Cycle service level

A less rigorous approach to finding a (Q, R) solution would be to solve for Q and R separately. Note that z = R - MoltV dlt gives a fractile of the distribution of demand over the lead time. Thus, we could set R to achieve a desired in-stock probability, along the lines of the newsvendor problem solution discussed earlier (i.e., to accumulate a given amount of probability under the DLT distribution). In this setting, the in-stock probability is typically referred to as the cycle service level (CSL), or the expected in-stock probability in each replenishment cycle. Specifically, for normally distributed lead-time demand, DLT, we set... 

Piii rate beta.TGT 99.00% Cycle Service Level CSl 77.76%... 

A replenishment policy consists of decisions regarding when to reorder and how much to reorder. These decisions determine the cycle and safety inventories along with the fill rate fr and the cycle service level CSL. Replenishment policies may take any of several forms. We restrict attention to two types ... 

Chapter 12 Managing Uncertainty in a Supply Chain Safety Inventory 319 Linking Safety Inventory and Cycle Service Level... 

We first show how cycle service levels can be evaluated given a replenishment poUcy (and thus the corresponding safety inventory). We then show how to determine the required safety inventory given a desired cycle service level. 

Evaluating Cycle Service Level Given a Replenishment Policy... 

EVALUATING REQUIRED SAFETY INVENTORY GIVEN DESIRED CYCLE SERVICE LEVEL Our... 

Evaluating Safety Inventory Given a Desired Cycle Service Level... 

EVALUATING FILL RATE GIVEN A REPLENISHMENT POLICY RecaU that fiU rate measures the proportion of customer demand that is satisfied from available inventory. EiU rate is generally a more relevant measure than cycle service level because it allows the retailer to estimate the fraction of demand that is turned into sales. The two measures are closely related, as raising the cycle service level also raises the fill rate for a firm. Our discussion focuses on evaluating fill rate for a continuous review policy under which Q units are ordered when the quantity on hand drops to the ROP. 

Both fill rate and cycle service level increase as the safety inventory is increased. For the same safety inventory, an increase in lot size increases the fill rate but not the cycle service level. 

Weekly demand for white shirts at a Target store is normally distributed, with a mean of 2,500 and a standard deviation of 800. The replenishment lead time from the current supplier is nine weeks. The store manager aims for a cycle service level of 95 percent. What savings in safety inventory can the store expect if the supplier reduces lead time to one week What savings in safety inventory can the store expect if reduced demand uncertainty results in a standard deviation of demand of 400 ... 

There are two ways to serve demand in the A regions. One is to have local inventories in each region and the other is to aggregate all inventories into one centralized facility. Our goal is to compare safety inventories in the two cases. With a replenishment lead time of L and a desired cycle service level CSL, the total safety inventory in the decentralized case is (using Equation 12.5) ... 

The safety inventory savings on aggregation increase with the desired cycle service level CSL. 

Describe different measures of product availability. The three basic measures of product availability are product fill rate, order fill rate, and cycle service level. Product fiU rate is the fraction of demand for a product that is filled from inventory. Order fill rate is the fraction of orders that are completely filled. Cycle service level is the fraction of replenishment cycles in which no stockouts occur. 

Currently, a production facility in Malaysia is used to manufacture, label, and pack all products. The manufacturing facility replenishes a DC in St. Louis, from which the contract manufacturer fills all customer orders. The manufacturing and transportation lead time from Penang to St. Louis is nine weeks. PE uses a continuous review policy to manage inventories at its DC and aims to provide a cycle service level of 95 percent for each product to every customer. 

Identify the factors affecting the optimal level of product availability and evaluate the optimal cycle service level. 

In this chapter, we explore the process of determining the optimal level of product availability to be offered to customers. The chapter examines factors that influence the optimal cycle service level. We discuss and demonstrate how different managerial levers can be used to improve supply chain profitability by increasing the level of product availability while reducing inventories. 

The level of product availability is measured using the cycle service level or the fill rate, which are metrics for the amount of customer demand satisfied from available inventory. The level of product availability, also referred to as the customer service level, is one of the primary measures of a supply chain s responsiveness. A supply chain can use a high level of product availability to improve its responsiveness and attract customers, thus increasing revenue for the supply chain. However, a high level of product availability requires large inventories, which raise supply chain costs. Therefore, a supply chain mnst achieve a balance between the level of availability and the cost of inventory. The optimal level of prodnct availability is one that maximizes supply chain profits. 

Under the old policy of ordering the expected value, the buyers would have ordered 1,000 parkas. However, demand is uncertain, and Table 13-1 shows that there is a 51 percent probability that demand wiU be 1,000 or less. Thus, a policy of ordering a thousand parkas results in a cycle service level of 51 percent at L. L. Bean. The buying conunittee must decide on an order size and cycle service level that maximize the profits from the sale of parkas at L. L. Bean. 

Optimal Cycle Service Level for Seasonal Items with a Single Order in a Season... 

Co. Cost of overstocking by one unit, Co = c — s C Cost of understocking by one unit, C = p — c CSL Optimal cycle service level 0 Corresponding optimal order size... 

CSL is the probability that demand during the season will be at or below 0. At the optimal cycle service level CSL, the marginal contribution of purchasing an additional unit is zero. If the order quantity is raised from O to O + 1, the additional unit sells if demand is larger than 0. This occurs with probability 1 — CSL and results in a contribution of p — c. We thus have... 

Because the expected marginal contribution must be 0 at the optimal cycle service level, we have... 

Example 13-1 illustrates the use of Equations 13.1 and 13.2 to obtain the optimal cycle service level and order quantity (see woiksheet Example 13-1 in spreadsheet Chapter 13-examples). 

Using Co = c — s and = p — c, evaluate the optimal cycle service level CSL and order size 0 without a discount using Equations 13.1 and 13.2, respectively. Evaluate the expected profit from ordering O using Equation 13.3. 

Desired Cycle Service Level for Continuously Stocked Items... 

In this case, the optimal cycle service level is obtained by equating the additional cost and benefit to be... 

Given the optimal cycle service level, the required safety inventory can be evaluated using Equation 12.5 if demand is normally distributed. 

From Equation 13.6, observe that increasing the lot size Q allows the store manager at Wahnart to reduce the cycle service level and, thus, the safety inventory carried. This is because increasing the lot size increases the fiU rate and thus reduces the quantity backlogged. One should be careful, however, because an increase in lot size raises the cycle inventory. In general, increasing the lot size is not an effective way for a firm to improve product availability. 

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