MTH784P – Optimisation for Business Processes Spring 2020 Coursework F. Fischer The objective for this coursework will be to solve two realistic business optimization problems, one concerned with the expansion of a broadband provider into a new market and one with training of manufacturing staff. The deadline for submission is 17:00 on Wednesday 22 April 2020. Late submissions are subject to School penalties. You should submit any source code you have used to solve the problems and a single pdf document of at most twelve pages at a font size of 11 points discussing your choice of mathematical model for each problem, any assumptions you have made, the techniques used to solve the problem, and the optimal solution. In particular you should justify the choice of model and optimality of the solution. Any illustrations, code fragments, references, and appendices must be included within the page limit. Up to 40 marks will be awarded for the solution of each of the two problems, and up to 20 marks for a clearly structured and logically coherent writeup and efficient and well-documented source code. The writeup should discuss any assumptions that were made about the problem and any limitations the solution may have in practice. The source code should be sufficiently general to allow for the analysis of new instances of the same problems. While you may discuss your general approach with others, the work you submit must be entirely your own. Submissions are subject to QMUL’s plagiarism policy and will be checked automatically for any overlap with other submissions and with existing material. 1. A broadband service provider is expanding its operations into a new city. Service to individual customers is provided through a network of switch boxes, none of which are currently connected to the provider’s network. Each box is of one of three types—A, B, or C—and is associated with a unique parent box. To connect a box to the network the service provider must first connect the parent box and then pay a fixed installation cost that depends on the type of the box itself. The installation cost for a box of type A, B, and C is £500, £700, and £1000, respectively. Other relevant information on switch boxes is given in the file network.csv, the first five entries of which are as follows: id parent type 1 1 C 2 1 C 3 2 C 4 1 C 5 4 B . . . In an effort to determine which boxes to connect, the service provider has asked potential customers to register their interest in the service for one of two bandwidths, X or Y. Each potential customer is associated with the unique box located closest to its physical address, and to offer service to the customer the provider would have to connect that box to its network. Past experience has shown that a customer who is offered the service will Coursework MTH784P (Spring 2020) accept the offer with a probability of 80%. If an offer is accepted the provider pays a local installation cost of £100 to connect the customer to its associated box and then makes a net yearly profit of £200 for bandwidth X and £125 for bandwidth Y. Other relevant information on potential customers is given in the file customers.csv, the first five entries of which are as follows: id box bandwidth 1 22 Y 2 22 X 3 6 Y 4 19 X 5 18 X . . . (a) Under the condition that it connects a particular switch box to its network, which potential customers associated with this box should the provider offer the service to? What is the expected net profit after one year from this set of potential customers? (b) If the goal is to maximize net profit after one year, should the service provider connect the box with id 1 to its network? What about the box with id 14 and the box with id 2? (c) Determine which boxes the service provider should connect to its network, and which customers it should offer the service to, in order to maximize its net profit after one year. 2. A manufacturing company is experiencing an increase in demand for its products and a high staff turnover, with 5% of employees leaving the company at the end of each month. To meet these challenges management can hire new employees at the end of each month, but it may also enroll some or all of its employees in a training program. Training takes one month, and participants do not contribute to manufacturing during this time. Upon successful completion of the training program an employee receives a 10% increase in salary and commits to stay with the company for the next twelve months. Experience has shown that 90% of employees who participate in the training complete it successfully, and that successful completion leads to a 20% increase in productivity. Employees who do not complete the training successfully return to the workforce without an increase in productivity but may participate in the training again at a later date. The company currently has 174 employees and incurs a payroll cost of £2500 per month for each untrained employee. The estimated demand for the next twelve months is given in the file demand.csv, the first five entries of which are as follows: month untrained employees required January 120 February 120 March 138 April 150 May 168 . . . (a) If the company does not send any employees for training and does not hire any new employees, in what month is it expected to no longer be able to satisfy demand? 2 Coursework MTH784P (Spring 2020) (b) What is the maximum number of employees that could be sent for training in Jan- uary? If management sends the maximum number of employees for training in Jan- uary and does not hire any new employees, what is the maximum number of employees that could be sent for training in February? (c) Develop a hiring and training schedule that ensures that demand can be met through- out the year and minimizes overall payroll costs. 3
