Handi Inc., a cell phone manufacturer, procures a standard display from LCD Inc. via an ?options supply contract?. At the start of quarter 1 (Q1) Handi pays LCD $15 per option. At t
I need Help with the L(z) score in the middle.
Handi Inc., a cell phone manufacturer, procures a standard display from LCD Inc. via “an options supply contract”. At the start of quarter 1 (Q1) Handi pays LCD $15 per option. At that time Handi’s forecast of demand in quarter 2 (Q2) is normally distributed with mean 15,000 and standard deviation 5,000. At the start of Q2 Handi learns exact demand for Q2 and then exercises options at the fee of $45 per option (for every exercised option LCD delivers one display to Handi). Assume Handi starts Q2 with no display inventory and displays owned at the end of Q2 are worthless. Should Handi’s demand in Q2 be larger than the number of options held, Handi purchases additional displays on the spot market for $80 per unit. a. How many optimum options should Handi purchase from LCD, Inc. at the start of Q1 to minimize expected total procurement cost? b. What is the chance that there is a need to procure at the spot market with only 7500 options signed? c. Compute Expected Total Procurement Cost with 10,000 options.
The one file is the Excel that needs to be worked on and check if right. the other is for reference on how to get the solutions. I need the answers based on what I put under "your question"
Q#1
| Zach Johns and Abigail Hunt |
100% efficient supply chain contracts imply that both the supply chain and the supplier supplying the firm with its raw materials are highly effective. The contract implies that the provider is in a relationship with the organization and provides the organization with raw materials and other supplies in a reliable, effective manner without wasting anything, and the quality of the supply is consistent with the standards upon which the contract is based.
Q#2
Buy-Back Contract is an operations management tool in which a manufacturer specifies a ……Buy-Back………………………….……..…. price and a …………..Resale………………….…….. price at which the retailer can return any unsold items at the end of the season. The buy-back contract results in an increase in the salvage value for the retailer, which induces the retailer to order a larger quantity. The manufacturer is willing to take on some of the cost of overstocking, because: ……….It enables the company to lower the possibility that they will have too much inventory and may have to sell it at a loss.… and ……..It helps the manufacturer to get a guaranteed amount of sales from the store, which can help them organize their operations and manufacturing more effectively.
Q#3
| Initial Price (Ci) | 15 | Expected Demand E(D) | 15000 | |||
| Exercise Price (Ce) | 45 | 𝛔D | 5000 | |||
| Expensive Price (Cexp) | 80 | |||||
| Cost of Overstocking (Co) | 15 | |||||
| Cost of Understocking (Cu) | 20 | Q | 7500 | |||
| P(D>=7500) | 0.93 | |||||
| Critical Ratio | 0.57 | P(D>7500) | 0.07 : b) Probability that the demand will exceed the order quantity at 7,500 options |
|||
| Q* | 15900 : a) Optimal order quantity to maximize profit |
z-score | 0.18 | |||
| z-score | 0.18 | L(z) | 0.4349 | |||
| L(z) | 0.3154 | Expected Lost Sales | 2175 | |||
| Expected Lost Sales | 1577 | Expected Sales | 12826 | |||
| Expected Sales | 13423 | |||||
| Total Initial Payment | $ 150,000 | |||||
| Total Exercise Payment | $ 577,148 | |||||
| Total Expensive Payment | $ 173,960 | |||||
| Total Procurement Cost | $ 901,108 : c) Total Procurement Cost equals the sum of the procurement cost for the number of options purchased, expected sales * excercise cost, and expected lost sales * expensive cost |
|||||
| : a) Optimal order quantity to maximize profit | : b) Probability that the demand will exceed the order quantity at 7,500 options |
Standard Normal Loss Function Table,L( z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.3989 0.3940 0.3890 0.3841 0.3793 0.3744 0.3697 0.3649 0.3602 0.3556 0.1 0.3509 0.3464 0.3418 0.3373 0.3328 0.3284 0.3240 0.3197 0.3154 0.3111 0.2 0.3069 0.3027 0.2986 0.2944 0.2904 0.2863 0.2824 0.2784 0.2745 0.2706 0.3 0.2668 0.2630 0.2592 0.2555 0.2518 0.2481 0.2445 0.2409 0.2374 0.2339 0.4 0.2304 0.2270 0.2236 0.2203 0.2169 0.2137 0.2104 0.2072 0.2040 0.2009 0.5 0.1978 0.1947 0.1917 0.1887 0.1857 0.1828 0.1799 0.1771 0.1742 0.1714 0.6 0.1687 0.1659 0.1633 0.1606 0.1580 0.1554 0.1528 0.1503 0.1478 0.1453 0.7 0.1429 0.1405 0.1381 0.1358 0.1334 0.1312 0.1289 0.1267 0.1245 0.1223 0.8 0.1202 0.1181 0.1160 0.1140 0.1120 0.1100 0.1080 0.1061 0.1042 0.1023 0.9 0.1004 0.0986 0.0968 0.0950 0.0933 0.0916 0.0899 0.0882 0.0865 0.0849 1.0 0.0833 0.0817 0.0802 0.0787 0.0772 0.0757 0.0742 0.0728 0.0714 0.0700
L(z) lost function of emand evaluated at the z-statistic
z statistic
z statistic
L(z) lost function of demand evaluated at the z-statistic
Stdard Normal Loss Function Table,L(z) z 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 -4.0 4.0900 4.0800 4.0700 4.0600 4.0500 4.0400 4.0300 4.0200 4.0100 4.0000 -3.9 3.9900 3.9800 3.9700 3.9600 3.9500 3.9400 3.9300 3.9200 3.9100 3.9000 -3.8 3.8900 3.8800 3.8700 3.8600 3.8500 3.8400 3.8300 3.8200 3.8100 3.8000 3.7 3.7900 3.7800 3.7700 3.7600 3.7500 3.7400 3.7300 3.7200 3.7100 3.7000 -3.6 3.6900 3.6800 3.6700 3.6600 3.6500 3.6400 3.6300 3.6200 3.6100 3.6000 -3.5 3.5900 3.5800 3.5700 3.5600 3.5500 3.5400 3.5301 3.5201 3.5101 3.5001 -3.4 3.4901 3.4801 3.4701 3.4601 3.4501 3.4401 3.4301 3.4201 3.4101 3.4001 -3.3 3.3901 3.3801 3.3701 3.3601 3.3501 3.3401 3.3301 3.3201 3.3101 3.3001 -3.2 3.2901 3.2801 3.2701 3.2601 3.2502 3.2402 3.2302 3.2202 3.2102 3.2002 -3.1 3.1902 3.1802 3.1702 3.1602 3.1502 3.1402 3.1302 3.1202 3.1103 3.1003 -3.0 3.0903 3.0803 3.0703 3.0603 3.0503 3.0403 3.0303 3.0204 3.0104 3.0004 -2.9 2.9904 2.9804 2.9704 2.9604 2.9505 2.9405 2.9305 2.9205 2.9105 2.9005 -2.8 2.8906 2.8806 2.8706 2.8606 2.8506 2.8407 2.8307 2.8207 2.8107 2.8008 -2.7 2.7908 2.7808 2.7708 2.7609 2.7509 2.7409 2.7310 2.7210 2.7110 2.7011 -2.6 2.6911 2.6811 2.6712 2.6612 2.6512 2.6413 2.6313 2.6214 2.6114 2.6015 -2.5 2.5915 2.5816 2.5716 2.5617 2.5517 2.5418 2.5318 2.5219 2.5119 2.5020 -2.4 2.4921 2.4821 2.4722 2.4623 2.4523 2.4424 2.4325 2.4226 2.4126 2.4027 -2.3 2.3928 2.3829 2.3730 2.3631 2.3532 2.3433 2.3334 2.3235 2.3136 2.3037 -2.2 2.2938 2.2839 2.2740 2.2641 2.2542 2.2444 2.2345 2.2246 2.2147 2.2049 -2.1 2.1950 2.1852 2.1753 2.1655 2.1556 2.1458 2.1360 2.1261 2.1163 2.1065 -2.0 2.0966 2.0868 2.0770 2.0672 2.0574 2.0476 2.0378 2.0280 2.0183 2.0085
Q#4 a-c
| Dan McClure | ||
| Buy-Back Procurement Contract | ||
| New Data | ||
| Inputs | ||
| Wholesale price | $ 60.00 | |
| Retail price | $ 120.00 | |
| Salvage value | $ 12.00 | |
| Production cost | $ 30.00 | |
| E(D) | 200 | |
| St Dev (D) | 50 | |
| Co | $ 48.00 | c-s |
| Cu | $ 60.00 | r-c |
| C* | 0.5556 | |
| Optimal Q | 207 SEKIL: a. |
|
| z-score | 0.14 | |
| L(Z) | 0.3328 | |
| Expected Lost Sales | 17 | Std. Dev* L(z) |
| Expected Sales | 183 | E(D)-E(Lost Sales) |
| Expected Leftover Inventory | 24 | Q-E(Sales) |
| Expected Profit | $ 9,867.58 SEKIL: b. |
|
| Publisher's Expected Profit | $ 6,209.57 SEKIL: c. |
Q#4 d-h
| Dan McClure | |||||
| Buy-Back Procurement Contract | |||||
| New Data | |||||
| Inputs | |||||
| Wholesale price | $ 60.00 | ||||
| Retail price | $ 120.00 | ||||
| Buy-back price | $ 45.00 | ||||
| Production cost | $ 30.00 | ||||
| Shipping cost | $ 5.00 | ||||
| E(D) | 200 | ||||
| St Dev (D) | 50 | ||||
| Co | $ 20.00 | c-b+t | |||
| Cu | $ 60.00 | r-c | |||
| C* | 0.7500 | ||||
| Optimal Q | 234 SEKIL: d. |
||||
| z-score | 0.67 | ||||
| L(Z) | 0.1503 | Returned book salvage at the publisher site | $ 15.00 | ||
| Expected Lost Sales | 8 | Std. Dev* L(z) | |||
| Expected Sales | 192 | E(D)-E(Lost Sales) | |||
| Expected Leftover Inventory | 41 | Q-E(Sales) | Publisher | ||
| Expected Profit | $ 10,724.31 SEKIL: e. |
Expected sales revenue | $ 14,023.47 | ||
| Production cost | $ 7,011.73 | ||||
| Leftover cost | $ 1,855.78 | ||||
| Salvage revenue | $ 618.59 | ||||
| Expected Profit | $ 5,774.55 SEKIL: f. |
||||
| SEKIL: d. | Optimum Buy-Back Price | $ 55.00 SEKIL: g. |
|||
| Dan's Net loss per book returned | $ 10.00 Likes: h. |
||||
| SEKIL: e. |
i. 100% efficient. The supply chain allows the retailer (i.e. the buyer, Dan McClure) to purchase enough units to comfortably cover demand and not lose out to lost sales. In the case of overage, the seller will buy-back the leftover units, mitigating much of the risk of an overage. This allows the supply chain to operate with the largest possible "pie."
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RICHARD T. DOERMER SCHOOL OF BUSINESS
Prof. C.Z. Gurgur
Handi, Inc. Options Supply Contract Management
Before you attempt and work on this scenario, you must have worked on the Flextrola Software Systems Integrator case study where you were introduced to the pertinent concepts and management of an option supply contract. As such, please first refer to the course videos and posted/written solutions for Flextrola. Otherwise, you will have issues in the comprehension of the Handi, Inc. scenario analysis and execution of the full solutions on the provided Excel template comfortably.
Handi Inc., a cell phone manufacturer, procures a standard display from LCD Inc. via “an options type of supply contract”. At the start of quarter 1 (Q1) Handi pays LCD $20 per option. At that time Handi’s forecast of demand in Q2 is normally distributed with mean 20,000 and standard deviation 4000. At the start of Q2 Handi learns exact demand for Q2 and then exercises options at the fee of $50 per option (for every exercised option LCD delivers one display to Handi). Assume Handi starts Q2 with no display inventory and displays owned at the end of Q2 are worthless. Should Handi’s demand in Q2 be larger than the number of options held, Handi purchases additional displays on the spot market for $100 per unit.
a. How many options should Handi purchase from LCD, Inc.? (I.e. the optimum options) to minimize Expected Procurement Cost?
b. Suppose Handi purchases 12,000 options. What is the probability that he will need to do procurement on the spot market?
c. Given that Handi purchases 12,000 options, what is the expected number of displays Handi will buy on the spot market?
d. Given that Handi purchases 12,000 options, what is the expected number of options that Handi will exercise?
e. What is Handi’s expected total procurement cost given that he purchases 12,000 options?
f. What is the fill-rate Handi implies by purchasing 12,000 options?
g. What is Handi’s expected total procurement cost given the number of purchased options from part (a)?
h. Suppose Handi were to procure exclusively from the spot market? What would be his expected procurement cost? What would be his fill-rate in this arrangement? Also, what is the mismatch cost he incurs with this arrangement?
RICHARD T. DOERMER SCHOOL OF BUSINESS
Prof. C.Z. Gurgur
RICHARD T. DOERMER SCHOOL OF BUSINESS
Prof. C.Z. Gurgur
Handi, Inc. Options Contract Management Solutions
a. To find the number of options Handi should purchase from LCD, you must calculate the
critical ratio by using the unit overstocking and understocking cost.
Cu = Cost of buying an option that was needed Cu = Spot Market Cost – (Initial Cost + Exercised Cost) Cu = $100 – ($20 + $50)
Cu = $30
Co = Cost of an option that is not used (Initial Cost)
Co = $20
With the Understocking and Overstocking Cost, we calculate the critical ratio:
Critical Ratio = (Cu) / (Cu + Co) Critical Ratio = $30 / ($30+$20) Critical Ratio = .60
NORMSINV (0.60) returns a z-statistics: 0.25
The optimal number of options =
Expected Demand + (Z-Stat * Std. Dev. of Demand)
The optimal number of options = 20000 + (0.25*4000)
The optimal number of options to sign for = 21013
b. If Handi decided to purchase 12,000 options, the probability he would need to procure
more on the spot market (given the mean and standard deviation) would be as follows:
P(D> 12000) = 1 – NORMDIST (12000, 20000, 4000,1) = 0.98 P(Z> -2.00) = 1 – NORMSDIST (-2.00) = 0.98
RICHARD T. DOERMER SCHOOL OF BUSINESS
Prof. C.Z. Gurgur
c. Had Handi purchased the 12,000 options, the expected number of displays Handi
would buy in the MTO setting would be as follows — i.e. ON THE SPOT MARKET:
EXPECTED LOST SALES: 4000 * L (-2.00) = 8034
d. With the 20,000 options, the expected number of options that Handi will exercise:
EXPECTED SALES: 20000 – 8034 = 11,966
e. With the 12000 options Handi purchased, the total procurement cost would include
multiple additions, from the original option purchase, the exercising of the options, and
then the emergency procurement cost.
f. The fill rate of 12,000 options would be as follows:
Handi
E (Sales) 11966 = = 59.83%
E (Demand) 20000
g. The expected number of purchases on the spot market is equal to
Expected Lost Sales.
Expected lost sales = Std. Dev. * L (Z-Stat) Expected lost sales = 4,000* L (0.25) = 4000*0.2863 Expected lost sales = 1145
Handi
Option Purchase + Options Exercised + MTO Purchase of
Items = Total Cost
12000($20) 11966($50) + 8034($100)
$ 240,000 $ 598300 + $ 803400 $ 1,641,700
Fill Rate =
RICHARD T. DOERMER SCHOOL OF BUSINESS
Prof. C.Z. Gurgur
Expected sales = Expected demand (mean) – Expected Lost Sales Expected sales = 20000 – 1145 Expected sales = 18855
The cost of buying 21,013 options
Ci*Qi = $20*21013 = $ 420,260
Plus exercising options
Ce*Qe = $50*18855 = $ 942750
Plus purchases on spot market
Total Expected Procurement Cost $ 1,477,510
h. If Handi were to exclusively have an MTO agreement, i.e. purchasing only from the spot
market, then the fill-rate for this would be 100%, as there would be no lost sales.
Expected Sales = Expected Demand.
As such, there is NO mismatch cost. All demand will be met. There is NO mismatch risk, the cu and co are simply equal to zero.
Cs*Qs = $100*1145 = $ 114,500
Handi
Expected
Procurement Cost
= Purchase Cost*E(Demand) =
$100*20000
2,000,
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