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Solving Real life decision problems in business - Linear programming

Project Paper/Home-work [20 POINTS]

Project Paper/Home-work RUBRIC

The purpose of this project/home-work is to model and solve real life decision problems in business using decision tools such as projects controlling, waiting lines, and linear programming. The project/home-work is based on all the materials studied and the discussions held during the course. This exercise will help you relate the theory to the real world.

The project/home-work will include a cover page and references pages. Maintain a font size 12 and use Times New Roman. Do not use single or double spacing - kindly use 1.5 spacing. Make sure to keep your data (and the source of the data) as an evidence.

Note that a maximum of 20 Points will be awarded to your report based on the quality of your report and individual contributions and presentations. PLAGIARISM WILL NOT BE EXCUSED.

Please provide a well-organized report covering all the questions, and submit your report in soft copy (through Moodle)

NOTE: If needed, you may be asked to present (on-line or face to face) your report.

1.      Project scheduling:

Search (you may use google search) for a real-life project (e.g. house construction, setting up a business, ). For this project, come up with a list of activities to be accomplished. For each of the activities identify the predecessors and set the time to accomplish each activity. [In case time is not known for sure, set the optimistic, most likely, and pessimistic time to accomplish each activity].

Once you have these information, compile a report providing your analysis including the following:                                                                                                       (5 Points, 1 point each)

a.       A project network for your project.

b.      The Earliest starting (ES), Earliest finishing (EF), Latest starting (LS), and Latest finishing (LF) time of each project activity. Explaining the purpose of identifying this information (Hint: Allowing vacation time for workers).

c.       Identifying the critical path, and the critical activities of your project.

d.      Estimation of the expected time to complete your project.

e.     [In case of using the optimistic, most likely, and pessimistic time] Estimation of the probability that your project will be completed within 3 Months (12 Weeks or 30 days)?                      

2.      Waiting time (Queuing theory):

Search (you may use google search) for a service provision company (e.g. Etisalat or Du service center at a mall, EPCO fuel station, MacDonald,). For this company, identify the number of arrivals per a specific period of time (e.g. per hour). This will help you to get the average arrival rate (?). Also get information on the service rate (?) at each counter, and the number of service counters (?) in the company.

Once you have the above information, compile a report providing your analysis including the following:

a.       Introduction section Providing a complete background information of the company (you selected), the average arrival rate (?), the service rate (?), and the number of service counters (?) of the company.                                                                                                         (1 point)

b.      Following the introduction section, your analytical report should determine the operating characteristics (performance measures) for the waiting line of the company, including:

(5 Points, 1 point each)

                       i.            the probability that no customers are in the company (system),

                     ii.            the average number of customers in the system (waiting + being served),

                   iii.            the average time a customer spends in the system,

                   iv.            the probability that an arriving customer has to wait for service, and

                     v.            forecasting the probability that 10 customers will be in the system (company)

c.        Based on your above findings, what are your recommendations to the company in terms of improving its service provision.                                                                                     (1 point)                                                                                                       

3.            Linear Programming:

Many problems in real life are concerned with obtaining the best result within given constraints. In the business world, people would like to maximize profits and minimize loss; in production, people are interested in maximizing productivity and minimizing cost. However, there are constraints like the budget, costs, time, number of workers, production capacity, space, etc. Linear programming deals with this type of problems.

A pharmaceutical company manufactures two types of medicine-tablets: Tablet-A and Tablet-B. Each case of tablet-A requires 3 hours of processing time and 1 hour of curing time per week. Each case of Tablet-B requires 5 hours of processing time and 5 hours of curing time per week. The schedule allows 55 hours of processing time and 45 hours of curing time weekly. The company must produce no more than 10 cases of Tablet-A and no more than 9 cases of Tablet-B. If the company makes a profit of AED320 on each case of Tablet-A and AED500 on each case of Tablet-B.                                                                                                                                             (8 Points, 2+2+2+1+1)

a.         Develop the linear programming model for this problem? [You must clearly define the decision variables]  

b.        Use a GRILL-LINE to clearly and neatly show the feasible region. 

c.         Find the optimal solution (i.e. How many cases of each tablet should be produced in order to maximize profit?

d.      How much (in AED) will be the maximum profit?  [Clearly show your calculation]

e.Calculate the slack for each constraint.

Solving Real life decision problems in business - Linear programming

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