ISE 421 Operations Research 2 Uncategorized Exam Questions

1. Take the LP model:

   

   Assume that we will apply only one iteration of the revised simplex. Perform the following:

   1. Write the LP model in equation form.
   2. Choose a suitable starting basis.
   3. Compute the reduced costs corresponding to the chosen basis.
   4. Determine the nonbasic variable that will be part of the basis in the following iteration.
   5. Write the new basis.
2. Use the revised simplex method to solve bounded variable LP:

   

3. An LP model with parametric resource availabilities is given by

   

   Obtain the optimal solution for t ≥ 0.

4. Consider the following production planning problem. There are two production lines in a plant; and both lines produce the same product. The production capacity of each line is 3,000 units in one week. Due to high setup costs, the second production line is started only when the first line has reached its capacity. Define the decision variables:

   x₁ : production volume in one week from the first production line
   x₂ : production volume in one week from the second production line

   Write only the constraints that will enforce the production restrictions explained above.

5. Saudi Tables produces three kinds of tables; school tables, four-leg tables, and single-drawer tables. Each kind requires wood, paints, and labor hours for assembly. The requirements for labor hours, wood, and paints are shown in the table below. The unit revenues are also shown.

   Kind	Labor hours	Wood (kg)	Paint (kg)	Unit revenue (riyals)
   School	1.5	2	3	260
   Four-leg	3	3	2	280
   Single-drawer	2	4	2	310

   The available resources are: 900 labor hours; 1,600 kg of wood; and 1,550 kg of paint. Answer the following:

   1. The goals of the company and their priorities are as follows:
      • Priority 1: obtain revenue of at least 105,000 riyals
      • Priority 2: reduce any additional labor hour
      • Priority 3: reduce any additional paint
      • Priority 4: reduce any additional wood
      The industrial engineer needs to plan the production that will meet the goals of the company. Write the preemptive goal model (do not solve) that will give a suitable production mix.
   2. Additional resources can be purchased as follows:
      • labor hour can be purchased by 6 riyals
      • 1 kg of wood can be purchased by 3 riyals
      • 1 kg of paint can be purchased by 2 riyals
      The goals and their priorities are
      • Priority 1: obtain revenue of at least 105,000 riyals
      • Priority 2: reduce any additional labor hour cost
      • Priority 3: reduce any additional paint cost
      • Priority 4: reduce any additional wood cost
      Revise the preemptive goal model in (a) to include these costs.
6. The industrial engineer in the Arab Paper Manufacturing Company (WARAQ) is planning the installation of paper waste gathering system inside the plant. The system consists of a single line conveyor that will connect the six work stations inside the plant to a gathering bin. It has been estimated that the cost of the conveyor gathering system increases linearly with the length of the conveyor. The figure below shows the layout of the plant; and the gathering bin is indicated by the label ‘0’. The distances in meters between the work stations are also shown.

   

   Write the mathematical model that will find the least cost conveyor system.

7. Consider the two-goal model:

   

   If P₁ is more important than P₂, find the efficient solution using the goal simplex.

Instructor: Dr Muhammad Al-Salamah