1. Description of the subject area (4 tasks)

     Sources of income (SI) are here piece goods of different types (cars, electronics, household appliances, furniture, etc.), acquired by a merchant from a wholesaler or a manufacturer for further retail sale.

     We consider four solvable tasks on finding optimal strategies of investing funds in acquisition of such SI from a given set of them, when is maximized a specified quality criterion, which can be:

  • absolute income from the future realization of SI with fixed profitability and excluding a period of their realization (task 1);
  • absolute income or total proceeds from realization of SI with varying profitability (see definit. below), with an account of their realization period (via its limitation or control) and with three possible options of payback factor:
    • without return (task 2);
    • return on investment in absence of initial SI (task 3);
    • return on initial SI cost in absence of investment (task 4).

Definition. Varying profitability is called a property of SI to change their profitability either forced (under some control), or under the influence of some random factors. In our case SI are piece goods, for which only a seller can change their retail prices (profitability), therefore we have here the forced varying profitability.

Note. Return on investment (in absence of initial SI) or return on initial SI cost (in absence of investment) takes place in case when actual proceeds from realization for a specified period of acquired SI will not be less thana returm sum, which is equal to the product of a cost of this SI by a given rate of return.

     The main difference of the task 1 from the group of tasks 2–4 is that for it is considered a simplified case where wholesale and retail prices of all goods are fixed, and the period of their realization is unlimited. In practice, this case occurs very rarely. Much more often we have the following set of conditions, which are specific to the tasks 2–4:

  • purchases of goods from a wholesaler occurs regularly through a specified period of time;
  • purchase price of a certain goods can depend on the size of its batch;
  • selling price of goods can vary by a merchant at his discretion;
  • merchantability of goods is determined by the intensity of entry of requests from potential buyers for acquisition of goods, which directly depends on their costs.

     For tasks 2–4 were introduced the following assumptions, which in practice occur quite often:

  • stream of requests from buyers to purchase goods of a certain type is the simplest (Poisson);
  • by one such request is purchased only one sample of goods.

     Thus, the task 1 is considering simplified variant of the purchase of goods from a wholesaler (a manufacturer) for their subsequent retail sale, and the tasks 2–4 — real variants commonly encountered in practice. At that, it should be borne in mind that for successful solution of the last three tasks you need to know the statistics of selling different types goods in a considered shopping entity, i.e. the intensity of entry of requestsfor goods realization at their different selling prices. The values of these intensities are given in the initial data of a task to be solved.

     All these four tasks on optimizing investments in piece goods are a particular case of the tasks of seven types on optimizing investments in any SI. They can be solved numerically by using the new science-intensive network technology called "Information technology of automation of control of discrete technological and information processes (in short — IT AC DTIP)", because optimizable process has all necessary properties for that. This process is discrete and is classified as an instant process of selecting choices. Its elements in terms of DTIP are:

  • piece goods — demands;
  • amount of investment — a device of service.