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A candle vendor can keep at most 80 candles in the inventory and reviews the inventory at the end of every three days. The vendor places an order if the ending inventory is at most 20 candles at the end of each cycle such that the maximum inventory capacity is reached. The demand for candles depends on the power outages and the probability distributions of the demand on days when there is a power outage and days without a power outage are given in Table 1 below. Table 1: Demand Probability Distribution Power Demand Outage (O) No Outage (NO) 10 0 0.4 20 0.3 0.3 30 0.4 0.2 40 0.2 0.1 50 0.1 0 The lead time, that is the time between placing an order and the time the order is received, is randomly distributed between 1 day and 4 days with the probability distribution given in Table 2 below. The lead time, that is the time between placing an order and the time the order is received, is randomly distributed between 1 day and 4 days with the probability distribution given in Table 2 below. Table 2: Lead Time Probability Distribution Lead Time Probability (Days) 1 0.25 2 0.30 2 3 0.35 4 0.10 (a) Given the random digits in Table 3 below, generate four random lead time values using the lead time probability distribution. Fill in the empty column of the table with these lead time values. This list of random lead times should be used one by one in the given order when this inventory system is simulated. Table 3: (a) Given the random digits in Table 3 below, generate four random lead time values using the lead time probability distribution. Fill in the empty column of the table with these lead time values. This list of random lead times should be used one by one in the given order when this inventory system is simulated. Table 3: Random Lead Times Order Index Random Digits Lead Time (Days) 1st 24 2nd 55 3rd 91 4th 78 (b) Assume that the vendor has 60 candles at the beginning of the first simulated day, backorders are allowed (shortages will be met once enough units are available, therefore, it is possible to order more than the inventory holding capacity of 80 candles), and there are no backorders at the beginning. Simulate this system for three cycles using the table below. In the "Beginning Inventory" and "Ending Inventory" columns, you can enter negative values as well as positive values or zero. In the "Shortage Quantity" column, for each day, report the shortage quantity of the specific day only, not the cumulative shortage values, as a non-negative value. Random Digits Beginning Shortage Cycle Day Power Demand for Demand Inventory Ending Inventory Quantity (b) Assume that the vendor has 60 candles at the beginning of the first simulated day, backorders are allowed (shortages will be met once enough units are available, therefore, it is possible to order more than the inventory holding capacity of 80 candles), and there are no backorders at the beginning. Simulate this system for three cycles using the table below. In the "Beginning Inventory" and "Ending Inventory" columns, you can enter negative values as well as positive values or zero. In the "Shortage Quantity" column, for each day, report the shortage quantity of the specific day only, not the cumulative shortage values, as a non-negative value. Random Digits Shortage Beginning Cycle Day Power Demand Ending Inventory for Demand Inventory Quantity 1 1 NO 28 2 NO 74 3 17 2 0 0 0 4 80 5 55 6 NO 67 3 3 7 O 96 8 25 9 NO 90 9 NO 90 (c) Answer the following two questions based on the simulation above. (1) What is the average amount of shortage per day over the simulation period? ANSWER: (i) What is the average number of units ordered per cycle? ANSWER: (ii) What is the total lead time demand over the simulation period? ANSWER: 10 20 30 || 40 || 50 60 70 80 90 || 100 0 -10 || -20 || -30 || -40 || -50 || -60 -70 -80 1 || 2 || 3 | 4 210 | 220 || 230 || 240 40 50 60 70 110 | 120 | 130 | 140 | 250 | 260 270 || 280 3 A candle vendor can keep at most 80 candles in the inventory and reviews the inventory at the end of every three days. The vendor places an order if the ending inventory is at most 20 candles at the end of each cycle such that the maximum inventory capacity is reached. The demand for candles depends on the power outages and the probability distributions of the demand on days when there is a power outage and days without a power outage are given in Table 1 below. Table 1: Demand Probability Distribution Power Demand Outage (O) No Outage (NO) 10 0 0.4 20 0.3 0.3 30 0.4 0.2 40 0.2 0.1 50 0.1 0 The lead time, that is the time between placing an order and the time the order is received, is randomly distributed between 1 day and 4 days with the probability distribution given in Table 2 below. The lead time, that is the time between placing an order and the time the order is received, is randomly distributed between 1 day and 4 days with the probability distribution given in Table 2 below. Table 2: Lead Time Probability Distribution Lead Time Probability (Days) 1 0.25 2 0.30 2 3 0.35 4 0.10 (a) Given the random digits in Table 3 below, generate four random lead time values using the lead time probability distribution. Fill in the empty column of the table with these lead time values. This list of random lead times should be used one by one in the given order when this inventory system is simulated. Table 3: (a) Given the random digits in Table 3 below, generate four random lead time values using the lead time probability distribution. Fill in the empty column of the table with these lead time values. This list of random lead times should be used one by one in the given order when this inventory system is simulated. Table 3: Random Lead Times Order Index Random Digits Lead Time (Days) 1st 24 2nd 55 3rd 91 4th 78 (b) Assume that the vendor has 60 candles at the beginning of the first simulated day, backorders are allowed (shortages will be met once enough units are available, therefore, it is possible to order more than the inventory holding capacity of 80 candles), and there are no backorders at the beginning. Simulate this system for three cycles using the table below. In the "Beginning Inventory" and "Ending Inventory" columns, you can enter negative values as well as positive values or zero. In the "Shortage Quantity" column, for each day, report the shortage quantity of the specific day only, not the cumulative shortage values, as a non-negative value. Random Digits Beginning Shortage Cycle Day Power Demand for Demand Inventory Ending Inventory Quantity (b) Assume that the vendor has 60 candles at the beginning of the first simulated day, backorders are allowed (shortages will be met once enough units are available, therefore, it is possible to order more than the inventory holding capacity of 80 candles), and there are no backorders at the beginning. Simulate this system for three cycles using the table below. In the "Beginning Inventory" and "Ending Inventory" columns, you can enter negative values as well as positive values or zero. In the "Shortage Quantity" column, for each day, report the shortage quantity of the specific day only, not the cumulative shortage values, as a non-negative value. Random Digits Shortage Beginning Cycle Day Power Demand Ending Inventory for Demand Inventory Quantity 1 1 NO 28 2 NO 74 3 17 2 0 0 0 4 80 5 55 6 NO 67 3 3 7 O 96 8 25 9 NO 90 9 NO 90 (c) Answer the following two questions based on the simulation above. (1) What is the average amount of shortage per day over the simulation period? ANSWER: (i) What is the average number of units ordered per cycle? ANSWER: (ii) What is the total lead time demand over the simulation period? ANSWER: 10 20 30 || 40 || 50 60 70 80 90 || 100 0 -10 || -20 || -30 || -40 || -50 || -60 -70 -80 1 || 2 || 3 | 4 210 | 220 || 230 || 240 40 50 60 70 110 | 120 | 130 | 140 | 250 | 260 270 || 280 3
