The M2Machines Corporation is a UK-based company producing industrial machines and tools as well as assemblies of cranes used in harbors
Business Analytics Questions – Network Flow Problem and Integer Programming Model
Business Analytics
The M2Machines Corporation is a UK-based company producing industrial machines and tools as well as assemblies of cranes used in harbors, selling their line of products both nationally and overseas. The company produces make-to-order, i.e., orders for each product is received in advance, and the company makes sales contracts that are financially binding, i.e., any shortfall in sales carry penalty charges. The new production manager Henry Walker, who is responsible for the product DR35, a machine tool used widely in the manufacturing industry, realizes that the current production facilities are not sufficient to meet the contracted sales, and he would like to hire you for your consulting services as a Business Analyst. Mr. Walker provides you a data file that includes numbers of contracted sales for clients around U.K. and Europe as well as shortfall penalties to be paid if demands are not met. Moreover, the data file presents production capacities of the current facilities (Cardiff, Coventry, Glasgow and Manchester) and potential future facilities, as well as transportation costs between facilities and clients.
1. Mr. Walker currently considers three scenarios:
a. Do not open any new facilities and use only current facilities.
b. Open facilities in Nottingham and Plymouth in addition to current facilities.
c. Open facilities in Southampton and Sunderland in addition to current facilities.
The first scenario does not carry any extra facility charge, whereas the second and third options carry each an estimated cost of £800,000. Also note that the company would like to not exceed 50,000 units of DR35 on any shipping route.
Help Mr. Walker decide the best of these three options by modeling each of these scenarios as a network flow problem. You need to prepare an Excel file with three sheets for three network models. In addition to the Excel file, you need to send him a 1-page summary letter, where you explain him briefly your approach, your recommendation and why. (Note: Mr. Walker has a business degree and is therefore not familiar with technical terms, so your letter should not involve any technical terms. Also note that you can simply include the fixed costs for 2nd and 3rd scenarios manually after solving the network models.)
2. After receiving your recommendations and report, Mr. Walker heard about sensitivity analysis from another colleague at M2Machines Corporation, and he wonders if he could make any use of it in this context. In particular, he is interested to know what would happen if the routes leaving Cardiff were cost slightly differently (i.e., how much the cost of each route leaving Cardiff can change without changing the optimal flows) for the best scenario you picked. Write for him a 1-page letter about this matter with a brief explanation of how you could read the sensitivity report to identify these numbers so that Mr. Walker can himself have a more thorough look into the report in the future. (Note: You should generate the sensitivity report for your best scenario and include it in the Excel file you submit for the first part.)
3. After more thought, Mr. Walker decided that there might be many more scenarios rather than only the 3 considered before. In particular, he found out that some of the current facilities are in prime locations in city centers with high real estate values and hence can be sold for high prices. However, to keep production flow smooth, he would consider closing down at most one current facility and sell it. On the other hand, he thinks there should not be any constraint on potential candidates, i.e., any combination of these facilities can be bought, especially since these are in cheaper locations. The sale prices for current facilities (if closed down) as well the cost of potential facilities are given as follows:
Sale Price Purchase Cost
Current (in £1,000) Potential (in £1,000)
Cardiff £850 Nottingham £550
Coventry £1,450 Plymouth £350
Glasgow £1,700 Southampton £550
Manchester £3,400 Sunderland £250
The company does not consider anymore route capacities as in question 1. Mr. Walker wants to test the model where shortfalls are allowed at the cost levels as in question 1.
Help Mr. Walker by preparing the integer programming model, provided in a separate Excel file. Also write a 1-page summary letter on the comparison of the optimal solutions of both options.
Answer preview the M2Machines Corporation is a UK-based company producing industrial machines and tools as well as assemblies of cranes used in harbors
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