A1PartAQuestion ETF2480 Business Modelling: Assignment 1 Part A Question 1 [ XXXXXXXXXX = 25 marks] The company Rail Systems Inc. (RSI) has been awarded the contract to operate the rail system in the...

question 1 part a to e


A1PartAQuestion ETF2480 Business Modelling: Assignment 1 Part A Question 1 [4+4+4+4+9 = 25 marks] The company Rail Systems Inc. (RSI) has been awarded the contract to operate the rail system in the Greater Railtown area. The Traffic Analytics Department has estimated the staff requirements during each four-hour period as follows: Table 1 Time period Number of staff required 6am – 10am 700 10am – 2pm 200 2pm – 6pm 800 6pm – 10pm 300 10pm – 2am 100 2am – 6am 100 Even though the staff requirements relate to four-hour time periods, all staff work eight- hour shifts. The starting times of shifts are 6am, 10am, 2pm, 6pm, 10pm, and 2am. Of course, the company wishes to minimise the wage bill. The normal daytime hourly rate is $30 per hour, but some hours attract penalty rates. Specifically, between 8pm and midnight the hourly salary is 50% above the normal rate; while between midnight and 6am the hourly salary is double the normal rate. Provide answers for (a) to (d) in a Word document. Parts (a) through (d) should total about 300 words. In some parts it may be convenient to use tables. (These are included in the word count.) (a) In two or three brief non-technical sentences, explain the problem to be solved, including the objectives, the resources available, and the constraints. (b) Consider a linear programming set-up for this scenario: In the Word document, explain: i. what the decision variables are, and ii. what quantity the objective function (OF) represents. (c) Provide appropriate notation for the decision variables. (d) Explain what constraints apply, and write them in terms of the decision variables. (e) Set up an easy-to-read self-contained Excel spreadsheet, Sheet 1 showing the following: the decision variable cells; all relevant parameters; setting up the required constraints; and creating a table that can be used to calculate the objective function. The spreadsheet should be set out in such a way that you can easily organise a linear programming approach to the problem. Do not attempt to solve the problem at this stage. This will be done in part B. A printout of the spreadsheet should be arranged so as to fit easily on one page, and should be attached to the printout of the Word document. Hints for Question 1: 1. Think carefully about the relationship between the four-hour blocks and the shifts. How many shifts contribute to a single four-hour block? You could summarise the following information in a table: For each four-hour block, • Which shifts is it included in? • What is the minimum number of staff required? Use this information to express the constraints in terms of the decision variables. 2. For part (e), here is one possible framework for a table to organise some of the information given. The number of staff supplied is of course a function of the decision variables. This table will help in the calculation of the OF, though it is only part of the set-up. Four-hour time period Number of base rate hours Number of 50% penalty hours Number of 100% penalty hours Staff supplied Staff required Staff total cost 6am - 10am 10am - 2pm 2pm-6pm 6pm 10pm 10pm - 2am 2am - 6am