Final-Fall2004-05 - (>ng "100 flarian...

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Unformatted text preview: (>ng "100 flarian UM’VERSITYOT $031397 Suliman S. Olayan School of Business OPIM 205: Computer Modeling for Management Fall 2003-2004 Final Exam Date, Jan 21st , 2004; Time: 5:30 pm-7:30 pm. Question 1. (15 marks) A portfolio Manager has been given $100,000 to invest; (S)He will choose inVestments from a list offive projects. The projects require the cash flows at time 0 and yield the net present values (NPV) shown in the tabie. Projects Cash at time 0 in $10005 NPV in $1000s l 10 15 2 15 3O 3 20 30 4 30 20 5 40 50 (i) Build a linear programming model to determine the investment plan that maximizes NPV. [9] (ii) In order to minimize the investment risks, the portfolio manager has decided on the following: a. If either projects 1 or 2, or even if both, are selected then a handling fixed charge of $5,000 Should be incurred. [3] b. If both projects 1 and 2 are selected, then project 5 must not be selected. [3] Modify the formulation in (i) to meet the above two conditions. Question 2 (30 marks). Nation’s Bank is in the process of designing a new product. Lunching it is a substantial undertaking that requires significant amounts of time and resources. To make managing and controlling the project practical, related activities have been collected into ‘work packages’ and the corresponding PERT network has been drawn. The following table details the status of the work packages at the start of the project. Activity Immediate Expected Variance Predecessors Duration (weeks) i. Determine the critical path and the expected completion time for this project. [5] ii. What is the effect of a 3 weeks delay to activity B combined with a 3 weeks delay to activity C? [5] iii. Suppose the bank stands to gain $40,000 if project is completed in less than 28 weeks, $ 0 if project is completed within 28 and 32 weeks, but actually incur a loss of S 10,000 if the project takes longer than 32 weeks. What is the expected gain or loss that the bank would assume this in this case? Clearly state your assumptions.[5] iv. At week 15, the status of the project was updated with additional information on crashing cost and expenses. Percent Expenses Completed to Date A n—— n I. a) Is the project currently experiencing a cost overrun or cost underrun? [5] Activity Maximum Crashing Time it can C est be crushed per Week b) Is the project on target to be completed within its minimum completion time? {5] c) Given the reward and penalty previously mentioned in part 3, what is your recommended corrective decision and its associated cost and benefit? [5] Question 3 (20 marks). The manager of ‘PIZZAS R US’, a SUCCESSfiJl local pizza restaurant, happens to be a resourcefiil OSB graduate that had a great time in her OPIM 205 course. She is contemplating the introduction of ‘pizza on wheels’, a new evening service in her restaurant designed to reduce the delivery times to relatively distant evening customers, thereby expanding her customer base. The idea is to place several pizzas in a special oven that preserves the freshness of the pizzas for a long time. The relatively small oven is mounted on a scooter that could deliver several orders in a row before coming back to the restaurant for replenishment. Assume that the hourly demand of 24 pizzas is constant throughout the evening. The manager estimates that ordering a scooter out costs 600 LL. a trip (in fixed costs) and that keeping one pizza ‘on wheels', hot and fresh, costs 800 L.L. per pizza per hour. i. How would the manager decide on the nu er of pizzas a scooter should carry on onerun tie. tri ? ii: “I 011%“ ‘ 5 l P) V. x l l ii. What is the average number of pizza runs per hour that the manager should expect to send out? D: a v 1.5) \Q 9kg; [5] iii. Would your answers to parts (a) and (b) change if we assume that the oven can fit at most 4 pizzas? (a qualitative answer suffices here, if you want) [5] iv. Assume during an evening of/glworking hours, one run could not be carried out due to a scooter breakdown. [5] a) What is the scooter-cycle service level? b) What is the pizza service level? n , A W <\ j t— ' j Question 4 (15 marks). ‘PIZZAS R US’ and its main competitor, ‘PIZZA KING’, are in the process of reviewing their pizza prices, p1 and p2 respectively. The manager at ‘PIZZAS R US’ believes that the price of its competitor ( p2 ) is a random variable with distribution: P(p2 = 9000 LL) = 0.25, P(p2 = 11000 LL) = 0.50 and Ptpz = 13000 LL) = 0.25. She also estimates that her daily demand is a function of the pnces at both restaurants as follows: Pizza R US demand = 100 + 25(p2 ~ p;)/1000 pizzas. The following prices are under consideration for a single PIZZAS R US pizza that costs 9,000 LL to prepare: 10000 LL, 12000 LL and 14000 LL. She has constructed the payoff table below in order to help her determine the best pricing decision. 7 1000 L.L. 175000 75000 225000 125000 375000 i. Fill in the missing values in the table. [6] ii. Suppose our ‘PIZZAS R US’ manager were: [9] a. Risk neutral. What would her pricing decision be? b. Optimistic. What would her pricing decision be? c. Pessimistic. What would her pricing decision be? Question 5 (20 marks). Nagham and Sondos are two young stockbrokers that have a bet with one another to see whose hot stock would be the better performer in one week on the stock market (5 trading days). Nagham’s pick is Intel‘s stock which over the past year was up by a 1/2 at the end 50 trading days, unchanged for 40 but down by a 1/4 for the remaining 150 days. Sondos‘s pick is IBM‘s stock which over the past year was up 1/2 over 100 days, stayed the same for 80 days but otherwise went down by 1/4 for the remaining 60 days. Assume both stocks are at $50 a share at the start of the betting week. i. Develop a relative frequency distribution for each stock with tow decimal places. [5] ii. What is the expected value of the change in each stock for the last year? [2+2] iii. Simulate a run of 5 days of the two stocks using, for each stock, the following random numbers: 7606, 4391, 2952, 8734, and 1468. [5} iv. Who is the winner of the bet in the simulation experiment? {3] v. Compare the answer in (iii) with the expected stock prices for the last year in (ii), comment on the difference between the values. [3] (t) Let Xi = l ifproject i is selected, 0 otherwise [2] The problem i.5'.‘Max 15X] +... + 50X5 [2.5] s.t.lOXl + + 40X5 5100, X1, X5 in {0, l}- (iija. Let Y = l ifafixed charge is paid, 0 otherwise. [3] Add to the objective the term: ~5000l’ Add to the constraints: X l + X2 5 2 Y. b. Add to the constraints: X5 5 2 — Xi - X2. 2(i)The critical path of a project is the longest path of the network. In this case, it is easy to identify the Start-A-D-E—End path of length 30 weeks as the critical path (there are only 3 Start to End paths). +the graph. (it) The simultaneous delay of B and C by 3 weeks causes the critical path to become Start—B-C—E—End of length 3] weeks. In other words, the combined delay delays the project completion time by 1 week. (iii) Assuming that the model is indeed a PERT model. the project completion time is normally distributed with mean 30 weeks and-standard deviation sqrttl +2+l) = 2 weeks. LetX be the r.v. associated with the project completion time. E[gain] = 40,000*P{X< =28) + 0*P(28<X<=32) ~ 10,000*P(X>32) : 40,000*P(Z< =-l) - 10,000*P(Z> l), where Z is Normal(0.l‘) : (40,000-10,000)*0.l587 * S4 75 9. 68 a) Is the project currently experiencing a cost overrun or cost unden'un? [5] The total expenses to date = 3 23,600. The project value to date = S 18. 750. Therefore, there is a cost overrun ofS 4,850. b) Is the project on target to be completed within its minimum completion time? [5] The remaining activities that are still incomplete are C, D, F and E. The longest path with the remaining activities is D-E-End of duration 20.5 weeks. Add 15 weeks of elapsed time and the whole project is estimated to last 15 + 20.5 = 35.5 weeks. This is 5.5 weeks beyond its initial estimate. Therefore, the project is definitely not on target. 0) Given the reward and penalty previously mentioned in part 3, what is your recommended corrective decision and its associated cost and benefit? {5] The critical path of the remaining project consists of activities D and E. The time by which we need to crash those activities, so as to collect the 540000 reward, is 35 .5 — 28 = 7.5 weeks. But the maximum these activities can be crashed is 3 +4 2 weeks. So collecting the reward is not possible. 13" the project continues on the current track though, there will be a penalty of 310000. In order to avoid the penalty, we need to crash it by 35.5 — 32 z 3.5 weeks. The crashing can be done because the two activities are in sequence and their combined crash time is 7 2 3.5 weeks. The least costly way to do this is to crash E by 3 weeks and D by 0.5 weeks for a cost of S35 00. This is the recommended action because it avoids a larger cost ofS 10000, in the form ofthe penalty. i. How would the manager decide on the number of pizzas a scooter should carry in one run (i. e. trip)? [5] This is an EOQ model with demand 24, holding cost 800 and ordering cost of 600. Q* : sart(2 *24*600/800) = 6. The number of runs to he sent out per hour is 6. ii. What is the average number of pizza runs per hour that the manager should expect to send out? [5] The demand is 24 per hour. During each run 6 pizzas are delivered. Therefore, the average number of runs should he 24/6 = 4. iii. Would your answers to parts (a) and (b) change if we assume that the oven can fit at most 4 pizzas? (a qualitative answer suffices here, if you want) [5] in this situation, the total variable cost. TWQ) = QCh/2 + DCo/Q, should be minimized u itional restriction that Q S 4.‘ not only that Q 2 0. Because thgjypggigpflj ' > ' ver the inte J _. constrained minimum" Occurs at ___Q*_ = V4._;Hence there should be an average of 24/4 = 6 runs an our in order to satist the pizza demand. iv. Assume during an evening of 5 working hours, one run could not be carried out due to a scooter breakdown. [5] a) What is the scooter-cycle service level? There should be 5 *4 = 20 pizza runs per evening. One run uncompleted yields a scooter cycle service level of 1 9/20 = 95%. b) What is the pizza service level? There should be 5 *24 I 120 pizzas delivered per evening. One run uncompleted yields a pizza service level of { l 9*6)/l 20 = 95% also. i. Fill in the missing values in the table. [6] The payoflfs are [100 + 25(p3 —pi)./1000]*(p,n—9000), if[100 + 25(1); ivy/1000] a 0 and 0 otherwise: 0 (or -l25000, they don ’t pay attention to negative demand) in the first column, 1 25 000 in the second and 3 75 000 in the third. Expected 9000 1 1000 13000 val. 75000 125000 175000 175000 125000 75000 225000 375000 375000 225000 0 125000 375000 375000 125000 ii. Suppose our ‘PIZZAS R US’ manager were: [9] a. Risk neutral. What would her pricing decision be? She would choose the Expected Value Criterion and so select 12000 LL for her pizza price. b. Optimistic. What would her pricing decision be? She would choose Maxiinax Criterion and so select 12000 LL or 14000 LL for her pizza price. c. Pessimistic. What would her pricing decision be? She would choose .Maximin Criterion and so select 10000 LL 0r 12000 LL for her pizza price. i. Develop a relative frequency distribution for each stock with tow decimal places. [5} The total number of days is 240. me change in INTEL) = 5/24 P(0 change in INTEL) = 1/6 P(-1/4 change in INTEL) = 5/8 PHI? change in IBM 2 5/12 P('0 change in IBM’) 2 1/3 P('—}/4 change in IBM) = 1/4 ii. What is the expected value of the change in each stock for the last year? [2+2] E (Intel change) = (1/2)(5/24) + 0 (1/6) + (-t/4)(5/8) = —5/96. E (IBM change) 2 (1/2){5/12) + 0 (1/3) + (-1/4)(1/4) = 7/48. iii. Simulate a run of 5 days of the two stocks using, for each stock, the following random numbers: 7606, 4391, 2952, 8734, and 1468. [5] The simulations require that random number mappings be generated Let x be a random number between 0 and 1 generated according to a uniform distribution. Based on thefi’equency distribution for Intel stock changes and IBM stock changes, Uhiwj; m“ 750“ SW“ .1?" :7. ;QEC‘¢mL.>;\A-.z) b 4 ‘ .v-J'c‘x aw r . j. M: pawl OLWJm fl : 395 . (x - . , . I ' ,_ :1 , « b v ' A ‘1 J pfi‘i—A ‘ r ‘— L.—3 LL ' 'h h - : < I g .1 Q { J £15 W 2 L' C/Lchh Fj/ 3'4;~tf_,['(._§;\ 1 —‘\ .F‘ Wifi ) I t...— f... 7 7 ML pvjéc/faLAa/A'pn 5-; ,, 30‘ Ms ,, JL..I_.Q~—E".._._ 7 _ ._ . gaflflfA@mW&a¢:$&qx y .‘ (“fie—MN?» IMGwM 6W5}. flaw! a}: _ 7 ,, £0 7 _ £{mi'5k f"; 189L932 Lil/HQ KS Ric) ., 7 Nitric __?‘5/~\I~cn) é \Cf- a? “HM—it;- f; "fl, {3.} I I firmK KA’L‘CHfaA/I. 084.3; 32.1” WWW? c7- .Il'f/k 7‘ I -' gag“: rj . 1)-, E. manna/.5, ’féack’caf pyth- —_'———__. _ . <3M%m,gmawfl,g_ flmaarcmv ’UWI’VERSIWOT (Banter Suliman S. Olayan School of Business DCSN 200: Managerial Decision Making Fall 2004-2005 Final Exam Date: January 25‘“, 2005; Time: 6:00 pm—8:00 pm. Version A This exam is administered in full observance of the Olayan School of Business Honor Code and the penalties it sets for violations of the standard of academic conduct. You are required to fully understand the code and to strongly adhere to it. In particular, cellular telephones, and computers of any shape or size are not allowed. No questions, no comments, no borrowing and no disturbance of the peace of any kind will be permitted or tolerated. You are required to stop working on the exam and hand it immediately when a proctor instructs you to do so. Any cheating or attempted cheating will subject the offender to a zero on the exam and a referral to the Student Affairs Committee for further penalties. Please, sign the following pledge and return these question sheets inside your answers’ booklet. “I fully understand and strongly adhere to the School of Business Honor Code.” Signature Name Question 1 (25 pts.) Flavin Cosmetics produces 80,000 tubes of lipstick monthly. It currently purchases the cases used in its lipsticks from Metal Works. The cases cost Flavin $045 each and the cost to place an order with Metal Works is estimated to be $150. Approximately 3 half percent of all cases delivered by Metal Works are defective so that F lavin requires 80,402 (80,000/ .995) cases to support its monthly production. F Iavin is considering producing the cases in-house. It can do this by leasing a casing machine at a cost of $9,000 per year which is capable of producing 200,000 tubes per month. The production setup cost to use this machine is $200 and the incremental production cost of cases is 3.038 each. In this case, there will be no defective cases. F lavin estimates its annual holding cost rate for cases is 20% whether they are purchased or produced in-house. Determine whether Flavin should continue to purchase cases from Metal Works or Ym\ (m c 0‘7 max A ‘ “- C/m}: oohg’ CAM-3:55.033, Co a \5—0 1 <3 0 l 9329‘ begin in-house production if their objective is to minimize the total annual cost. Question 2 (35 pts.) Lebanon imports most of its goods by ships. The Lebanese port authority is interested in analyzing the capability of accommodating the freighters at one of its piers. According to the policy of the port authority freighters will be custom cleared at the end of the arrival day whatever is the arrival time. Freighters are ready for unloading at the beginning of the next day depending on the availability of the pier. We assume the service policy at the pier is First Come First Served. The pier may service at most two ships at a time. Cargo ships arrive randomly according to the following distribution: Number of Shi hr, ’ Waiting time for a ship starts from the beginning of the next day it' arrives. The time required to unload a shipis also variable, depending on the vessel's capacity and configuration as well as available dockside manpower and equipment. Unloadin Time in Da 8 —- Probabili O (—0 a. Using the probability distributions of arrival of ships and un-loading time, determine 0 the mean dail arri Is and mean dail unloadin time. 10 ts £:&KO.\-i'laka—‘Ly+ EKQH+ 3Ka¥i+l1gxml ( p) b. Assuming it is Monday morning, perform a fixed time simulation for a 5—day working week ending on Friday evening. The purpose is to estimate the average number of ships waiting to unload (after clearance) and the average length of time a ship must wait. Use the follo'wing two pseudo random number rows: the first one for arrivals and the second one for the unloading times. (20 pts) .74 .74 .40 .33 .62 .54 .10 .16 mm% Probabili - . - . ,. . . m 2 WM» 1‘ Oar-0C?) \d-io} fame-6‘3 ‘- Lo '— ‘ (1)0 _ \00 OW D O l 9. 3 tr Question 3 (40 pts.) Cedars Developers, recently purchased land on the outskirts of Beirut and is attempting to determine the size of a condominium deve10pment it should build. It is considering two sizes of developments: small, d}, and large, d2. At the same time, an uncertain economy makes ascertaining the demand for the new condominiums difficult. Cedars’ management realizes that a large developmentfollowed by low demand could be very costly to the company. However, if Cedars makes a conservative small-development decision and then finds a high demand, the firm’s profits will be lower than what they might have been. With the two levels of demand, 5; for low and s; for high, Cedars’ management has prepared the following profit payoff table (in thousands of dollars). Low demand s1 Small development :1; 400 r 0'5 600 "~ 0‘ Large develo n ment d; 300 Hwy 900 ENG: (i) Assuming Cedars has to make a decision on choosing a development plan under uncertainty, what would be the decisions under an aggressive approach High demand S; _ and under a minimax regret criterion? (10 pts) ' If 13(81) = 0.35, what is the recommended decision using the expected value ,,. a approach? 9 SL1 : O ‘C 5 ’ (5 pts) - (iii) What is the expected value of perfect information? (5 pts) =3, 'v) Suppose that Cedars conducts a survey to evaluate the demand for the new ment. The survey reports on two indicators of demand: K c dominium develop:Z w - 'q weak- I] , or stron . The conditional bab'l'ties are: P 11 31 = 0.6 a d Q2): 03 ) pro 11 ( ,I ) n i l a. What is Cedars’ optimal strategy? Draw the corresponding Decision Tree. (15 pts) (5 ts) ,.-. {5s}- t b. What is the value of the survey information? K. ...
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Final-Fall2004-05 - (&amp;gt;ng &amp;quot;100 flarian...

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