JP2002244718A - Optimum production method for repairing parts - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an optimum production method for repairing parts capable of determining an optimum production lot number by considering manufacturing setup cost. SOLUTION: In this method, a production lot number L and the stock period T are determined so that stock storage cost N (T)×z based on a demand number of the repairing parts determined by multiplying a total cumulative number N (T) in the stock period T of the repairing parts of an estimated demand number (a) and annual storage cost Z per each part may be equal to the manufacturing setup cost y required for manufacturing of one time.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a method for optimally producing a repair part.

[0002]

2. Description of the Related Art Generally, if all parts or products are to be covered by inventory, a huge inventory storage cost will be incurred. Therefore, in order to maintain an appropriate inventory, if the inventory falls below a certain limit, a predetermined number of parts or products must be manufactured. Was manufactured for the amount shipped to.

However, since the number of repair parts used in products whose mass production has been completed decreases over time, the above-mentioned production method requires more inventory as time passes, and inventory storage costs become unnecessarily large.

[0004] Therefore, for the repair parts, a method of producing the order quantity as the production lot number according to the order,
In general, a method of empirically producing a large amount in consideration of a decrease in demand has been performed.

[0005]

However, in the method of producing the number of orders as it is as the number of production lots, since the number of orders is small, the work is troublesome, and the production setup costs (mold transportation costs, etc.) are reduced. Is required every time, so that the cost increases.

[0006] In addition, a method of empirically manufacturing a large number of parts in consideration of a decrease in demand, but there is no clear standard, so there is a difference between people, and repair parts that are overmanufactured are kept in stock forever. It costs money.

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and an object of the present invention is to provide an optimal production method of a repair part capable of determining an optimal number of production lots in consideration of production setup costs. It is in.

[0008]

SUMMARY OF THE INVENTION In order to achieve the above-mentioned object, the present invention provides a method for producing a spare part in such a manner that an inventory storage cost based on a demand number of repair parts is equal to a production setup cost required for one production. The optimal production method for repair parts that determines the number of lots and their stock period was determined.

[0009] The total production cost of the repair parts includes production costs such as material costs and processing costs, production setup costs such as mold transportation costs, mold maintenance costs, mold setup costs, component transportation costs, and storage of parts. It is the sum of inventory storage costs, which are costs.

[0010] The manufacturing cost is a cost irrespective of the number of manufacturing times, whereas the manufacturing setup cost is a fixed amount of cost for each manufacturing, and therefore increases in proportion to the number of manufacturing times. . In addition, the stock keeping cost is a cost proportional to the number of stocks. Therefore, the cost can be reduced by increasing the number of productions and keeping the number of stocks small each time.

[0011] The sum of the production setup cost that increases according to the number of production times and the inventory storage cost that decreases is the minimum when the number of production times at which the production setup cost equals the inventory storage cost (see FIG. 1). .

Therefore, the number of production lots and the stock period are determined so that the inventory storage cost based on the demand number of the repair parts becomes equal to the production setup cost required for one production.
Regardless of the number of productions, the accumulation of the stock keeping cost and the accumulation of the production setup cost are equal, and therefore, the total production cost of the repair parts obtained by adding the production cost to them can be minimized.

According to a second aspect of the present invention, there is provided an inventory accumulation function representing a temporal change of the accumulated number of inventory when only the inventory is required based on the expected annual number of repair parts, and integrating the inventory accumulation function with the inventory period integration. The total cumulative number of repair parts of the expected demand number obtained by subtracting the total cumulative number obtained by integrating the cumulative number of inventory after the inventory period from the total cumulative number of inventory after the inventory period is obtained, The inventory storage cost is calculated by multiplying the annual storage cost per piece to calculate an inventory period in which the inventory storage cost is equal to the production setup cost required for one production of the repair parts of the expected demand. ,
An optimal production method for repair parts, wherein a reduction in inventory during the inventory period is determined as an optimal number of production lots based on the inventory accumulation function.

An inventory storage cost of the repair parts of the expected demand is calculated based on the stock accumulation function obtained from the annual expected demand of the repair parts, and an inventory period in which the inventory storage cost is equal to the production setup cost required for one production. Is calculated, and the reduction in inventory during this inventory period is set as the optimal number of production lots, so that the total production cost of the repair parts can be minimized.

According to a third aspect of the present invention, in the method for optimum production of repair parts according to the second aspect, the stock accumulation function is:
One year later, it is an exponential function in which the cumulative number of stocks decreases by the expected annual demand.

[0016] The inventory accumulation function in the case where it is assumed that only the inventory can be covered based on the expected annual number of repair parts in which the number of demands decreases with time, an index function is used in which the decrease in the number of inventory after one year is calculated as the expected annual number of demands. Since it attenuates dynamically, it is possible to derive the optimum number of production lots in accordance with reality.

According to a fourth aspect of the present invention, in the repair part optimum production method according to the third aspect, the stock accumulation change function is an exponential function having a base of 0.6.

As the inventory accumulation function, an exponential function having a base of approximately 0.6 is more realistic.

According to a fifth aspect of the present invention, in the repair part optimum production method according to the second aspect, the stock accumulation function is:
One year later, it is obtained as a linear function in which the cumulative number of stocks decreases by the annual expected demand number.

The calculation can be simplified by making the stock accumulation function a linear function.

[0021]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The total production cost of a repair part is, as described above, a production cost X such as a material cost and a processing cost, a mold transportation cost, a mold maintenance cost, a mold setup cost, a component transportation cost, and the like. Is the total X + Y + Z of the manufacturing setup cost Y and the stock storage cost Z, which is the cost of storing parts.

The production setup cost Y is a fixed amount of cost y that is required for each production, and therefore increases in proportion to the number of productions k. Alternatively, the cost is proportional to the stock quantity. Therefore, the cost can be reduced by increasing the number of productions k to keep the stock quantity small each time.

Manufacturing setup cost Y based on the number of productions k
FIG. 1 shows a graph of the change of the stock keeping cost Z. The production setup cost Y increases linearly with the gradient y with respect to the number of productions k, and the inventory storage cost Z increases with respect to the number of productions k.
It decreases exponentially in proportion to 1 / k.

The total cost Y + Z of the production setup cost Y and the inventory storage cost Z is a downwardly convex curve as shown in FIG. 1 and has a minimum value. The minimum value is the production setup cost Y and the inventory storage cost. This is the case of the number of productions at which the cost Z is equal. Since the manufacturing cost X is a cost regardless of the number of manufacturing times,
The total production cost X + Y + Z also shows the lowest value when the number of productions at which the production setup cost Y and the inventory storage cost Z are equal.

An embodiment according to the present invention will be described below with reference to FIGS. The optimal production method of the repair part according to the present embodiment is to determine the optimal production lot number at which the production setup cost Y and the inventory storage cost Z, which can suppress the total production cost X + Y + Z to the minimum value, are equal.

This repair part is an automobile part whose demand decreases with time, and FIG. 2 shows the procedure for calculating the optimum production lot number of this repair part. First, an expected demand number a for estimating the annual demand number of the repair part is set (step 1).

In step 2, the annual storage cost z per piece of the repair part is calculated. The annual storage cost z per piece is
It is calculated from the cost map per unit volume for each storage area warehouse and the size of the repair parts.

In step 3, manufacturing setup cost y per operation
Is calculated. The production setup cost y per time includes the mold transportation cost, the mold maintenance cost, the mold setup cost,
It is calculated from each map such as parts transportation cost.

Then, in step 4, an inventory accumulation function F (t) representing a change over time of the inventory accumulation number when it is assumed that only the inventory can cover the expected demand a is determined. The cumulative number of stocks generally decreases exponentially, and as an exponential function at this time, an exponential function 0.6 ^t with a base of 0.6 is empirically observed as a function of yearly (t) unit aging. .

The number of shipments is also an exponential function of 0.6
decreases along ^t . Therefore the expected demand number a is initially shipped expected number is set (step 1), the change in shipments becomes a · 0.6 ^t (see FIG. 3).

In step 4, the expected demand number a is obtained one year later.
To find the stock accumulation function F (t) that decreases. That is, F (t)
= A 0.6^tAnd find A from F (0) -F (1) = a
And A = 2.5a, so that F (t) = A · 0.6^t= 2.5a ・
0.6^tIs determined. FIG. 3 shows the elapsed year t (year) on the horizontal axis,
The vertical axis is a graph with the number of parts n (pieces), where n = F (t)
= 2.5a ・ 0.6^tExponential curve shows the change in cumulative inventory,
n = a · 0.6 ^tIndicates the change in the number of shipments.

Next, in step 5, the total cumulative number N (T) of the repair parts having the expected demand number a in the stock period T is obtained. The total cumulative number N (T) corresponds to the area of the hatched portion up to year T in FIG.

Therefore, the inventory period (T years) is calculated from the total cumulative number obtained by integrating the inventory accumulation function F (t) over the inventory period T years.
The total cumulative number N (T) in the inventory period T of the repair part having the expected demand number a is subtracted by subtracting the total cumulative number obtained by integrating the subsequent cumulative number F (T) over the inventory period T years.

That is,

(Equation 1) It is.

By multiplying the total cumulative number N (T) by the annual storage cost z per piece of the repair part calculated in step 2, the stock storage cost of the repair part having the expected demand number a for T years is obtained. (Step 6).

In the next step 7, this inventory storage cost N
An inventory period T in which (T) × z is equal to the production setup cost y per operation calculated in step 3 is obtained. That is, T is obtained by solving N (T) × z = y.

When the stock period T is obtained, the accumulated number of stocks reduced during this period becomes the number of production lots L. In step 8, the optimum number of production lots L is calculated from F (0) -F (T). ing.

The optimum production lot number L calculated in this way is to make the inventory storage cost N (T) × z in the inventory period T equal to the production setup cost y required for one production. By performing production according to the optimal production lot number calculated by the same method in the subsequent production, the inventory storage cost and the production setup cost y are equal each time. And the above logic minimizes the total cost of repair parts.

The following is an example in which actual numerical values are entered. It is assumed that the annual expected demand number (expected shipping number) a of a certain repair part is set to 1000 (step 1). And one of the repair parts
It is assumed that the annual storage cost z per unit is calculated as 4,260 yen (step 2), and the manufacturing setup cost y per operation is calculated as 104,580 yen (step 3).

The only number 1000 expected demand after one year reduced inventory accumulation function F (t) is, F (t) = 2.5a · 0.6 t = 2.5 × 1000 × 0.6 t = 2,500 × 0.6 from step 4
^t . The stock accumulation function F (t) shows a curve that decreases exponentially from 2500 parts as shown in FIG.

Inventory period T of repair parts with the expected number of demand of 1000
Is N (T) = 2,500 × {(0.6 ^T −1) / ln 0.6−0.6 ^T · T} in step 5, and the inventory storage cost for the inventory period T is N (T) × z =
N (T) × 4,260 (yen) (step 6).

Therefore, in step 7, this inventory storage cost N
(T) × 4,260 (yen) for the production setup cost of 104,580 yen
When the inventory period T is calculated from N (T) × 4,260 = 104,580 under the condition of a circle, T = 0.2029 (year) is calculated.

The cumulative number of stocks after the stock period of 0.2029 years has elapsed is F (0.2029) = 2,253.8 (pieces), and initially F (0) = 2,500.
F (0) -F (0.2029) = 246.2 (pieces) less than (pieces), and this 246.2 pieces are rounded off to obtain 246 pieces as the optimum production lot number L. That is, by setting the number of production lots of the repair parts for about 0.2 years to 246, the stock keeping cost and the cost of one production setup can be made equal.

Next, in order to obtain the optimum number of production lots for the second time about 0.2029 years later, first, the change in the number of shipments n = 1000 × 0.6 ^t
From the estimated demand number a. That is, t = 0.2029 is substituted and 1000 × 0.6 ^0.2029 = 901.5 pieces are set as the expected demand number a, and the stock period T and the optimum production lot number L are obtained based on the expected demand number 901.5 by the same procedure as described above.

As a result of the calculation, the optimal production lot number is 233.5 in a stock period of 0.2141 years. The third time in the same way,
The results of calculating the inventory periods and the optimal number of production lots for the fourth time,..., Are shown on the graph of FIG. 4 and partially shown in the table of FIG.

In the graph of FIG. 4, n = F (t) = 2.5a
-The height of the substantially triangular portion hatched along 0.6 ^t corresponds to the optimum number of production lots for each time. The first optimal production lot number of 246 is produced in 0 years, the second optimal production lot number of 234 is produced in 0.2029 years, the third optimal production lot number of 221 is produced in 0.4170 years, and so on. Produced and shipped sequentially, inventory is decreasing. As shown in the table of FIG. 5, the inventory storage cost and the production setup cost are equal every time.

As described above, if the annual storage cost z per unit and the manufacturing setup cost y per unit for a certain repair part are determined, the optimum production lot number L is calculated based only on the expected annual demand number a. FIG. 6 shows the optimum production lot number L for the representative example of the expected annual demand number a in the above example.

The optimum number L of production lots shown here is only a guide, and actually varies slightly depending on other factors such as storage conditions such as how many units are convenient for storage.

In the above embodiment, the stock accumulation function F (t)
The actually conformity was calculated expressed in 2.5a · 0.6 ^t and exponentially, which can also be represented by a linear function (straight line) per year, as shown in FIG. 7, calculation is simplified .

Assuming that the expected number of demands per year is a, the inventory accumulation function F (t) until one year elapses becomes F (t) = − at · t + c assuming that the inventory accumulation number decreases by a after one year. Can be expressed.
The total cumulative number N (T) of the repair parts with the expected demand number a in the stock period T is the area of the triangle indicated by the oblique line in FIG. 7, and N (T) = a · T × T / 2 = a · T the ^2/2.

Therefore, by multiplying the total cumulative number N (T) by the annual storage cost z per piece, the inventory storage cost becomes N (T)
^{× z = a · T 2 ·} z / 2 , and the the at equal production setup cost y of per ^{a · T 2 · z / 2} = Solve y seek inventory period T, T = (2 · y / a · z) ^1/2 .

The optimum number L of production lots corresponds to the height a · T of the triangle indicated by the diagonal lines. Therefore, from the stock period T, the number L of optimum production lots is: L = a · (2 · y / a · z) ) ^1/2 = (2 · a · y /
z) ^1/2 .

As in the case of the above embodiment, the annual storage cost z per unit of the repair part is 4,260 yen, the production setup cost y per unit is 104,580 yen, and the expected demand number a
Is 1000, the optimal production lot number L is 22
It is calculated as two.

The above formula of the optimum production lot number L is obtained by substituting the annual storage cost of 4,260 yen and the production setup cost of 104,580 yen, and leaving only the expected demand number a as a variable. L = 7 · a ^1/2 When the expected demand number a is set, the optimum production lot number L can be easily obtained.

The table of FIG. 6 also shows, for reference, the optimum production lot number L for a typical example of the expected annual demand number a when the stock accumulation function F (t) is a linear function. As described above, if the stock accumulation function F (t) is a linear function, the calculation is greatly reduced.

[Brief description of the drawings]

FIG. 1 is a graph showing changes in a production setup cost Y, an inventory storage cost Z, and a total thereof with respect to the number of productions k.

FIG. 2 is a flowchart showing a procedure for calculating an optimum number of production lots according to one embodiment of the present invention.

FIG. 3 is a graph showing changes in an inventory accumulation function of an exponential function and the number of shipments.

FIG. 4 is a graph showing a change in the stock accumulation function and the number of shipments in an example in which actual numerical values are entered.

FIG. 5 is a table showing calculation results in the same example.

FIG. 6 is a table showing an optimum production lot number L for a representative example of an expected annual demand number a.

FIG. 7 is a graph showing changes in a stock accumulation function of a linear function and the number of shipments according to another embodiment.

[Explanation of symbols]

X: production cost, Y: production setup cost, Z: inventory storage cost, k: number of productions, a: expected demand number, y: production setup cost per operation, z: annual storage cost per unit, F ( t)…
Inventory cumulative function, T: inventory period, N (T): total cumulative number, L
… Optimal production lot number.

Claims (5)

[Claims] 1. The optimal production of repair parts, wherein the number of production lots and the stock period are determined so that the stock keeping cost based on the demand number of the repair parts becomes equal to the production setup cost required for one production. Method. 2. An inventory accumulation function representing a change over time in the cumulative number of inventory when only the inventory is to be used based on the expected annual number of repair parts, and calculating the inventory from the total cumulative number obtained by integrating the inventory cumulative function over the inventory period. Obtain the total cumulative number of repair parts of the expected demand number by subtracting the cumulative total number obtained by integrating the cumulative number of stocks after the period for the inventory period, and store the total cumulative number of repair parts of the expected demand number per year for each repair part. Multiplying the cost to obtain an inventory storage cost, calculating an inventory period in which the inventory storage cost is equal to a production setup cost required for one production of the repair parts of the expected number of demands; An optimal production method for repair parts, wherein a reduction in inventory during the inventory period is determined as an optimal number of production lots. 3. The method according to claim 2, wherein the inventory accumulation function is an exponential function in which the inventory accumulation number decreases by the annual expected demand number one year later. 4. The optimum production method of a repair part according to claim 3, wherein the stock accumulation change function is an exponential function with a bottom being 0.6. 5. The method according to claim 2, wherein the stock accumulation function is obtained as a linear function in which the stock accumulation number decreases by the annual expected demand number one year later.