 5043.981739 5044 5044.145907 5044.163523 5044.315559 5044.410533 5044.808169 5044.872432 5044.975082 5045 5045 5045.193782 5045.377253 5045.387592 5045.441223 5045.653598 5045.672726 5045.72577 5045.877501 5045.889819 5046.01742 5046.047783 5046.048649 5046.091179 5046.168037 5046.246604 5046.272145 5046.41277 5046.461265 5046.464301 5046.729683 5046.782132 5046.829459 5046.888235 5047 5047.029942 5047.231122 5047.389787 5047.458878 5047.551307 5047.638875 5047.939996 5047.984952 5048.017181 5048.020285 Dmd 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - Leadtime Inv. before orders Order Pipeline, Arrival Times Demand Delivery crossed 1 2 3 4 5 -37 -70 5041 1 5045 0 5045 5045 -38 -7 -69 -38 5045 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 5052 0 5052 Runin Periods Run Periods Q = S-s Exp. Demand Var. Dmd (approx) RNSeed Periodic Review? Gamma LT? Gamma IDT? Exp. Inter-Demand Time StDev Inter-Demand Time Exp. LT StDev LT Exp LTD Var LTD Exp D(LT+1) Var D(LT+1) SimTime Demands Orders Deliveries Crossings Cross/Deliv LTD Avg. LTD var. "LT+1 Dem" or "LTD", Avg. "LT+1 Dem" or "LTD", Var. S-Inv. (Time Av) Avg. S-Inv. (Time Av) var. s-Inv @Deliv. 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35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 -Inv 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 -Inv 0 5.39E-06 2.805E-05 7.196E-05 0.0001714 0.0003403 0.0006986 0.0010466 0.0015789 0.0022252 0.0028909 0.0037181 0.0043397 0.0051222 0.0060303 0.0068243 144 145 146 147 148 149 150 151 152 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0.0201099 0.0193407 0.0208791 0.0202198 0.0195604 0.0189011 0.0156044 0.0221978 0.0192308 0.0183516 0.0240659 0.0184615 0.0202198 0.0181319 0.0205495 0.0186813 0.0206593 0.0215385 0.0192308 0.0207692 0.017033 0.0181319 0.0201099 0.0167033 0.0179121 0.0154945 0.0185714 0.0153846 0.0159341 0.0132967 0.0127473 0.0108791 0.0092308 0.0082418 0.0075824 0.006044 0.006044 0.0065934 0.0046154 0.0003194 0.0001597 3.992E-05 7.984E-05 3.992E-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 0.0039777 0.00358 0.0022872 0.0020883 0.0013425 0.0012928 0.0011436 0.0011436 0.0004475 0.0002983 0.0003481 0.0002486 9.944E-05 0.0001989 4.972E-05 4.972E-05 0 4.972E-05 9.944E-05 4.972E-05 4.972E-05 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 0.0045675 0.0032793 0.002723 0.0021959 0.0016689 0.0014347 0.0012297 0.0009955 0.0010833 0.0004977 0.0003513 0.0001464 0.000205 0.0001464 0.000205 8.784E-05 5.856E-05 2.928E-05 0 0 2.928E-05 0 2.928E-05 0 0 2.928E-05 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0037363 0.0027473 0.002967 0.0017582 0.0017582 0.0014286 0.0017582 0.0005495 0.000989 0.0004396 0.0003297 0.0003297 0.0005495 0 0.0002198 0.0001099 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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) Discrete F(IDT) Discrete F(IDT) Discrete F(IDT) Discrete 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 1 Discrete 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) Discrete F(LT) Discrete F(LT) Discrete F(LT) Discrete F(LT) 0 0 0 0 0.2 0.2 0.2 0.2 0.4 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 5,000 50,000 50 10 1.6 5235 TRUE FALSE TRUE 0.1 0.04 3 1.4142136 30 204.8 40 206.4 50,000 500,285 9,205 9,205 0 0 30.322651 205.12545 40.574253 206.88588 57.890613 458.26579 34.671157 217.07481 x 0 1 2 3 4 5 6 7 8 9 10 11 5,000 50,000 50 10 1.6 5235 FALSE FALSE TRUE 0.1 0.04 3 1.4142136 30 204.8 40 206.4 50,000 500,203 10,004 10,004 0 0 29.434026 210.07711 29.434026 210.07711 54.706093 419.01377 29.434026 210.07711 x 0 1 2 3 4 5 6 7 8 9 10 11 5,000 50,000 50 10 10 5235 FALSE FALSE TRUE 0.1 0.1 3 1.4142136 30 230 40 240 50,000 500,771 10,015 10,015 32 0.0031952 30.02666 232.50503 30.02666 232.50503 54.482139 440.23707 30.02666 231.62635 x 0 1 2 3 4 5 6 7 8 9 10 11 5,000 50,000 50 10 10 5235 TRUE FALSE TRUE 0.1 0.1 3 1.4142136 30 230 40 240 50,000 500,784 9,100 9,100 0 0 29.98033 230.03291 41.017363 239.76981 57.046254 489.28271 35.013956 242.52035 x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 -Inv 0 0 0 0 0 0 5.41E-06 6.858E-05 0.0003221 0.0007977 0.0014986 0.0022171 0.0029673 0.0033857 0.003497 0.0035626 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 -Inv 0 0 0 0 0 0 1.274E-05 0.0001772 0.0005403 0.0012819 0.0021571 0.0031584 0.0037694 0.0041092 0.0042022 0.0042344 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 -Inv 0 1.494E-05 2.651E-05 7.946E-05 0.0001832 0.0002769 0.0006138 0.0009107 0.0013714 0.0017294 0.0023351 0.0029807 0.0033138 0.0037514 0.0041895 0.0042563 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 -Inv 0 3.341E-05 1.26E-05 8.524E-05 0.0001675 0.0002705 0.0005051 0.0008976 0.0011896 0.0014794 0.0021735 0.0026129 0.0030778 0.0034604 0.0037958 0.0040066 0.0037227 0.0039013 0.0040981 0.0047755 0.0051969 0.0056314 0.0063585 0.0066801 0.0071485 0.007208 0.0074757 0.0078056 0.0080426 0.0084772 0.0087867 0.0094378 0.0098189 0.0100284 0.0105418 0.0107534 0.0111211 0.0112604 0.0119238 0.0122151 0.0125262 0.0129686 0.0134952 0.0137968 0.0140892 0.0145886 0.0150238 0.0152636 0.0157277 0.0158568 0.0164053 0.0168378 0.0170838 0.0176013 0.0176275 0.0179724 0.0185533 0.0186034 0.0186459 0.0182133 0.0042676 0.0046395 0.0049026 0.0055519 0.0062682 0.0069855 0.0075745 0.0079758 0.0081725 0.0081785 0.0083876 0.0087221 0.0089721 0.0094762 0.0101282 0.0106916 0.0112872 0.0117812 0.0118338 0.0121516 0.0124728 0.0125568 0.0130987 0.0134413 0.0141926 0.0144382 0.0151892 0.0154375 0.0158633 0.016073 0.0162939 0.0166225 0.0170551 0.0174587 0.0180052 0.0185253 0.0189861 0.0194166 0.0195895 0.019815 0.01981 0.019966 0.0196233 0.0190064 0.0049591 0.0050332 0.0057097 0.0059432 0.0066084 0.0067803 0.0073057 0.0074776 0.0082476 0.0083344 0.0089633 0.0091628 0.0096219 0.0101633 0.0104474 0.0107436 0.0112902 0.011633 0.0116918 0.0120839 0.0126102 0.0133272 0.0137409 0.01407 0.0145164 0.015038 0.0151015 0.0155995 0.0157743 0.0163068 0.0165279 0.0173991 0.0173817 0.0172491 0.0178794 0.018371 0.0183541 0.0181321 0.0185445 0.0184929 0.0186464 0.0185336 0.0181812 0.0178828 0.0045078 0.0046368 0.0051967 0.0054742 0.0057886 0.0062942 0.0066731 0.0069427 0.007189 0.0076418 0.0082318 0.0083975 0.0087557 0.0089793 0.0093796 0.0099374 0.0101457 0.0106357 0.0111452 0.0113045 0.0116326 0.0119498 0.0123727 0.0125313 0.013323 0.0134063 0.0137704 0.0144156 0.0143963 0.0146179 0.0150305 0.0153612 0.0155286 0.0160701 0.0163454 0.016465 0.0172905 0.0167918 0.0173585 0.0172673 0.0173441 0.0176212 0.0175408 0.0170605 0.0181625 0.0177012 0.0172089 0.0171109 0.0164836 0.0162114 0.0161613 0.015901 0.0156038 0.0150751 0.0148303 0.0141184 0.0137094 0.0134346 0.0130292 0.0128513 0.0126425 0.012173 0.01196 0.0115263 0.0110232 0.0105659 0.0101311 0.0097975 0.0094959 0.009108 0.0088615 0.008538 0.0082729 0.0079091 0.0074739 0.00699 0.0065957 0.0063081 0.0058463 0.0055363 0.0051419 0.0047879 0.0044714 0.0040431 0.0035685 0.0031609 0.0028977 0.0024442 0.0175417 0.0165079 0.0159598 0.0156787 0.0157156 0.0157507 0.0157103 0.0157424 0.0153626 0.0144321 0.0137607 0.012913 0.0123117 0.0119525 0.0119234 0.0116331 0.0115726 0.0114225 0.0110938 0.0107004 0.0098339 0.0091739 0.008553 0.0083075 0.0080424 0.0079662 0.0077538 0.00751 0.0070868 0.0064289 0.0059003 0.0053121 0.0048805 0.0044512 0.0042007 0.0039733 0.0036776 0.0034981 0.003066 0.0026147 0.0019711 0.0014542 0.0009652 0.0005859 0.0175116 0.0168613 0.016419 0.0161042 0.0158032 0.0158615 0.0152213 0.0148847 0.0144912 0.0135176 0.0134812 0.0132191 0.0126915 0.0121874 0.0121468 0.0115597 0.0111195 0.0105052 0.0105779 0.009972 0.009684 0.0091492 0.008792 0.0083889 0.0081624 0.0078752 0.0071352 0.0067203 0.0063323 0.0060877 0.0056185 0.0053086 0.0048281 0.0045172 0.0040206 0.0037065 0.003469 0.0029638 0.0025486 0.0023841 0.002009 0.0018601 0.0015901 0.0013177 0.0172055 0.0172291 0.0165939 0.0165851 0.0160283 0.0158873 0.0157737 0.0150993 0.0148333 0.0142462 0.0141148 0.0137565 0.0132967 0.0131786 0.0129615 0.0124334 0.0120802 0.0115348 0.0110938 0.011124 0.0105466 0.0100465 0.0098815 0.0091364 0.0093107 0.0088438 0.008378 0.0079701 0.0076158 0.0071293 0.0069482 0.0065961 0.0062243 0.0057947 0.005551 0.0052786 0.0047339 0.0044904 0.0040532 0.0036575 0.0032626 0.0031173 0.0027299 0.0024427 0.0022106 0.0018083 0.0015015 0.0011924 0.0009468 0.0007132 0.0004899 0.0002888 0.0001734 0.0001001 5.357E-05 3.267E-05 9.491E-06 2.245E-06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0003096 0.0001459 7.449E-05 3.118E-05 1.092E-05 5.792E-06 1.398E-06 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0011393 0.000993 0.0008017 0.0006016 0.0005021 0.0004031 0.0002617 0.0002386 0.0001538 0.000118 7.862E-05 8.871E-05 4.917E-05 1.921E-05 1.553E-05 6.476E-06 1.1E-05 8.386E-06 8.723E-06 1.264E-06 2.795E-07 2.503E-06 2.442E-06 2.247E-06 3.981E-07 2.649E-09 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0021407 0.0019214 0.0016252 0.0014863 0.0013282 0.0011454 0.0008808 0.0008689 0.0006779 0.0005182 0.0004595 0.0003402 0.0002479 0.0002348 0.0001817 0.0001534 0.0001289 7.318E-05 5.985E-05 6.286E-05 5.306E-05 2.576E-05 2.415E-05 2.214E-05 1.007E-05 4.035E-06 1.582E-06 1.888E-06 6.731E-07 3.045E-06 3.164E-06 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 0 0 0 0 0 0 0 0 0 0 0 0 LTD 0 0 0 0 0 0 0.0002173 0.0036936 0.0185769 0.0463878 0.057686 0.0429115 0.0175991 0.0052146 0.0014123 0.0003259 0.0029332 0.0117328 0.0267246 0.0379142 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 LTD 0 0 0 0 0 0 0.0007997 0.0090964 0.0318872 0.0615754 0.0592763 0.0315874 0.0126949 0.002399 0.0010996 0.0019992 0.004898 0.0159936 0.0319872 0.0420832 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 LTD 0 0.0001997 0.0005991 0.0012981 0.0033949 0.0060909 0.0132801 0.0187718 0.0231653 0.0215676 0.030654 0.0271593 0.0204693 0.0215676 0.0203694 0.0161757 0.0161757 0.0182726 0.0218672 0.01997 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 LTD 0 0.0003297 0.0001099 0.0012088 0.0040659 0.0068132 0.0110989 0.0193407 0.0212088 0.0242857 0.0281319 0.0263736 0.0220879 0.0208791 0.0184615 0.0178022 0.0198901 0.016044 0.0198901 0.0212088 0.0416078 0.0380228 0.0237914 0.0124932 0.0046714 0.0038023 0.0077132 0.0142314 0.0231396 0.0305269 0.0344378 0.0322651 0.0212928 0.01434 0.0090168 0.0077132 0.00956 0.0158609 0.0249864 0.0310701 0.0333514 0.0321564 0.0228137 0.0148832 0.0137968 0.0117328 0.0130364 0.0181423 0.0216187 0.0296578 0.0285714 0.0239001 0.0225964 0.0183596 0.0103205 0.005975 0.0031505 0.0010864 0.0006518 0.0003259 0 0 0 0 0.0408836 0.0312875 0.0193922 0.0077969 0.0039984 0.0038984 0.0087965 0.0178928 0.0268892 0.0288884 0.0364854 0.0288884 0.0208916 0.0112955 0.0082967 0.0076969 0.0114954 0.0185926 0.0291883 0.0288884 0.0287885 0.0257897 0.019892 0.0161935 0.010096 0.010096 0.0131947 0.0182927 0.02509 0.0272891 0.0290884 0.0259896 0.0188924 0.014994 0.0088964 0.0045982 0.0022991 0.0008996 0.0004998 0.0001999 9.996E-05 0 0 0 0.0207688 0.0197703 0.0204693 0.0208687 0.0202696 0.0201697 0.0198702 0.0171742 0.0181727 0.020669 0.0201697 0.0198702 0.0193709 0.018672 0.0187718 0.0215676 0.0208687 0.0211682 0.0204693 0.0172741 0.0184723 0.0204693 0.0204693 0.0201697 0.0202696 0.0163754 0.0181727 0.0168747 0.0156765 0.015976 0.0143784 0.0123814 0.0127808 0.012681 0.010684 0.0096855 0.0083874 0.0065901 0.0061907 0.0053919 0.0042936 0.0037943 0.0024963 0.0024963 0.0224176 0.0213187 0.0193407 0.0189011 0.0189011 0.023956 0.019011 0.0191209 0.0194505 0.0206593 0.0197802 0.0198901 0.0201099 0.0213187 0.0201099 0.0198901 0.0196703 0.0195604 0.0172527 0.0194505 0.0198901 0.0197802 0.0172527 0.0181319 0.0172527 0.019011 0.0184615 0.0186813 0.0184615 0.0176923 0.0162637 0.0145055 0.0134066 0.0108791 0.0092308 0.0074725 0.007033 0.0063736 0.0045055 0.0051648 0.0050549 0.0040659 0.0020879 0.0024176 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.001997 0.0014978 0.0015976 0.000699 0.0002996 0.0004993 0.0001997 0.0001997 0.0001997 0 0 0 9.985E-05 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 0.0020879 0.0013187 0.0005495 0.000989 0.0008791 0.0004396 0.0006593 0.0003297 0 0.0002198 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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.s-Inv @Deliv.s-Inv @Deliv.s-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 0.0018681 0.0006518 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 0.0217582 0.0196632 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 0.0174905 0.015535 0.0159696 0.0189028 0.021836 0.0237914 0.023031 0.0217273 0.0217273 0.0181423 0.0172732 0.018251 0.0166214 0.0153178 0.0200978 0.0221619 0.0216187 0.0246605 0.0221619 0.0190114 0.0180337 0.0190114 0.0200978 0.01912 0.0220532 0.0231396 0.0208582 0.0204237 0.020315 0.0183596 0.0192287 0.0168387 0.01673 0.0142314 0.0127105 0.0120587 0.0111896 0.0074959 0.0041282 0.00239 0.0014123 0.0013036 0.0006518 0.0001086 0.0039984 0.0038984 0.0087965 0.0178928 0.0268892 0.0288884 0.0364854 0.0288884 0.0208916 0.0112955 0.0082967 0.0076969 0.0114954 0.0185926 0.0291883 0.0288884 0.0287885 0.0257897 0.019892 0.0161935 0.010096 0.010096 0.0131947 0.0182927 0.02509 0.0272891 0.0290884 0.0259896 0.0188924 0.014994 0.0088964 0.0045982 0.0022991 0.0008996 0.0004998 0.0001999 9.996E-05 0 0 0 0 0 0 0 0.0202696 0.0201697 0.0198702 0.0171742 0.0181727 0.020669 0.0201697 0.0198702 0.0193709 0.018672 0.0187718 0.0215676 0.0208687 0.0211682 0.0204693 0.0172741 0.0184723 0.0204693 0.0204693 0.0201697 0.0202696 0.0163754 0.0181727 0.0168747 0.0156765 0.015976 0.0143784 0.0123814 0.0127808 0.012681 0.010684 0.0096855 0.0085871 0.00669 0.0063904 0.0055916 0.0043934 0.0041937 0.0022966 0.002696 0.0015976 0.0013979 0.0015976 0.0003994 0.0205495 0.0192308 0.0205495 0.0205495 0.0193407 0.0210989 0.0204396 0.0176923 0.0195604 0.0213187 0.0183516 0.0178022 0.0194505 0.0216484 0.0206593 0.0193407 0.019011 0.0204396 0.0201099 0.0183516 0.0191209 0.0198901 0.0178022 0.0216484 0.0175824 0.0189011 0.0201099 0.0186813 0.0186813 0.0142857 0.0149451 0.0159341 0.0124176 0.0120879 0.0112088 0.0104396 0.0083516 0.0068132 0.0071429 0.0064835 0.0053846 0.0045055 0.0043956 0.0034066 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0001997 0.0001997 0.0001997 0.0001997 0.0001997 0 0 0 9.985E-05 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 0.0024176 0.001978 0.0010989 0.0015385 0.0014286 0.0006593 0.000989 0.0006593 0.0006593 0.0006593 0.0003297 0.0001099 0.0002198 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0001086 0.0004345 0.0024986 0.0099946 0.0202064 0.0326996 0.0424769 0.0382401 0.0256382 0.0141228 0.0055405 0.0029332 0.0060837 0.0128191 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 LTDem 0 0 0 0 0 0 0.0007997 0.0090964 0.0318872 0.0615754 0.0592763 0.0315874 0.0126949 0.002399 0.0010996 0.0019992 0.004898 0.0159936 0.0319872 0.0420832 0.0408836 0.0312875 0.0193922 0.0077969 0.0039984 0.0038984 0.0087965 0.0178928 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 LTDem 0 0.0001997 0.0005991 0.0012981 0.0033949 0.0060909 0.0132801 0.0187718 0.0231653 0.0215676 0.030654 0.0271593 0.0204693 0.0215676 0.0203694 0.0161757 0.0161757 0.0182726 0.0218672 0.01997 0.0207688 0.0197703 0.0204693 0.0208687 0.0202696 0.0201697 0.0198702 0.0171742 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 LT+1 Dem 0 0 0 0 0 0 0 0 0.0002198 0.0001099 0.0002198 0.000989 0.0017582 0.0025275 0.0052747 0.0071429 0.0106593 0.0131868 0.0148352 0.0181319 0.0223077 0.0191209 0.0214286 0.0207692 0.0212088 0.0213187 0.0195604 0.0194505 0.0240087 0.0284628 0.036176 0.0346551 0.0268332 0.0178164 0.0091255 0.0077132 0.0101032 0.0127105 0.0171646 0.0299837 0.0286801 0.0270505 0.0257469 0.0184682 0.0121673 0.0114068 0.0105378 0.0159696 0.0223791 0.0258555 0.0307442 0.0298751 0.025421 0.0175991 0.0154264 0.0126018 0.0170559 0.0184682 0.0222705 0.020641 0.026616 0.0262901 0.0217273 0.0185769 0.0121673 0.0082564 0.0052146 0.0024986 0.001195 0.0005432 0 0 0.0268892 0.0288884 0.0364854 0.0288884 0.0208916 0.0112955 0.0082967 0.0076969 0.0114954 0.0185926 0.0291883 0.0288884 0.0287885 0.0257897 0.019892 0.0161935 0.010096 0.010096 0.0131947 0.0182927 0.02509 0.0272891 0.0290884 0.0259896 0.0188924 0.014994 0.0088964 0.0045982 0.0022991 0.0008996 0.0004998 0.0001999 9.996E-05 0 0 0 0 0 0 0 0 0 0 0 0.0181727 0.020669 0.0201697 0.0198702 0.0193709 0.018672 0.0187718 0.0215676 0.0208687 0.0211682 0.0204693 0.0172741 0.0184723 0.0204693 0.0204693 0.0201697 0.0202696 0.0163754 0.0181727 0.0168747 0.0156765 0.015976 0.0143784 0.0123814 0.0127808 0.012681 0.010684 0.0096855 0.0083874 0.0065901 0.0061907 0.0053919 0.0042936 0.0037943 0.0024963 0.0024963 0.001997 0.0014978 0.0015976 0.000699 0.0002996 0.0004993 0.0001997 0.0001997 0.0205495 0.0201099 0.0220879 0.02 0.02 0.0201099 0.0193407 0.0208791 0.0202198 0.0195604 0.0189011 0.0156044 0.0221978 0.0192308 0.0183516 0.0240659 0.0184615 0.0202198 0.0181319 0.0205495 0.0186813 0.0206593 0.0215385 0.0192308 0.0207692 0.017033 0.0181319 0.0201099 0.0167033 0.0179121 0.0154945 0.0185714 0.0153846 0.0159341 0.0132967 0.0127473 0.0108791 0.0092308 0.0082418 0.0075824 0.006044 0.006044 0.0065934 0.0046154 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0001997 0 0 0 9.985E-05 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 0.0037363 0.0027473 0.002967 0.0017582 0.0017582 0.0014286 0.0017582 0.0005495 0.000989 0.0004396 0.0003297 0.0003297 0.0005495 0 0.0002198 0.0001099 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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) Discrete F(IDT) Discrete F(IDT) Discrete 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 1 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) Discrete F(LT) Discrete F(LT) Discrete F(LT) 0 0 0 0 0.2 0.2 0.2 0.2 0.4 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