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

Business

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. img So, the number of desks to be ordered = img b. Note that the order-up-to level, S = 220. img So, the number of desks to be ordered = img as the inventory level plus the scheduled receipt is more than S. c. The average weekly demand, img The standard deviation of weekly demand, img Replenishment lead time, img Review period, img Service level is 98%. So, the corresponding img img Since fractional value for order-up-to level is infeasible, the optimal order-up-to level is img d. img The order-up-to level, S = 120. So, the value of z -statistic can be computed as: img The corresponding loss function value, img from the table is 0.3989. Therefore, img img Since fractional value for on-hand inventory is infeasible, the on-hand inventory is img e. img The order-up-to level, S = 120. So, the value of z -statistic can be computed as: img The corresponding loss function value, img from the table is 0.3989. Therefore, img img img So, the annual cost of capital blocked for inventory is img

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 img periods img units In-stock probability = 99% From the Poisson distribution table, for mean equal to 2.5, img and img . Since img the optimal order quantity is img b. The pipeline inventory is computed by multiplying the lead time img by the expected demand in one period. img So, the average pipeline inventory is img c. Base stock level, S = 5 From the Poisson table, for mean equal to 2.5, img img So, the expected inventory held at the end of the week is img d. Base stock level, S = 6 From the Poisson distribution table, for mean equal to 2.5, img So, the in-stock probability is 0.9858 or 98.58% Therefore, the probability of stock out img e. There will be stockout at the end of week when the demand for the img periods is less than S = 6. From the Poisson distribution table, for mean equal to 2.5, img So, the probability of stockout img So, the probability of stockout at the end of the period is img f. The probability that there will be one or more units at the end of week img So, the probability that there will be one or more units at the end of week is img g. Average lead time, img Review and ordering period, img The mean demand over img periods img units In-stock probability = 99% From the Poisson distribution table, for mean equal to 3, img and img Since img the optimal order quantity is img h. img So, the average pipeline inventory is img

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, img The standard deviation of weekly demand, img Replenishment lead time, img Review period, img a. Note that the order-up-to level, S = 700. img So, the number of units to be ordered = img as the inventory level plus the scheduled receipt is more than S. b. Service level is 99%. So, the corresponding img img Since fractional value for order-up-to level is infeasible, the optimal order-up-to level is img