Inventory systems are parts of supply chains. In this section, we consider invento- ries belonging to supply chains, keeping in mind that the relationship between
RFID and inventories is only one aspect of the influence of RFID on supply chains.
A more complete analysis of this influence is developed in Section 5.6.
5.4.2.1 A Three-echelon Supply Chain: Description and Management
To illustrate the influence of RFID on supply chains, a simple three-echelon sup- ply chain that is composed of a manufacturing system (MS), a distribution centre (DC) and n retailers (see Figure 5.5) is considered.
The daily production of the MS is shipped to the DC once a day. We assume that one day is required to transfer products from MS to DC. This includes the packaging, transportation, physical assignment in the DC and, if applicable (that is if RFID is not used), registration of the transfer.
A retailer is composed of a storage facility (called the backroom (BR)) and a shelf (SH) to display the products. Two days are required to transfer products from the DC to any one of the retailers’ BRs. The replenishment of a shelf decided at day j takes effect at day j+1.
Only one product type is concerned in this example for simplicity.
The dynamics and management of the supply chain can be summarized as fol- lows:
• Every single day, shelf i, i∈{1,2,...,n}, has to meet the demands of custom- ers. The sum of the demands during one day is the value taken by a random variable that obeys a Poisson distribution of parameter λi.
• The replenishment of shelf i is based on a (si,Si) policy: as soon as the num- ber xi of products in the shelf becomes less than si, a quantity Si−xi is taken from the BR and transferred to the shelf. This quantity will be available to cus- tomers the next day.
• The replenishment of backroom i is based on a (ssi,SSi) policy, and replen- ishments are ordered from the DC.
• Every evening, each retailer i informs the MS of the quantities di sold during the day. The MS will launch the total demand, that is ∑
=
= n
i
di
D
1
, in production the next day. We assume that the MS is able to perform the production of D units in one day.
The model is represented in Figure 5.5.
176 5 Radio-frequency Identification (RFID): Technology and Applications
MS DC BRi
BRn
Transfer: 1 day
Transfer: 2 days
M
M
BR1 SH1
SHi
SHn
D E M A N D S M
M
Figure 5.5 A three-stage chain We assume that:
• At the MS level, the manufacturing problems (lack of quality, for instance) are solved by the end of the same day. In other words, the efficiency of the MS can be considered as being perfect.
• The shrinkage in the DC is equal to a% of the items that are present in DC at the beginning of the day. This percentage includes the shrinkage during the transfer between MS and DC.
• The shrinkage in the backroom of retailer i is equal to vi% of the inventory at the beginning of the day. This percentage includes the shrinkage during the transfer between DC and the backroom.
• The shrinkage in the shelf of retailer i is equal to wi% of the items held in the shelf at the beginning of the day. This percentage includes the shrinkage during the transfer between the backroom and the shelf.
We assume that a stock taking is done once every Js days by the retailers in the BRs and SHs and every Jd days in the DC.
When a retailer takes stock, they observe that the quantities in the shelves and the backrooms are less than the theoretical quantities (i.e., the quantities registered in the computer). This is due to the shrinkage. As a consequence, the numbers of items in the shelves and the backrooms, that are stored in a file of the computer, should be reduced to match with the real values provided by the stock taking. Due to the management of the system presented above, i.e., the ( s, S ) policy, addi- tional items are automatically ordered by the shelves to the backrooms, and by the backrooms to the DC. The management of the DC is slightly different: when a stock taking happens, the total shrinkage from the previous stock taking is added to the quantity to be manufactured by the MS the next day.
5.4.2.2 Deployment of RFID
We assume that an RFID is deployed and that tags are introduced at the item level (in other words, one tag is attached to each item). Thus, each single item is tracked
in the supply chain, which ensures that each item that disappears from the system is detected the same day. Indeed, some undetected shrinkages (for instance, shrinkages due to lack of quality) exist. This is the case of items that belong physically to the inventory, but are not usable because of damage or defects.
When an RFID is not deployed, the existence of shrinkage is detected and cor- rected only periodically, at the time an inventory is performed. In the meantime, the system is managed based on the data stored in the computer, which are usually inaccurate. This leads to stock shortage and delays to customers.
To deal with shrinkages, one solution is to increase the initial inventory level of the shelves, backrooms and DC.
The numerical examples presented in the next section will illustrate these re- marks.
5.4.2.3 Illustrative Examples
We consider the three-echelon supply chain presented in Figure 5.5, with three re- tailers.
The daily demands to the retailers are the same and follow the Poisson distribu- tion of parameter 2, which means that the mean daily demand to a retailer is 2 items.
We assume that Js = 100 and Jd = 300. Simulations of 15 000 days have been performed to evaluate the average number of stock shortages at the different levels of the supply chain according to the percentage of undetected shrinkage. The
) ,
(s S replenishment policy is (15, 20) for the shelves and (20, 30) for the back- rooms. Note that retailers’ behaviors are identical on average.
As you can see in Figures 5.6–5.8, when the proportion of shrinkages increases, the system is more often out of stock at each level of the supply chain.
Proportion of shrinkages 0
5 10 15 20 25 30 35 40
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Number of stock shortages
Figure 5.6Stock shortages in the DC according to the proportion of undetected shrinkages
178 5 Radio-frequency Identification (RFID): Technology and Applications
0 10 20 30 40 50 60 70
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Proportion of shrinkages
Retailer 1: backroom Retailer 2: backroom Retailer 3: backroom Number of stock shortages
Figure 5.7 Stock shortages in the backrooms according to the proportion of undetected shrink- ages
0 10 20 30 40 50 60 70 80 90 100
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Proportion of shrinkages
Number of stock shortages
Retailer 1: shelf Retailer 2: shelf Retailer 3: shelf
Figure 5.8 Stock shortages in the shelves according to the proportion of undetected shrinkages To manage this situation when RFID is not in use, you have to postpone deliv- eries and/or keep inventories to avoid stock shortages. Another solution is to in- crease the frequency of taking stock. The best behavior of the supply chain arises when daily inventories are performed, which is what RFID makes possible, at least partially.