Determination of optimal parameters of the inventory management system

Let’s apply the inventory management model discussed in 4.1 to a specific example, which is as follows: three types of semi-finished products are produced on the same equipment.

The object of modeling is a warehouse of finished products, a system for managing the movement of stocks, taking into account restrictions on warehouse space and working capital.

Problem situation – determination of the optimal values of the batch of delivery of semi-finished products, their maximum stock level, production time, deficit-free and scarce operation of the inventory management system for each type of semi-finished products under given conditions.

Observed parameters:

the cost of adjustments of Ki equipment [d. units], which does not depend on the order of release of semi-finished products, which are then sent to nearby warehouses with a total area of F = 300 m?; the cost of maintaining a unit of stock of semi-finished products Si
[den. units/ (unit p/fabr.: ed. time)]; λi rate of arrival  [ unit p/factory: (unit time) ]; velocity of expenditure Vi [ unit n/factory: (unit time) ]; standards for warehouses fi [ m/(unit p/factory) ]; standards for working capital αi  [ d. units / units p / fabr.]; losses from deficiency di [ d.u./(unit p/fabr.:ed. time) ]; the amount of working capital should not exceed the value; A0 = 20000 [ di. units].

Unobservable parameters:

batches of delivery of semi-finished products Qi* ; maximum level of stocks of semi-finished products Yi* ; production time of semi-finished products ?pri*; time of stock formation ?i1*; time to eliminate the deficit ?i4*; the time of expenditure of the stock ?i2*; Hi* deficit-free operation time; operating time in the presence of a deficiency of Ni* for each type of semi-finished product.

Adequacy – compliance with the estimated and actual parameters of the inventory management system.

Mathematical apparatus – differential calculus, partial derivatives, algebraic equations.

The result of the simulation is the organization of the optimal inventory management system; optimal values of the batch of delivery of semi-finished products qi*, the maximum level of stocks of semi-finished products Yi*; production time of semi-finished products ?pri*; time of stock formation ?i1*; time to eliminate the deficit ?i4*; the time of expenditure of the stock ?i2*; Hi* deficit-free operation time; operating time in the presence of a deficit of Ni* for each type of semi-finished product (Table. 4.1.).

Table 4.1.

Initial data on semi-finished products.

To solve this problem, a model should be used taking into account the unmet requirements of multi-product production.

In this regard, auxiliary data are preliminarily calculated:

Vi/λi ,  Аi=1 – Vi/λi ,  Mi= S i / d i ,  Bi=1 – S i / d i ,  R i = S i· Vi · Ai/Bi

Then the optimal time to resume deliveries:

?c*=?2· ?i Ki / [?i(S i· Vi · Ai / Bi)]

Substituting the numeric values of the original data, we get the values of the auxiliary data (Table. 4.2.).

Table 4.2.

Auxiliary data values

The required optimal parameters of inventory management are calculated using the following formulas:

qi*= Vi ·? c*

?pri*= qi*/λi

?i1*= ?pri*/ Bi

?i4*= ?pri*- ?i1*

?i2*= ?c*· Ai/ Bi     (4-31)

Hi* = ?i1*+ ?i2*

Ni* = Hi*+ Mi

Yi* = qi· (1+ Vi)/λi

Substituting numerical data, we get (Table 4.3.):

Table 4.3.

Optimal parameters of the inventory management system

Let’s check the restrictions:

by warehouses

? F =F/?i fi· Vi,  ? F  = 0.35 times

on working capital

? A= A0/?i αi · Vi,  ? A = 0.53 times

Since ?c* < ? F < ? A, then recalculation of the obtained optimal parameters (Table. 4.3.) is not required.