Impact of Replenishment Policies on Safety Inventory in a Supply Chain

In this section, we describe the evaluation of safety inventories for both continuous and periodic- review replenishment policies. We highlight the fact that periodic review policies require more safety inventory than continuous review policies for the same level of product availability. To simplify the discussion, we focus on the CSL as the measure of product availability. The mana­gerial implications are the same if we use fill rate; the analysis, however, is more cumbersome.

1. Continuous Review Policies

Given that continuous review policies were discussed in detail in Section 12.2, we reiterate only the main points here. When using a continuous review policy, a manager orders Q units when the inventory drops to the ROP. Clearly, a continuous review policy requires technology that moni­tors the level of available inventory. This is the case for many firms such as Walmart and Dell, whose inventories are monitored continuously.

Given a desired CSL, our goal is to identify the required safety inventory ss and the ROP. We assume that demand is normally distributed, with the following inputs:

D: Average demand per period

σD: Standard deviation of demand per period

L: Average lead time for replenishment

The ROP represents the available inventory to meet demand during the lead time L. A stockout occurs if the demand during the lead time is larger than the ROP. If demand across peri­ods is independent, demand during the lead time is normally distributed with the following:

Given the desired CSL, the required safety inventory (ss) obtained using Equation 12.5 and the ROP obtained using Equation 12.3 are

A manager using a continuous review policy has to account only for the uncertainty of demand during the lead time. This is because the continuous monitoring of inventory allows the manager to adjust the timing of the replenishment order, depending on the demand experienced. If demand is very high, inventory reaches the ROP quickly, leading to a quick replenishment order. If demand is very low, inventory drops slowly to the ROP, leading to a delayed replenish­ment order. The manager, however, has no recourse during the lead time once a replenishment order has been placed. The available safety inventory thus must cover for the uncertainty of demand over this period.

Typically, in continuous review policies, the lot size ordered is kept fixed between replen­ishment cycles. The optimal lot size may be evaluated using the EOQ formula discussed in Chapter 11.

2. Periodic Review Policies

In periodic review policies, inventory levels are reviewed after a fixed period of time T and an order is placed such that the level of current inventory plus the replenishment lot size equals a prespecified level called the order-up-to level (OUL). The review interval is the time Tbetween successive orders. Observe that the size of each order may vary, depending on the demand expe­rienced between successive orders and the resulting inventory at the time of ordering. Periodic review policies are simpler for retailers to implement because they do not require that the retailer have the capability of monitoring inventory continuously. Suppliers may also prefer them because they result in replenishment orders placed at regular intervals.

Let us consider the store manager at Walmart who is responsible for designing a replenish­ment policy for Lego building blocks. He wants to analyze the impact on safety inventory if he decides to use a periodic review policy. Demand for Legos is normally distributed and indepen­dent from one week to the next. We assume the following inputs:

D: Average demand per period

sD: Standard deviation of demand per period

L: Average lead time for replenishment

T: Review interval

CSL: Desired cycle service level

To understand the safety inventory requirement, we track the sequence of events over time as the store manager places orders. The store manager places the first order at time 0 such that the lot size ordered and the inventory on hand sum to the OUL. Once an order is placed, the replenishment lot arrives after the lead time L. The next review period is time T, when the store manager places the next order, which then arrives at time T + L. The OUL represents the inventory available to meet all demand that arises between periods 0 and T + L. The Walmart store will experience a stockout if demand during the time interval between 0 and T + L exceeds the OUL. Thus, the store manager must identify an OUL such that the following is true:

Probability (demand during T + L < OUL) = CSL

The next step is to evaluate the distribution of demand during the time interval T + L. Using Equation 12.2, demand during the time interval T + L is normally distributed, with

The safety inventory in this case is the quantity in excess of DT+L carried by Walmart over the time interval T + L. The OUL and the safety inventory ss are related as follows:

Given the desired CSL, the safety inventory (ss) required is given by

The average lot size equals the average demand during the review period T and is given as

Average lot size, Q = DT = D X T                                                                                          (12.20)

In Figure 12-7, we show the inventory profile for a periodic review policy with lead time L = 4 and reorder interval T = 7. On day 7, the company places an order that determines avail­able inventory until day 18 (as illustrated in Figure 12-7 by the dashed line from point 1 to point 2). As a result, the safety inventory must be sufficient to buffer demand variability over T + L = 7 + 4 = 11 days.

We illustrate the periodic review policy for Walmart in Example 12-13 (see worksheet Example 12-13).

EXAMPLE 12-13 Evaluation Safety Inventory for a Periodic Review Policy

Weekly demand for Legos at a Walmart store is normally distributed, with a mean of 2,500 boxes and a standard deviation of 500. The replenishment lead time is two weeks, and the store man­ager has decided to review inventory every four weeks. Assuming a periodic-review replenish­ment policy, evaluate the safety inventory that the store should carry to provide a CSL of 90 percent. Evaluate the OUL for such a policy.

Analysis:

In this case, we have

Average demand per period, D = 2,500

Standard deviation of demand per period, sD = 500

Average lead time for replenishment, L = 2 weeks

Review interval, T = 4 weeks

We first obtain the distribution of demand during the time interval T + L. Using Equation 12.2, demand during the time interval T + L is normally distributed, with

From Equation 12.19, the required safety inventory for a CSL = 0.90 is given as

Using Equation 12.18, the OUL is given by

OUL = DT + L + ss = 15,000 + 1,570 = 16,570

The store manager thus orders the difference between 16,570 and current inventory every four weeks.

We can now compare the safety inventory required when using continuous and periodic review policies. With a continuous review policy, the safety inventory is used to cover for demand uncertainty over the lead time L. With a periodic review policy, the safety inventory is used to cover for demand uncertainty over the lead time and the review interval L + T. Given that higher uncertainty must be accounted for, periodic review policies require a higher level of safety inven­tory. This argument can be confirmed by comparing the results in Examples 12-4 and 12-13. For a 90 percent CSL, the store manager requires a safety inventory of 906 boxes when using a con­tinuous review and a safety inventory of 1,570 boxes when using a periodic review.

Of course, periodic review policies are somewhat simpler to implement because they do not require continuous tracking of inventory. Given the broad use of bar codes and POS systems as well as the emergence of RFID technology, continuous tracking of all inventories is much more commonplace today than it was a decade ago. In some instances, companies partition their products based on their value. High-value products are managed using continuous review poli­cies, and low-value products are managed using periodic review policies. This makes sense if the cost of perpetual tracking of inventory is more than the savings in safety inventory that result from switching all products to a continuous review policy.

Source: Chopra Sunil, Meindl Peter (2014), Supply Chain Management: Strategy, Planning, and Operation, Pearson; 6th edition.

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