# Quiz 14: Service Levels and Lead Times in Supply Chains: the Order Up-To Inventory Model

The order-up-to-level inventory model is a fixed time period model where the review is carried out after a fixed interval of time. The order quantity depends on the existing inventory, scheduled receipts, and the protection level i.e. the order-up-to-level. In other words, the existing inventory level and scheduled order receipts are subtracted from the order-up-to-level to find the order quantity. a. Note that the order-up-to level, S = 220. So, the number of desks to be ordered = b. Note that the order-up-to level, S = 220. So, the number of desks to be ordered = as the inventory level plus the scheduled receipt is more than S. c. The average weekly demand, The standard deviation of weekly demand, Replenishment lead time, Review period, Service level is 98%. So, the corresponding Since fractional value for order-up-to level is infeasible, the optimal order-up-to level is d. The order-up-to level, S = 120. So, the value of z -statistic can be computed as: The corresponding loss function value, from the table is 0.3989. Therefore, Since fractional value for on-hand inventory is infeasible, the on-hand inventory is e. The order-up-to level, S = 120. So, the value of z -statistic can be computed as: The corresponding loss function value, from the table is 0.3989. Therefore, So, the annual cost of capital blocked for inventory is

In a single-period inventory model, the order size decision is made by a marginal analysis. In this analysis, the optimal order quantity occurs at the point where the marginal benefit of stocking one additional unit is just less than its expected marginal cost. a. The mean demand over periods units In-stock probability = 99% From the Poisson distribution table, for mean equal to 2.5, and . Since the optimal order quantity is b. The pipeline inventory is computed by multiplying the lead time by the expected demand in one period. So, the average pipeline inventory is c. Base stock level, S = 5 From the Poisson table, for mean equal to 2.5, So, the expected inventory held at the end of the week is d. Base stock level, S = 6 From the Poisson distribution table, for mean equal to 2.5, So, the in-stock probability is 0.9858 or 98.58% Therefore, the probability of stock out e. There will be stockout at the end of week when the demand for the periods is less than S = 6. From the Poisson distribution table, for mean equal to 2.5, So, the probability of stockout So, the probability of stockout at the end of the period is f. The probability that there will be one or more units at the end of week So, the probability that there will be one or more units at the end of week is g. Average lead time, Review and ordering period, The mean demand over periods units In-stock probability = 99% From the Poisson distribution table, for mean equal to 3, and Since the optimal order quantity is h. So, the average pipeline inventory is

The order-up-to-level inventory model is a fixed time period model where the review is carried out after a fixed interval of time. The order quantity depends on the existing inventory, scheduled receipts, and the protection level i.e. the order-up-to-level. In other words, the existing inventory level and scheduled order receipts are subtracted from the order-up-to-level to find the order quantity. Consider the data given below: The average weekly demand, The standard deviation of weekly demand, Replenishment lead time, Review period, a. Note that the order-up-to level, S = 700. So, the number of units to be ordered = as the inventory level plus the scheduled receipt is more than S. b. Service level is 99%. So, the corresponding Since fractional value for order-up-to level is infeasible, the optimal order-up-to level is