SYST 4050 Supply Chain Management
SYST 4050 Supply Chain Management – Homework 5
1. Weekly demand for HP printers at a Sam’s Club store is normally distributed, with a mean of 250 and a standard deviation of 150. The store manager continuously monitors inventory and currently orders 1,000 printers each time the inventory drops below 600 printers. HP currently takes two weeks to fill an order.
a) How much safety inventory does the store carry?
ROP = 600
DL = DL = 250*2 = 500
ss = ROP – DL = 600 – 500 = 100
b) You may use Excel or the table below. What CSL does Sam’s Club achieve as a result of this policy?
|F(600,500,300) |0.631 |
|F(600,250,212.13) |0.951 |
|F(600,500,212.13) |0.681 |
|F(1000,500,300) |0.952 |
|F(1000,250,212.13) |0.999 |
|F(1000,500,212.13) |0.991 |
(L = (L(D = (2*150 = 212.13
CSL = F(ROP,DL,(L) = F(600,500,212.13) = 0.681
c) You may use Excel or the table below. What product fill rate does Sam’s Club achieve as a result of this policy?
| |ESC |
|–100*(1 – Fs(0.471)) + 212.13*fs(0.471) |43.861 |
|–100*(1 – Fs(0.471)) + 426.26*fs(0.471) |120.317 |
|–50*(1 – Fs(0.235)) + 212.13*fs(0.235) |62.356 |
|–50*(1 – Fs(0.117)) + 426.26*fs(0.117) |146.221 |
|–200*(1 – Fs(0.471)) + 426.26*fs(0.471) |87.723 |
|–200*(1 – Fs(0.235)) + 426.26*fs(0.235) |88.001 |
Q = 1000
ss = ROP – DL = 600 – 500 = 100
(L = (L(D = (2*150 = 212.13
ESC = -ss(1 – F(ss/(L,0,1)) + (Lf(ss/(L,0,1) = -100*(1 – F(0.471,0,1)) + 212.13*f(0.471.13,0,1)
= 43.861
fr = 1 – ESC/Q = 1 – (43.861/1000) = 0.956
Sam’s Club wants to target a CSL of 95 percent. In order to achieve this it has to change its reorder point.
d) You may use Excel or the table below. What is the resulting safety inventory that is achieved as a result of the new CSL value?
|F-1(0.95,500,212.13) |848.926 |
|F-1(0.95,500,300) |993.456 |
|F-1(0.95,600,212.13) |948.926 |
|F-1(0.95,600,300) |1093.456 |
|F-1(0.95,1000,300) |1493.456 |
|Fs-1(0.95) |1.645 |
There are two ways to calculate the resulting safety inventory
Option 1
ss = Fs-1(CSL)*(L = Fs-1(0.95)*212.13 = 348.926
Option 2
ROP = F-1(CSL, DL, (L) = F-1(0.95, 500, 212.13) = 848.926
ss = ROP – DL = 848.926 – 500 = 348.926
In this lean operations world, in an effort to lower handling costs, speed delivery, and reduce inventory, retailers are forcing their suppliers to do more and more in the way of preparing their merchandise for their cross-docking warehouses, shipment to specific stores, and shelf presentation. Your company, a small manufacturer of aquarium decorations, is in a tough position. First, Mega-Mart wanted you to develop bar-code technology, then special packaging, then small individual shipments bar coded for each store (this way when the merchandise hits the warehouse it is cross-docked immediately to the correct truck and store and is ready for shelf placement). And now Mega-Mart wants you to develop RFID—immediately. Mega-Mart has made it clear that suppliers that cannot keep up with the technology will be dropped.
Earlier, when you didn’t have the expertise for bar codes, you had to borrow money and hire an outside firm to do the development, purchase the technology, and train your shipping clerk. Then, meeting the special packaging requirement drove you into a loss for several months, resulting in a loss for last year. Now it appears that the RFID request is impossible. Your business, under the best of conditions, is marginally profitable, and the bank may not be willing to bail you out again. Over the years, Mega-Mart has slowly become your major customer and without them, you are probably out of business.
e) What would you do?
There is no single correct answer, but not implementing RFID is not an option (you’ll go out of business). One thing that could be done is to negotiate with Mega-Mart to obtain more accurate demand data after the implementation. With better demand data you can make an improved demand forecast and as a result lower your safety inventory and lower (inventory holding) cost.
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