Operations Research in Economics IO Code 00
Replenishment date: 07.02.2012
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Question 1. What are the stages in the development of operations research as a science.
Question 2. Name the sciences on which operations research is based and where it is used.
Question 3. Briefly describe the distinguishing features of operations research.
Question 4. What classes of problems are considered in operations research.
Question 5. What mathematical methods are used to numerically substantiate management decisions?
Question 6. For the production of two types of products A and B are used three types of raw materials.
For the production of a unit of product A, it is required to spend 13 kg of raw materials of the first type, 32 kg of raw materials of the second type, 58 kg of raw materials of the third type. The production of unit B requires raw materials, respectively, 24 kg, 32 kg and 29 kg.
The production is provided with raw materials of the first type in the amount of 312 kg, raw materials of the second type - 480 kg, raw materials of the third type - 696 kg.
Profit from the sale of a unit of finished product A is 4 us. units, and products B - 3 us. units
It is required to draw up an optimal production plan for products A and B, ensuring the maximum profit from their sale, if it is planned in advance to manufacture at least 10 units of products A and B.
1. Formulate a mathematical model of a linear programming problem for a given condition.
2. Is it an integer programming problem? Why?
3. Solve the given problem by any method known to you.
4. Give a verbal answer to the question: "At what output of products A and B will the profit of the enterprise be the greatest?"
Question 7. The procurement shop supplies the assembly shop with parts of two types A and B. According to the contract between the shops, two delivery times for these parts are stipulated daily, and when the parts A are delivered in the first term, the assembly shop pays a procurement bonus of 50 rubles. When product A is delivered, a premium of 20 rubles is paid in the second line. When product B is delivered in the first term, the premium is 30 rubles, and in the second - 40 rubles. It is required to determine the optimal plan for the supply and receipt of parts.
1. Conditionally take the procurement shop for player A, the assembly shop for player B and make up the game matrix.
2. Is this task solvable in "pure strategies", why?
3. Solve this problem in mixed strategies.
4. Give a verbal answer to the question: "What is the optimal plan for the supply of parts, and what guaranteed bonus will the procurement shop receive?"
Question 8. At a garment factory, the fabric must pass through a conveyor belt through 3 blocks with operations: painting, drawing and cutting. During one work shift, three types of fabrics must pass through the conveyor (conventionally A, B and C). The time required to process tissue at each operation is shown in the table.
Determine in which order the worker needs to pass the fabric down the conveyor. Use the Gantt chart to solve. Determine the optimal order for the fabrics to pass the conveyor blocks in terms of time and equipment downtime.
Fabric type A Fabric type B Fabric type C
Painting 2 h. 1 h. 2 h.
Rolling pattern 3 h. 3 h. 1 h.
cut 1 h. 3 h. 2 h.
Question 2. Name the sciences on which operations research is based and where it is used.
Question 3. Briefly describe the distinguishing features of operations research.
Question 4. What classes of problems are considered in operations research.
Question 5. What mathematical methods are used to numerically substantiate management decisions?
Question 6. For the production of two types of products A and B are used three types of raw materials.
For the production of a unit of product A, it is required to spend 13 kg of raw materials of the first type, 32 kg of raw materials of the second type, 58 kg of raw materials of the third type. The production of unit B requires raw materials, respectively, 24 kg, 32 kg and 29 kg.
The production is provided with raw materials of the first type in the amount of 312 kg, raw materials of the second type - 480 kg, raw materials of the third type - 696 kg.
Profit from the sale of a unit of finished product A is 4 us. units, and products B - 3 us. units
It is required to draw up an optimal production plan for products A and B, ensuring the maximum profit from their sale, if it is planned in advance to manufacture at least 10 units of products A and B.
1. Formulate a mathematical model of a linear programming problem for a given condition.
2. Is it an integer programming problem? Why?
3. Solve the given problem by any method known to you.
4. Give a verbal answer to the question: "At what output of products A and B will the profit of the enterprise be the greatest?"
Question 7. The procurement shop supplies the assembly shop with parts of two types A and B. According to the contract between the shops, two delivery times for these parts are stipulated daily, and when the parts A are delivered in the first term, the assembly shop pays a procurement bonus of 50 rubles. When product A is delivered, a premium of 20 rubles is paid in the second line. When product B is delivered in the first term, the premium is 30 rubles, and in the second - 40 rubles. It is required to determine the optimal plan for the supply and receipt of parts.
1. Conditionally take the procurement shop for player A, the assembly shop for player B and make up the game matrix.
2. Is this task solvable in "pure strategies", why?
3. Solve this problem in mixed strategies.
4. Give a verbal answer to the question: "What is the optimal plan for the supply of parts, and what guaranteed bonus will the procurement shop receive?"
Question 8. At a garment factory, the fabric must pass through a conveyor belt through 3 blocks with operations: painting, drawing and cutting. During one work shift, three types of fabrics must pass through the conveyor (conventionally A, B and C). The time required to process tissue at each operation is shown in the table.
Determine in which order the worker needs to pass the fabric down the conveyor. Use the Gantt chart to solve. Determine the optimal order for the fabrics to pass the conveyor blocks in terms of time and equipment downtime.
Fabric type A Fabric type B Fabric type C
Painting 2 h. 1 h. 2 h.
Rolling pattern 3 h. 3 h. 1 h.
cut 1 h. 3 h. 2 h.