As for single-product deliveries, the total cost of the system consists of the cost of placing orders, maintaining stock and losses due to shortages.
Total costs of placing an order:
?i Ki = K0(1+ ?· N) , (4-23)
where K0 is the cost that does not depend on the number of simultaneously ordered products and the size of the delivery batch;
? – the share of costs, taking into account the placement of an order for each I product;
N is the number of products.
The right part of the formula (4-23) is used to calculate the optimal delivery kit. If the optimal batches of starting parts into production manufactured on the same equipment are calculated, then the left part of the formula (4-23) is used, where Ki is the cost of adjustments. Moreover, Ki does not depend on the sequence of launching parts into production. The period of renewal of orders is the same for all simultaneously ordered N products.
For the unit costs of the system, taking into account the intensity of income and losses from the deficit (i.e. taking into account unmet requirements), the formula is valid:
Lud = 1/ ?c· ?i Ki+0,5· ?c·? i[(1-νi / λ i)/(1+ S i / d i)] (4-24)
Taking the partial derivative and equating to zero ? Lud/? ?c=0, we get:
?c* = ?2· ?i Ki / [?i(S i·νi·( 1-νi / λ i)/(1+ S i / d i))] (4-25)
Then you can find the optimal batch sizes for starting parts into production from the formula:
qi* = ν i · ?c* (4-26)
The optimal value of unit costs, taking into account (4-24), will be:
Lude * = ?2· ?i Ki · [?i(S i·νi·( 1-νi / λ i)/(1+ S i / d i))] (4-27)
Minimization of costs from readjustments is achieved from the condition:
?i=1N(νi / λ i)?1 (4-28)
In general, the resource constraint can be reflected in the formula:
?i aij · qi ? Aj, j=1,n (4-29)
where aij is the consumption of the corresponding resource per unit of output;
Aj – the value of the restriction by type of resource (standard).
If the condition (4-29) is not met, a new value of the optimal period of release of parts or delivery batch from the condition is calculated:
?*= min{?/(?i ? i ·νi), A/(?i ? i ·νi)} (4-30),
where, for example, the first restriction refers to warehouse space and the second to working capital. And, further, all the parameters of the system are recalculated anew.