运筹学考试代写 Operations Research代写 Exam代写

Operations Research

BSc in Management

Final Test/1st Season Exam

Duration: 1h30/2h30

运筹学考试代写 1. [E] LightMeals needs to plan the production of its new energy wafers. The operations management team formulated the problem of

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· Questions for Exam: signed with E.

· Questions for Final Test: signed with T.

· Marks are given at the end of each question.

1. [E] 运筹学考试代写

LightMeals needs to plan the production of its new energy wafers. The operations management team formulated the problem of producing at least 1000 kilograms of wafers at minimum cost meeting the resource requirements, as presented below. The decision variables x1, x2, and x3 represent the kilograms of wafers manually, semi-automatically, and robotically produced, respectively. The first constraint imposes the minimum quantity of wafers required. The following three constraints respectively refer to the availability of skilled, unskilled, and assembly labor time (given in minutes).

Min Z = 7 x₁ + 9 x₂ + 6 x₃

s. to: x₁ +x₂ +x₃ ≥ 1000

x₁ + 4 x₂ + 8 x₃ ≤ 4000

40 x₁ + 30 x₂ + 20 x₃ £ 36000

3 x₁ + 2 x₂ + 4 x₃ £ 2400

x₁, x₂, x₃ ≥ 0

Using Excel Solver the following results were obtained:

a) Describe the optimal production plan and analyze the constraints within the problem context. Do not forget to mention the optimal cost. Justify. [E: 1.0]

b) Would the optimal production plan change if the unit cost of wafers manually produced decreased by 2 c.u.? And the optimal cost? If applied, write down the new optimal value. Justify. [E: 1.0] 

c) Suppose that the assembly labor time had to decrease by 60 minutes. Would the optimal production plan and the optimal cost change? If applied, write down the new optimal value. Justify. [E: 1.0]

d) An unexpected situation caused the simultaneous reduction of skilled and unskilled labor time respectively to 3000 and 35000 minutes. Would the optimal production plan change? Justify.[E: 1.25]

2. [E] 运筹学考试代写

An operations manager is trying to determine a production plan for the following week. There are three products – A, B, and C – to produce using machines M1 and M2. Each machine is available for 2400 minutes per week. Moreover, each product must be processed by both machines according to the processing times as follows:

a) Formulate as a linear program in order to maximize profits. Refer the meaning of the decision variables, and briefly describe the objective function and the constraints. [E: 1.5]

b) Production requirements state that production time on machine M2 must be at least 30% of total production time on machines. Update the formulation given in a) to handle this new requirement.[E: 0.5]

c) The idle time of machine M2 can be rented out at a profit of €0.50/minute. Update the formulation given in a) so as to include this new option. [E: 0.75]

d) Update the formulation given in a) to handle the following requirement: if the production of product A exceeds 60 kilograms then the joint production of products B and C cannot exceed 80 kilograms.[E: 1.0]

3. [E/T] Consider the following information about a project with 11 activities:

Draw an activity on arc (AOA) network for the project, and number its nodes. [E: 1.5/T: 2.5]

4.[E/T]

Consider the following AON network representing a project with 8 activities whose durations are given in days:

a) Determine the minimum project duration. Justify. [E: 1.0/T: 1.5]

b) Determine the critical activities and indicate the critical path(s). Justify. [E: 1.5/T: 2.5]

c) There are 20 workers daily assigned to this project. For each activity, the per day required number of workers is as follows:

Apply the SGS-Parallel heuristic to determine a feasible schedule. Consider the longest duration as priority rule, and to break ties the smallest number of workers per day. Also indicate the schedule and its respective duration. [E: 2.25/T: 4.0]

d) Write down a Linear Programming formulation for the following situation:

Suppose one wants to reduce the total direct cost of this project while maintaining its minimum duration. It is possible to reduce direct costs by increasing the duration of activities E and F according to the following information:

· increasing the duration of activity E by 1, 2 or 3 days represents a cost saving of respectively 25 c.u., 45 c.u., and 60 c.u.;

· for activity F, cost savings are 30 c.u. and 50 c.u. respectively for increasing its duration by 1 or 2 days.

The Linear Programming formulation aims to obtain the schedule that maximizes the total saving. [E: 1.75/T: 3.0]

5. [E/T] 运筹学考试代写

The OptFin enterprise needs to pay 300 c.u., 900 c.u. and 200 c.u. to suppliers A, B and C, respectively. Currently the enterprise has two bank accounts, one at bank X and the other at bank Y, with available funds of 1000 c.u and 700 c.u., respectively. This payment will be done by transferring money directly from the bank accounts of the enterprise to the bank accounts of suppliers (bank-to-bank transfer). Banks charge fees to these transfers that are proportional to the amount to be transferred, and accordingly with the rates shown in the table below:

The payment to each supplier may be split among the bank accounts of OptFin. The OptFin wants to minimize the amount by which it will be charged by the banks.

a) Indicate which network problem could be used to determine the optimal bank transfer plan and draw the corresponding network. Provide all the necessary justifications. [E: 2.25/T: 3.5]

b) New rules for bank-to-bank transfers have to be applied. More precisely: 1) from its account on bank X OptFin is not allowed to transfer amounts that exceed 500 c.u. for each of the suppliers; and 2) for bank transfers greater than 300 c.u., bank Y will charge plus 0,5% over the exceeding amount. How to incorporate these new conditions on the previous network? Provide all the justifications and, if applied, draw a new network and identify the problem. [E: 1.75/T: 3.0]

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