Of flexible manufacturing systems.

Bojan, Ioan

Abstract: Setting up a flexible manufacturing system (FMS) resembles to the manufacturing assimilation of a new product, particularly of a machine-tool. Consequently, the function of annual expenses for exploiting the machine-tools may be adjusted to calculate the annual expenses of the FMS. In order to determinate the economic flexibility of the FMS, the most important expenses will be expressed according to the number of different types of work pieces that must be machined.

Key words: flexibility, optimization, flexible manufacturing systems, exploitation expenses

1. INTRODUCTION

The flexibility of the manufacturing system, given by the number of different types of work pieces that it manufactures, is one of the technical factors that influence the system exploitation expenses. The increase of flexibility determines a good usage of technological, manipulation and transport equipment, though it also has unfavorable economic consequences.

Based on the reference material (Abrudan, 1996; Templemaier & Kuhn, 1993), we have developed a method for determining the economic flexibility of the FMS.

2. COMPUTATION OF THE FMS ECONOMIC FLEXIBILITY

The design of FMS must be preceded by the optimization of the flexibility-exploitation relation.

We consider that the decision of acquiring a FMS can be compared with the decision of the introduction of a new product (a new machine-tool) into fabrication. So, in order to determine the expenses for the certain objective, we can make an analogy between our expenses and the function of exploitation expenses for machines-tools (Stancioiu, 1974).

C = M+S+E+[C.sub.SDV]+[A.sub.1]+[A.sub.2]+R+[C.sub.C]+D [euro/piece] (1)

where:

M--average cost of work pieces material;

S--manual labor expenses (direct workers gross salary);

E--energy cost of machine-tool;

[C.sub.SDV]--expenses with the tools of machine;

[A.sub.1]--annual ratio of machine amortization;

[A.sub.2]--annual ratio of building amortization;

R--reparation and maintenance cost of machine-tool

[C.sub.c]--constant conventional expenses

D--tax for immobilization assets usage (tax for buildings and ground)

For the flexibility optimization of FMS, we will consider the basic expenses for which the volume is conditioned by the number of types of work pieces that can be manufactured.

In the field of FMS, the first and second elements from formula (1) have the following significance:

M--expenses for the immobilization of current assets; S--expenses for the adjustment of the system in view of the adaptation to the manufacturing of another type of piece.

If we don't have enough elements for determining the CSDV, we can turn to the references (Trandafir, 1992). These show the CSDV to represent 40% from the price of FMS.

After establishing the optimal configuration for FMS, following the desired criteria, we can estimate:

--the expenses for whole system;

--the reparation expenses;

--the expenses with the building regarding the system;

--the number of adjustments for each variant;

--the necessary time for adjustments in view of the system adaptation to the manufacturing of each type of piece;

--the waiting time in manufacturing for each type of part. Based on these estimations, we can determine the analytic expressions of the function components.

The amortization expenses for the equipment of FMS:

[A.sub.1] = [P.sub.s] / [t.sub.su] [s.summation of (i=1)] [N.sub.i] [euro / piece] (2) where:

[P.sub.s]--estimated price of the system, designed for the manufacturing of "s" types of work pieces, Euro;

[t.sub.su]--working duration of FMS, years;

[N.sub.i]--number of work pieces from type "i", annually manufactured, pieces/year;

S--number of types of work pieces manufactured in the system.

Similarly, we can determine the expenses with the building amortization.

The expenses with the adjustment of the system in order to adapt to the manufacturing of other type of piece, S:

S = [r.sup.*.sub.h][m.sup.*][sup.*]n [s.summation over (i=1)] [t.sub.pii] / [s.summation of (i=1)] [N.sub.i] [euro / piece] (3)

where:

[r.sub.h]--average salary/hour for workers;

m--number of adjustment workers;

n--number of plan periods of a year;

[t.sub.pii]--the necessary time for the adjustment of the system in view of its adaptation to the manufacturing the "i"-type of work piece, hours (it includes the duration of mechanic adjustments, software tests etc.).

In order to simplify the computing of the expenses with the current assets immobilization, M, the losses caused by the immobilization during the manufacturing cycle of each type of work piece and in the time interval between the moment of the end of the manufacturing and the moment of the usage of the work pieces at the fitting are neglected. If during the year we have "n" planning periods, in each period one lot from each work piece is launched, the lots of each piece having the same quantity in each period and the launching order being the same for each period, then these expenses are computed with the following formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

where:

[[epsilon].sub.n]--economic efficiency coefficient - it expresses the minimum limit of income for each Euro expensed;

[f.sub.n]--annual nominal time fund, hours/year;

[C.sub.semi]--cost of work part, Euro/piece;

[T.sub.ci]--manufacturing cycle for one lot of "i" pieces, hours.

If not all semi finished parts are obtained at the beginning of the manufacturing interval, the immobilization durations will be taken into consideration with the particular value of each type of piece; in this case, the formula becomes:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where:

[d.sub.i]--the duration of immobilization for current assets of work piece "i"

The reparation expenses R are determined taking into consideration the structure of the equipment reparation cycle and the cost expressed in % of the different types of reparations from the replacing value (Ceausu, 1980):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

where:

[VI.sub.j]--replacing value of the equipment "j";

[PRT.sub.j]--technical revision expense (%) from the replacing value of equipment "j";

PRC[1.sub.j]--current reparation I degree expense (%) from the replacing value of equipment "j";

PRC[2.sub.j]--current reparation II degree expense (%) from the replacing value of equipment "j";

[PRK.sub.j] - capital reparation expense (%) from the replacing value of equipment "j";

[n.sub.RTj]--number of the technical revision of the equipment "j" /life duration of FMS;

[n.sub.RC1j]--number of current reparations of I degree of the equipment "j" /life duration of FMS;

[n.sub.RC2j]--number of current reparations of II degree of the equipment "j" /life duration of FMS;

[n.sub.RKj]--number of capital reparations of the equipment "j" /life duration of FMS.

The other elements of expenses from formula (1) are negligible.

In the function of expenses the value "s" does not appear directly; it appears only through the expenses elements. To determine the flexibility degree of the system for which the expenses are minimal, we compute the values of the function C in some points corresponding to different types of pieces.

3. CONCLUSIONS

The method and the algorithm (Fig. 1) for the determination of the optimal level of the FMS flexibility are operational because the "s" variable is limited. The number of types of work pieces which will be manufactured in the system have a variation range that can be estimated (Fig.2.).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

4. REFERENCES

Abrudan, I. (1996). Flexible Manufacturing Systems, Ed. Dacia, ISBN 973-35-0568-4, Cluj-Napoca, Romania

Ceausu, I. (1980). Management of the Maintenance and Reparations Activities, Ed. Tehnica, Bucuresti, Romania

Stancioiu I. (1974). Economic Efficiency of New Machines, Ed. Tehnica, Bucuresti, Romania

Trandafir, M. (1992). Automation of Production Processes. Technological Elements, OID, ICM, Bucuresti, Romania

Templemaier, H., Kuhn, H. (1993). Flexible Manufacturing Systems, John Wiley & Sons Inc., ISBN 0-471-30721-1, New York