Mathematical models in economics and management. Topic 3

Transportation problems and tasks assignment

Task 1.
In this model, presented the task of delivery of goods from three plants to five regional warehouses. Goods can be delivered from any plant to any warehouse, production capacity are in line shipments and warehouse needs - in line with the appropriate name. Model unbalanced because deliveries ahead needs warehouses. Table of cost of transportation of goods between factories and warehouses (thous. Rub.) Is given below.
Find shipments from each plant to each warehouse, optimizing transportation costs. Consider the situation when shipped from the factory in Ukraine proved to be impossible. How to pose the problem in this case?

Task 2.
Companies need to send salespeople to new markets. There are three vacancies and four candidates. The result of the appointment of the candidate to a position determined by the expected increase in profit. Profit, which can give a candidate working on a given territory, is shown in the table.
The company is interested in maximizing the total profit. Requires create optimal distribution plan salesmen in the territories.

The task of inventory management

Small company produces complete sets of furniture for living rooms. Monthly data on the production of complete sets of furniture are presented in the table.
Manager of the enterprise is required to make optimal plan furniture by months, if the initial supply of 15 sets of furniture.
1) Create a mathematical model of the problem.
2) Create a table model and verify that the table model corresponds to a mathematical model.
3) Enter the required data into the Solver.
4) Using a sustainability report, answer the following questions:
a) change as the total cost for a production in March will be more on one set, compared with the optimum?
b) If the production capacity will help in March to produce 65 sets of furniture, how this will change in the total value of production and storage?

Decision making under uncertainty

The company, which produces washing powder, working in conditions of free competition. The powder is manufactured units, and the price per unit in the next month is uncertain 10 th. Rub. with a probability of 0.3; 15 thousand. Rub. with a probability of 0.5; 20 thousand. Rub. with probability 0.2. The total costs of production of detergent blocks are determined by the function cost (thous. Rub.). Determine the daily output of the company in the blocks in which the average income is highest. Try to estimate the maximum price that can be offered for the exact knowledge of the state of nature (price per unit).