M454 Logistics Modelling | My Assignment Tutor

1M454 Logistics ModellingCoursework 2Due Date: 03 June 2021 (by 5:00pm)This coursework is worth 20% of the total module mark.Submission details:1. Compile your answers to Problem 1, Problem 2 in a report, and submit it as asoftcopy to the module’s Moodle website. Your report must be typed and the fontsize used must be 11 or greater.2. Submit the SIMUL8 file from Problem 2, part b) in *.S8 format on the module‘sMoodle website.Please use your student ID number as your report and *.S8 file name (e.g.351363.S8).Do not mention your name anywhere in your submissions.This is an individual assignment. Plagiarism or copying is not permitted and anyoffence will be dealt with under the University procedures.Throughout this assignment please use the following constants:u = The first two digits of your student ID numberv = The third and fourth digits of your student ID numberw = The final two digits of your student ID number(e.g. A student ID number 351363 gives u = 35, v = 13, w = 63)Problem 1Orders are received for one of four types of parts. The interarrival time between ordersis exponentially distributed with a mean of 10 minutes. The table below shows theproportion of the parts by type and the time needed to fill each type of order by thesingle clerk. Part TypePercentageService Time (minutes)A40Normal (6.1, 1.12)B25Normal (8.0, 1.52)C25Normal (11.8, 2.02)D10Normal (15.0, 1.82) (For example, 40% of orders are for type A parts, and the service time by the clerk foran order of type A part is normally distributed with mean 6.1 and standard deviation1.1.)2Orders of types A and B are picked immediately after they are filled, but orders of typesC and D must wait with waiting time uniformly distributed between 5 minutes to 15minutes.Using SIMUL8, simulate 50 independent runs, of 8 hours in each run, to determine theproportion of orders that take less than or equal to 25 minutes through the process.Describe as clearly as possible in 300 to 500 words how your SIMUL8 model is builtand also how you obtain the answer to the question asked. Screenshots and computeroutputs should be provided in your report. In particular, a screenshot of your model isto be provided. You do not need to submit the SIMUL8 file used to solve the problem.Use the number 1 as your initial random seed.[25 marks]Problem 2The student-center cafeteria at the University of Portsmouth is trying to improve itsservice during the lunch rush hour from 11:30am to 1:00pm. Customers arrivetogether in groups of size 2, 3, 4 and 5, with respective probabilities 0.5, 0.3, 0.1 and0.1. Interarrival times between groups are exponentially distributed with mean 25seconds. Initially, the system is empty and idle, and is to run for the 90-minute period.Each arriving customer takes one of three routes through the cafeteria (groups ingeneral split up after they arrive):• Hot-food service, then drinks, then cashier.• Specialty-sandwich bar, then drinks, then cashier.• Drinks (only), then cashier.The probabilities of these routes are respectively 0.70, 0.20 and 0.10; see figurebelow. However, if there are more than 10 customers waiting in the queue at the hotfood counter or the specialty-sandwich bar which a customer intends to go to, then thecustomer will balk. At the hot-food counter and the specialty-sandwich bar, customersare served one at a time. The drinks stand is self-service, and we assume that nobodyever has to queue up here; this is equivalent to thinking of the drinks stand as havinginfinitely many servers. There are two cashiers, each having their own queue, andthere is no jockeying; customers arriving to the cashiers simply choose the shortestqueue. All queues in the model are FIFO.In the figure below, ST stands for service time at a station, and ACT stands for theaccumulated (future) cashier time due to having visited a station; the notation ~ U(a,b)means that the corresponding quantity is distributed uniformly between a and bseconds. For example, a route 1 customer goes first to the hot-food station, joins thequeue there if necessary, receives service there that is uniformly distributed between50 and 120 seconds, “stores away” part of a (future) cashier time that is uniformlydistributed between 20 seconds and 40 seconds, then spends an amount of timeuniformly distributed between 5 seconds and 20 seconds getting a drink, andaccumulates an additional amount of (future) cashier time distributed uniformlybetween 5 seconds and 10 seconds. Thus, his service requirement at a cashier willbe the sum of the U(20,40) and U(5,10) random variates he “picked up” at the hot-foodand drinks stations.Currently, there is only one employee at the hot-food counter and only one employeeat the specialty-sandwich bar.3Problem Situation: There is a need to improve the time a customer spends in thesystem. A suggestion is to employ an additional person used in one of the followingways:i. To help at the hot-food station. In this case, customers are still served one ata time, but their service time is cut in half, being distributed uniformly between25 seconds and 60 seconds. ii.To help at the specialty-sandwich bar, meaning that service is still one at a time,but distributed uniformly between 30 seconds and 90 seconds. a) Conceptual Model. Develop a conceptual model for the problem, by describingthe objectives, inputs, outputs, content (including a logic flow diagram),assumptions and simplications of the model, in approximately 300 to 500 words.[20 marks]b) Computer Model. Build a computer simulation model in SIMUL8 to model thesystem. A screenshot of your simulation model should be provided in your report.Run the model independently 100 times to find4 i.The average and maximum total time in the current system irrespective ofcustomer type and not including those who balked;Average delays in queue for hot food and specialty sandwiches in thecurrent system;Average number of customers who balked in the current system; andAverage number of customers who buy food (hot food or specialtysandwiches) and drink, and pay at a cashier in the current system;ii.iii.iv. from the “Results Manager” in SIMUL8. Use the number v as your initial randomseed.[30 marks]c) Report to Manager. Write a report of approximately 1500 to 2000 words to thesystem manager, explaining your recommendations to the problem situationdescribed above. Include the reasoning behind your choice and the comparativeadvantages and disadvantages of your choice. Include graphs/tables to illustrateand explain your recommendations. Remember that this report is for a businessmanager and should hence be of high quality and not overly-technical.[25 marks]5MARKING SCHEMEProblem 1Accurate and detailed working process 20 marksCorrect answers 5 marksSubtotal 25 marksProblem 2Part a): Conceptual ModelDevelopment of conceptual model• Objectives 2 marks• Inputs 2 marks• Outputs 2 marks• Content 12 marks• Assumptions 1 mark• Simplications 1 markSubtotal 20 marksPart b): Computer ModelProduction of model• Layout 3 marks• Clarity 3 marks• Accuracy 18 marksCorrect answers to questions 6 marksSubtotal 30 marksPart c): Production of ReportReasoning and consideration of objectives 15 marksGraphs and Illustrations 5 marksPresentation 5 marksSubtotal 25 marks


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