Читать книгу Mathematics in Computational Science and Engineering - Группа авторов - Страница 25

This model is the same as fixed setup cost for buying any units to renew Stock at start of period, say K, is related buy or making things in a given timeframe or cost of assembling. Leave I alone the Inventory stage toward the start of the level infers that a request size (Q-I) thing can be set to pass on the available Inventory up to Q. Hence, the anticipated cost transforms into,

(1.7)

The optimal value of Q says Q* that minimizes TEC₁ (Q)) is given by

(1.8)

where

Since K is constant, minimum value of TEC’ (Q) ought to additionally accept via the same condition as given in equation

(1.9)

Since K is constant, minimum value of

And consequently Q* can even decrease TEC (Q).

Let us present two new control factors S and s, where S represents the extreme Stock stage and s signifies the reordered stage that is while the Stock degree tumbles to s, a request is situated to bring the Stock of Inventory items up to S.

Thus, value of S= Q* and the price of s is determined by the relationship

(1.10)

As I the fundamental Inventory prior to starting the period, at that point to decide the request size to bring the available Inventory of articles as much as Q*, the ensuing three occasions might be examined.

Case 1: If we start the length with I unit of Inventory and do not now buy or produce more prominent, at that point TEC (I) is the foreseen cost. In any case, on the off chance that we expect to purchase extra (Q-I) units in the event that you need to convey Inventory stage as much as Q*, at that point TEC’ (Q*) will include the set-up expense furthermore. Subsequently, for all I<s, the condition for requesting is

(1.11)

That is, while Inventory stage arrives at S=Q*, request for Q-I units of Inventory might be put.

Case 2: For this situation, if I<Q, the request size is controlled by the condition

(1.12)

This implies that no ordering substantially less costly than ordering. Thus Q*=I.

Case 3: If Q>I, at that point foreseen cost for a request up to Q could be extra than generally speaking foreseen cost if no structure is found, that is

(1.13)

Consequently, it is better not to put request for acquirement of things and afterward Q*=I.