” 辅导Analytics课程程序、 写作c/c++，Java，Python程序Supply Chain Analytics AssignmentMaster in Business AnalyticsDue Date: 2 PM Tuesday, September 15, 2020Mark Component: 35% of overall assessment, consisting of six questions totalling 150 points:Question One 20 marksQuestion Two 25 marksQuestion Three 25 marksQuestion Four 25 marksQuestion Five 20 marksQuestion Six 20 marksTOTAL 150Marking Scheme:Questions One, Two, Four, Five and SixThe answers shall be self-contained with final conclusions, LP or ILP formulations and working (whererequired) and brief explanations stated succinctly for each sub-problem. All code/spreadsheets are to beprovided in an accompanying File or appendix.Question ThreeThe report has to be self-contained: It has to include an explanation of the model or models used and theapplied methodology to estimate the parameters of the proposed discrete choice model/models.The Excel and/or any other code or file developed to solve the problem must be provided. Nevertheless,it should be possible to understand what has been done by only reading the report.The overall report and methodology used to solve the revenue management questions has a weightof 25 points for the assignment. Another 15 points will be given based upon performance: Groups will beranked based on the quality of their predictions (the way in which predictions are evaluated is explainedat the end of the problem statement).The following table provides the Points given to each group based on the prediction ranking. Thetop group gets the maximum possible, (i.e. 15 marks), and the groups with lowest predicted power obtain3 marks. 辅导Analytics课程作业、 写作c/c++，Java，Python程序Ranking Marks Ranking Marks1 15 4 52 11 5 43 8 6 and less 31QUESTION 1 – Network Problem for Lifezest Drug manufacturingLifezest Drug manufacturing company processes four different chemicals in some or all of its 3 plants.Each month, these chemicals are transported to 4 warehouses which work as a link between the plantsand 6 distributors. The monthly demand from the 6 distributors is as follows:Demand of chemicals (in thousand litres per month)Distributor Chemical1 Chemical2 Chemiccal3 Chemical4Caremark 9.5 8 8 10MediCraft 8 4 8 2Greens 4 6 6 3Walkers 3 1 .5 1.5HealthAura 5 3 5 5FirstCare 4.5 3 4 6The monthly capacity in terms of total litres of chemicals for each of the three Lifezests manufacturingplants is shown below. In addition, if a plant produces any of the 4 chemicals during a month,there is a setup cost which is also shown below.Capacity and setup cost of the plantsPlant Capacity Setup CostNewham 30,000 750,000Springfield 72,000 1,800,000Benloch 50,000 1,000,000The warehouses at Lifezest have a limit on the amount of litres of chemicals they can handle in amonth. Those monthly Capacities are given below.Warehouse CapacityRomsey 30,000Broadford 35,000Kilmore 34,000Wallan 30,000The following tables show the transportation costs (in $ per litre) associated to the chemical tranferfrom plants to warehouses and from warehouses to distributors:2Cost($/litre) Romsey Broadford Kilmore WallanCaremark 20 33 26 18MediCraft 16 34 29 33Greens 24 46 21 48Walkers 23 19 23 28HealthAura 18 37 12 14FirstCare 17 34 43 16Cost($/litre) Newham Springfield BenlochRomsey 37 30 41Broadford 35 29 23Kilmore 13 41 25Wallan 22 37 15Questionsi) Propose an integer linear program to find a minimum cost solution for Lifezest manufacturer.Provide as well the optimal solution found, which must include the amount of each chemical produced ineach of the plants and how much it is transported between any pair of entities in the network.[10 marks]ii) Consider the scenarion in which additional capacity can be leased at any of the plants at the costof $35 per litre per month. For example, the capacity of Newham can be increased to 30,001 if we payan extra $35 per month and the same for all the other plants. Construct another ILP model taking inaccount this extra flexibility. Include the optimal solution, the amount of each chemical produced in eachof the plants, and report how much it is transported between any pair of entities in the network.[10 marks]3QUESTION 2A – Deterministic Inventory Models: In-LightPart 1 – Problem DescriptionIn-Light is a lighting company that has contracted you to manage the inventory of an LED strip light.In-Light sells a remarkably steady 700 units a year, each light costs $12 to buy from the wholesaler andtheir management Team estimates that each light has an associated annual holding cost of 20%. Thewholesaler contracts a transportation company who charges a fixed amount of $82 per delivery. Giventhat the wholesaler makes the lights to order, each delivery takes exactly 2 weeks to arrive.Questions1. Plot the inventory level over a year for an optimal solution of the standard EOQ model. Make sureto include the reorder point and label all relevant features describing the evolution of this periodicfunction.[4 marks]Part 2 – Problem DescriptionSuppose that In-Light considers setting up their own manufacturing process for LED strip lights. Theyestimate that their in-house process can produce up to 1,200 units a year. As a consequence of themanufacturing process, warehouse space is predicted to become more valuable, with the effect of increasingthe holding costs to 35% per unit. Rather than purchasing lights, each light is estimated to cost $9 tomanufacture. The transportation cost is also replaced by a fixed cost of running each batch, estimatedto be $15.Questions1. Plot the inventory level over a year of the optimal solution of the Economic Production Lot Sizemodel. Include all relevant features.[4 marks]2. It is estimated to cost $1,500 to complete the transition. Is switching to in-house manufacturingprofitable? Justify your answer and discuss relevance of the financial planning horizon.[1 mark]4QUESTION 2B – Deterministic Inventory Models: EOQ withplanned lost salesProblem DescriptionConsider the EOQ model Variation in which we are allowed to stock out. Now, consider a similar situationwhere rather than excess Demand being placed on back-orders, it is simply lost. Let x be the fraction ofdemand that is lost per cycle. In addition to losing money through lost sales, assume that also for everylost sale, a penalty cost of p is also acquired. Let c be the buying price of one unit. Notation from thestandard EOQ model should be used for the remaining variables and parameters.Questions1. Explain why the length of time with positive stock is QDand the length of time with 0 stock isQDx1x[2 marks]2. Derive an expression for the total cost per year, f, as a function of Q and x, i.e. f(Q, x) = ? Makesure to justify your choice.[6 marks]3. Show that Q =q2DC0Chin this context.[2 marks]4. Show that fx = D(p c) 2DChC0. Explain why f is a linear function of x.[2 marks]5. For which value(s) of x Gives us an optimal solution if:(a) D(p c) 2DChC0(b) D(p c) 2DChC0(c) D(p c) = 2DChC0Explain these results Mathematically and interpret these results.[4 marks]Hints: When determining an optimal order quantity with the standard EOQ model, we do not need toconsider the product cost, c, as we will always order D units a year. Now, since some demands are lost, the totalcost will depend on c.5QUESTION 3 – Revenue ManagementProblem descriptionConsider a large retailer that has 5 products in a specific small category. After several discussionswith the suppliers, and meetings at the marketing department the firm decides to standardize pricesamong their different retail branches. Along the past year, each product has been sold at three differentprices depending on the specific period and specific branch. Table 1 shows the three prices for eachproduct.Table 2 shows the per unit cost for the retailer. The profit per product sold is the price at whichthe item is sold minus its cost.Price level/Product A B C D E1 $23 $24 $22 $33 $282 $26 $29 $24 $43 $343 $29 $37 $32 $51 $37Table 1: Price per product {A, B, C, D, E} and price level {1, 2, 3}.Product A B C D EWholesale price $10 $11 $9 $14 $12Table 2: Costs per unit of product.Historical dataHistorical data of the monthly aggregate sales from different branches selling different assortments isavailable in the Excel file historical-data-2020.csv. In order to simplify this problem, we assume that thenumber of customers that arrive to each of the branches is the same. Without loss of generality will beassume that the total number of potential buyers per month is 1 (i.e. this is just a scaling). Thus, if 0.2consumers bought product A at a price of 26, it means that 20 percent of the buyers chose that particularproduct at that price.Each entry of the file shows the assortment of products displayed (a 1 denotes that product wasdisplayed and 0 otherwise). Next, follows the percentage of customers that bought each of the itemsdisplayed for that specific assortment. Note that the sum of the percentage of consumers that bought aproduct in the assortment is not necessarily 100%. This reflects the fact that some customers may decidenot to purchase any of the products that were available (for example they may decide to buy from acompetitor because the prices are too high for them). A hypothetical example of such an entry is shownin Table 3. As there cant be more than one price for each product, observe that at each entry of the file,there is at most one price level per product that has a value 1 whereas all the other classes have a valueof zero.Consumer behaviorEach consumers that arrives to the store is interested in buying at most one product. Think for exampleas an arriving consumer who is interested in purchasing a mobile phone, a flight ticket, a soft drink, or asnack. The demand of any product depends on the complete set of offered products since customers potentiallymake substitutions to an available product if their most preferred product is not available. Such6Product A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 E1 E2 E3Assortment 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0Percentage 0.45 0 0 0.13 0 0 0 0.045 0 0.36 0 0 0 0 0Table 3: Hypothetical example of historical data. For assortment {A1, B1, C2, D1} of products displayed,the percentage of customers that bought each product displayed is 45%, 13%, 4.5% and 36%respectively.substitution behavior is captured by a customer choice model that can be thought of as a heterogeneousdistribution over preference lists (or permutations of products). We explain:Consumers can be partitioned into customer types. Each customer type has associated a particularpreference list and will purchase the most preferable product that is available. If none of her preferableproducts are available, the consumers of that specific type will buy nothing. For illustration, considera potential consumer named Cecilia who belongs to a consumer type that is associated to the followingpreference list: [D1, A1, C1, D2, A2, B1, B2, C2]. For Cecilia, as for any other consumer that belongs tothis customer type, her most preferred product is D1, if that product is not available he will buy A1 ifavailable, otherwise if product A1 is not available she will buy the first available product in her preferencelist. If none of her preferred products are available, that is if the products displayed are contained in{A3, B3, C3, D3, E1, E2, E3} , Cecilia will leave the store without buying any product.Notice that Cecilia is rational and therefore, faced at the decision of buying the same product atdifferent prices, she will prefer the cheapest price. For example, for product A, Cecilia prefers A1 overA2 and the same for all products and their price points. For simplification, we assume all consumers arerational and that the distribution of consumer preferences is the same among all branches.A market research study has found that there are between 40 to 50 different customer types in thismarket. Moreover, 20 percent of the customer types have a preference list that has a length of at most3.QuestionsWrite a self-contained report with elaborate answers to the following questions. Max: 3 written pages(plus the prediction results in a file).1. Propose a discrete choice model for consumer behavior. Explain the reasons you selected that modeland not others.2. Estimate the parameters of your proposed model with the historical data, i.e., calibrate your model.Explain the method or methods you used.3. In order to test the accuracy of your prediction model, you will have to give the expected percentageof customers that buy each of the products for the assortments that appear in the filesolution2020.csv (Note: the quality of your predictions will be quantified as the sum of the squareddifferences between your predictions and the real observations (Refer to the next section to knowmore about the quality of the predictions).In order to compute the quality of your solutions automatically, enter your results in the same filesolution2020.csv following the exact format of the file. Please rename the file adding your groupnumber. For example: solution2019group-i where i is your group number. Please do not changeanything of the file solution2020.csv, except the changing the zeros with your market share predictions(each market share should be between 0 and 1, example: 0.024). Failure to abide to this ruleswill result in a point penalization.4. The retailer has to choose which elements to display for sale and what price each of the productsdisplayed will have. Based on your model, what assortment of products and prices according to7table 1 should the retailer choose to maximize the expected profit? Explain the method bywhich you select the assortment.5. Suppose you find a model that can fit perfectly the data of historical-data-2020.csv. Does thisguarantee that you can find the optimal assortment? If yes explain why. If not, explain whetheryou think there is a correlation between market share predictions and revenue.Quality of PredictionThe quality of your predictions will be quantified as the sum of the squared difference between yourpredictions and the real observations. For example, let us consider the assortment in Table 3, that isassortment {A1, B1, C2, D1} And that your model predicts that a, b, c, d percentage of customers will buyproduct A1, B1, C2, D1 respectively. Based on the real observations on 3, the quality of your predictionfor assortment {A1, B1, C2, D1} is quantified as follows:(a 0.45)2 + (b 0.13)2 + (c 0.045)2 + (d 0.36)2.That corresponds to the quality of the prediction of one assortment. In order to assess many assortments,we take the sum of the qualities over all assortments.8QUESTION 4 – Inventory Management with Stochastic DemandThe standard newsvendor model assumes that the decision maker knows the probability distribution ofthe demand. This is sometimes unrealistic, particularly when there is not much historical data. A muchweaker requirement is To assume that the decision maker only knows the mean and the standard deviationof the demand distribution (but not the whole demand distribution function).Imagine a scenario in which the decision maker knows that the demand distribution for a specificproduct has a mean of 10,000 and a standard deviation of 2,000. The product selling price (to consumers)is set to AUD 10. Additionally, assume that there is no salvage value.Questionsi) If the decision maker mistakenly assumes that demand follows a Normal distribution but the demanddistribution is NOT Normal, the optimal quantity calculated using a Normal distribution may not bein fact optimal. Provide an example where revenue gap between the optimal solution and the non-optimalsolution calculated by the decision maker assuming a Normal distribution is at least 3 percent.For this question you must assume that the per unit buying price for the retailer (per unit cost)is $1. You will need to explicitly show a demand distribution with a mean of 10,000 and a standarddeviation of 2,000 units.[4 marks]ii) Now suppose that the demand distribution is either: (1) Symmetric triangular (i.e. with b-a =c-b); (2) Poisson; (3) Normal. Plot a table varying the buying price (per unit cost) from 0.5 to 9.5 in50 cents increments (19 scenarios). For each scenario, evaluate the optimal order quantities the decisionmaker would choose if it knew the distribution was (1), (2) or (3). Perform a qualitative analysis of whatyou observed and provide a high level explanation of the results. For which buying prices do the optimalquantities from the different distribution assumptions differ the most?[4 marks](iii) Suppose you dont know the true distribution of demand, but you assume there is 10% chanceit is symmetric triangular; 40% it is Poisson; and; 50% it is Normal. Propose a method to choose theorder quantity and justify it. Additionally, describe at least 2 different objectives that would make senseto assess the performance of the method.[4 marks](iv) In 1957, Herbert E. Scarf solved a newsvendor problem which originates from some of the ideasdiscussed above. Explain in at most one page (and in your own words) what is the exact problemHerbert E. Scarf studied and its solution. Note: You dont need to understand the proof of this solution.You are only asked to understand well the problem statement and what is the solution.Relevant References Herbert E. Scarf, (2002) Inventory Theory. Operations Research 50(1):186-191. Scarf, Herbert E., A Min-Max Solution of an Inventory Problem. Santa Monica, CA: RANDCorporation, 1957.[8 marks]9QUESTION 5 – Inventory Management with Stochastic DemandNote: The use of Monte Carlo simulation would be helpful for this problem.United Global Imports (UGI) is a distributor of frozen fish. They distribute 4 kinds of fish: Tuna,Swordfish, Salmon and Barramundi. On any given day, there is a probability pi that an order will beplaced with UGI for a specific fish, i. If an order is placed, the size of the order will follow either a normaldistribution, or a log normal distribution. Parameters for either distribution are currently unknown. Thedaily sales for these fish over the past year are presented in the data file UGI fish imports.xlsx.Table 4 provides additional information regarding the costs associated with each fish. The holding costper year, is calculated to be a percentage of the buying price.UGI is considering adopting either a continuous or periodic review policy to manage its inventory. Asyou could imagine, UGI wants to maximise expected profit. Assume that demands will follow the samedistributions this coming year. Every fish that goes on back-order incurs a penalty cost of 80% of itsoriginal buying price. This value is set at this price so that it accounts for the associated goodwill coststoo.Assume for simplicity that the demand for each fish:1. Follows the same distribution (i.e. log normal or normal).2. Is the same across the entire year.3. Is independent of each other.Assumptions 2 And 3 apply to the pis too.Fish Lead Time(days)HoldingCosts (%)BuyingPrice($/Kg)SellingPrice($/Kg)Initial Inventory(Kg)Order Cost($)Tuna 11 32 22.00 42.50 3850 1050Salmon 10 36 12.90 26.50 1280 240Swordfish 12 31 14.50 29.00 240 42Barramundi 8 32 21.10 38.90 1980 250Table 4: Additional product data1. Questions(a) For each type of Fish, and for each distribution, determine the following:i. The mean for the daily demand distribution (approximately) (in case an order is placed).ii. The standard deviation for the daily demand distribution (approximately) (again, only incase an order is placed).iii. The expected proportion of days that the customer purchases the product.iv. The expected demand during the lead time (approximately).v. The standard deviation of the demand during the lead time (approximately).[4 marks](b) With reference to the actual distributions, discuss the suitability of using either the log-normal10or the normal distribution for modelling demand. Which distribution is a better fit? (Hint:use histograms of the actual demand with reasonable interval sizes and compare with thedistributions you produce. Alternatively, use statistical tests).[3 marks]Based on your chosen distribution in question 2, complete the following analysis of theboth the periodic review and continuous review using the same distribution.2. Periodic review(a) The first alternative UGI is considering is a Periodic Review policy to replenish stock. Usinga 1 month Review period, compute the following for each type of fish:i. The approximate optimal order up-to point value Mii. The approximate expected annual profit and its standard deviationiii. The approximate expected number of fish (in Kg) placed on back order (as a proportionof total expected sales)Please explain your procedure to respond to all the questions above. Specifically, explain withdetails how you constructed the Monte Carlo simulation.[6 marks]3. Continuous Review(a) Alternatively, management is considering a Continuous Review policy as they believe it will allowthem to respond better to changing stock levels. Use Monte Carlo simulation to determinefor each product:i. The approximate optimal order quantityii. The approximate optimal reorder point (in terms of both inventory position and inventoryon hand)iii. The approximate safety stockiv. The approximate expected annual profit and its standard deviationv. The approximate expected number of fish (in Kg) placed on back order (as a proportionof total expected sales)Again, please explain your procedure to respond to all questions above.[6 marks]4. Final Conclusion(a) Assuming that a continuous review policy would incur a 2% decrease in total expected profits(due to labour costs of constantly checking inventory levels), which of the two policies wouldyou recommend (continuous or periodic), based on total expected profits?[1 mark]11QUESTION 6 – Assignment Model for electronics supplierCompany A is a delivery company which deals in electronics. It has ties with 10 big firms which placetheir orders in bulk at the start of each quarter. The company has 5 warehouses where the electronicsare kept and then delivered to these firms.In the provided excel file (Question6.xlsx), you will find the location (coordinates) of all the firmsas well as the potential warehouses that the company can use. Using any given warehouse incurs a costof $6 per kilometre for a delivery for each customer (to be considered only for one way). You have beenhired by the company to decide which warehouses to use for which firm. Following are the questions youneed to address:QuestionsWrite a self-contained report with separate answers for each of the following sub-problems. Each answershall outline the decision variables, objective function and constraints for the ILP and thecomputed optimal Values for the objective function and decision variables. Do not simply state themathematical formulation of the ILP on its own, but also briefly include in words what the objective functionsand different constraints mean. In an appendix, include the file containing the code/spreadsheetsimplementing the ILPs developed in the report. A spreadsheet package such as Excel should suffice.1. The distributor has told you to measure distances using the 2-norm (that is, use Euclidean distances)and that each warehouse can only cover 35 kilometres in either direction. In addition, each firm canonly be assigned to one warehouse. Design an ILP model and solve it to find the optimal strategy tobe used by the company. Specify which warehouses should be used for which firm and the optimalcost. All demand must be satisfied.2. Suppose now that your budget is limited to $800 per quarter. What is the maximal coverage youcan achieve for that Amount of money in terms of number of firms?3. Evaluate and plot a graph depicting the relationship between the maximum budget available andthe maximum coverage. What can be inferred from the graph?[10+5+5=20 marks]12如有需要，请加QQ：99515681 或邮箱：99515681@qq.com
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