Economic Feasibility of Applying Standard Automatic Machine Setups in Small-Batch Production
Abstract Generated abstract
This paper examines the economic rationale for using standard automatic-machine setups in small-batch production, where individualized process planning often discourages the use of high-productivity equipment. It develops cost comparisons between special setups and standardized setups using shared cam sets, including setup, resetting, tooling, and machine-time losses. The analysis derives a condition under which standardized setups are economical and shows that permissible machine-time loss depends on the average annual production program rather than on the number of part names in the setup. An example for automatic machines 1112 and 1118 suggests that standard setups can substantially lower fixed costs and expand the practical use of automatic machines in small-batch manufacturing.
Full Text
ECONOMIC FEASIBILITY OF APPLYING STANDARD AUTOMATIC-MACHINE SETUPS IN SMALL-BATCH PRODUCTION
G. B. KATS
I
One of the main shortcomings of the existing system of individual technological development is that, when drawing up the technological process for each new part, the technologist often proceeds as if this process were being designed for the first time. Under these conditions, in order to establish the most expedient technological process, it is necessary each time to carry out anew a large amount of preparatory work: to develop several technically possible variants, standardize them, determine the costs of tooling, etc. Work of this kind is extremely rarely carried out in full—especially the economic analysis of machining variants—and therefore very often the solution of many basic questions is accidental in character.
In fact, given the existing variety of parts and, correspondingly, of technological processes for their manufacture, the technologist’s work on economic analysis is made difficult by the compilation of a large number of comparative variants and economic calculations. This work, especially with the frequent change of objects typical of small-batch production, requires much time and labor, and therefore technologists often neglect economic analysis, relying on their own experience and intuition. It is not surprising that, under such a system, technological developments often bear the stamp of subjectivism.
The absence of work on detailed economic analysis when designing technology, as experience shows, can lead in factories to an underestimation of questions concerning the effectiveness of introducing high-productivity equipment and special tooling under conditions of small-batch production. This, as a rule, leads to a considerable overloading of lathes, incomplete loading of turret lathes, and especially of automatic machines.
It is known that the most effective means making it possible, under conditions of small-batch production, to apply high-productivity equipment and fixtures is the standardization of technological processes.
The standardization of technological processes on the basis of economic analysis creates the conditions for the rational application of high-productivity machining methods, in particular, standard automatic-machine setups.
With standard automatic-machine setups, as will be shown below, the permissible losses of machine time do not depend on the number of part names in the type and can reach a considerable value even with a small annual production program for the parts.
II
In practice, cases have long been known in which individual, most experienced setup men for automatic machines use one and the same set of cams for machining parts of different names and standard sizes, limiting themselves only to the appropriate resetting when changing from one part to another. However, such work, as a rule, is of an accidental character.
The literature likewise lacks a proper generalization of the experience of work in this direction and its theoretical substantiation for the conditions of small-batch production.
Let us consider the economic feasibility of applying standard automatic-machine setups.
When special (nonstandard) setups are available for different names of parts \((n)\), the annual costs \((P)\) for setting up and operating the special tooling (cams) will be:
\[ P = nHC_n + nC_p = nHT_n Z_n + \frac{nS_p}{v}, \]
where
\(H\) — number of batches of parts per year;
\(C_n\) — cost of a single setup;
\(C_p = \dfrac{S_p}{v}\) — annual cost of operating one set of cams;
\(T_n\) — duration of setup;
\(Z_n\) — setup man’s wage;
\(S_p\) — cost of manufacturing a set of cams;
\(v\) — number of years during which the given product will be in production.
If, however, for machining these names of products a standard setup is used, consisting of one set of cams, the annual costs for setup and operation of the set of cams will be:
\[ P = H\left[C_n + (n - 1)C_{pn}\right] + C_p, \]
where
\(C_{pn}\) — cost of resetting when changing over to the machining of analogous parts included in the standard setup.
It is quite obvious that the annual costs in the second case will be considerably lower, since \(n - 1\) setups are replaced by resettings, and the cost of operating only one set of cams is also taken into account.
The use of standard setups on automatic machines causes unproductive losses of machine time for some part,
\[ \Delta T_m = T'_m - T''_m, \]
where
\(T'_m\) — machining time for the part of greatest complexity and length;
\(T''_m\) — machining time for the corresponding part with a special setup of the automatic machine.
It is obvious that the annual cost of losses of machine time will be:
\[ P_p = \sum_{1}^{n-1} m_x \Delta T_m \Pi, \]
where
\(m_x\) — cost of operating 1 minute of machine time;
\(\Pi\) — annual production program of parts.
Then the condition for the economical use of a standard setup can be expressed by the inequality:
\[ H\left[C_n+(n-1)C_{pn}\right]+C_n+\sum_{1}^{n-1} m_x \Delta T_M P<nHC_n+nC_n, \tag{1} \]
i.e., the annual costs for setup and operation of the set of cams plus the annual cost of machine-time losses under the standard setup must be less than the annual costs for setup and operation of the tooling under a special (non-standard) setup.
The annual cost of machine-time losses \(\left(\sum_{1}^{n-1} m_x \Delta T_M P\right)\) may be replaced by the expression
\[ (n-1)m_x \Delta T_{M\,av} P_{av}, \]
in which
\(\Delta T_{M\,av}\) is the average amount of time lost during machining;
\(n-1\) is the number of simpler parts included in the standard setup;
\(P_{av}\) is the average annual program.
Inequality (1) will take the form:
\[ H\left[C_n+(n-1)C_{pn}\right]+C_n(n-1)m_x\Delta T_{M\,av}P_{av}<nHC_n+nC_n. \]
After the following transformations,
\[ HC_n+H(n-1)C_{pn}+C_n+(n-1)m_x\Delta T_{M\,av}P_{av}<nHC_n+nC_n, \]
\[ (n-1)m_x\Delta T_{M\,av}P_{av}<(n-1)(C_n-HC_{pn}+HC_n), \]
we obtain:
\[ \Delta T_{M\,av}<\frac{H(C_n-C_{pn})+C_n}{m_xP_{av}}. \tag{2} \]
Consequently, the permissible machine-time loss does not depend on the number of part names included in one standard setup and can be expressed, for average data on the duration of setup and resetting, as well as for the average cost of cams, by the simplest formula for each type of automatic machine:
\[ \Delta T_{M\,av}<\frac{A}{P_{av}}\ \text{(min.)}, \tag{3} \]
where
\[ A=\frac{H(C_n-C_{pn})+C_n}{m_x}. \]
Thus, for example, for automatic machines 1112 and 1118, taking \(T_n=3.4\) hours; \(T_{pn}=1\) hour; \(Z_n=3\) rubles 13 kopecks per hour; \(H=6\) batches per year;
\[ C_n=\frac{S_n}{v}=\frac{90}{3}=30 \text{ rubles} \]
and assuming that one third-grade machine operator services 3 automatic machines, consequently,
\[ m_x=3c+Cc=\frac{3.39}{3}+1.7=2.83 \text{ kopecks}, \]
we obtain:
\[ \Delta T_{M\,av}<\frac{6(3.4-1)313+3000}{2.83\cdot P_{av}}<\frac{2650}{P_{av}}\ \text{min.}, \]
i.e., for this type of automatic machine, with an average program of parts \(P_{\mathrm{sr}} = 2650\) pieces per year, losses of machine time per part equal to one minute may be allowed.
The value \(\Delta T_{m\mathrm{sr}}\), as a function of the program for this type of automatic machine, is given in the graph (Fig. 1).
In an analogous manner, the permissible losses of machine time for other types of automatic machines are determined by formula (3).
Thus, the theoretical substantiation derived for the economic feasibility of applying standard automatic-machine setups makes it possible
Fig. 1. Permissible losses of machine time per part with standard setups on automatic machines 1112–1118.
to introduce automatic machines even with small production programs for parts, provided that the technological processes for machining the latter are standardized.
Standard automatic-machine setups considerably expand the field of application of automatic machines in small-batch production; this can also be derived from the well-known formula, according to the method of comparing variants, for the cost of machining:
\[ P_g < \frac{C_1 - C_2}{V_2 - V_1}, \tag{a} \]
where
\(P_g\) is the annual production program at which equality is achieved between the costs of the two variants being compared,
\(C\) and \(V\) are the fixed and variable costs, respectively, of the variants being compared.
With a special setup, the amount of fixed costs \(C_1\) for the automatic machine will be:
\[ C'_1 = H C_n + C_p; \]
with a standard setup
\[ C''_1 = \frac{H\left[C_n + (n - 1)C_{nm}\right] + C_p}{n}; \]
the use of standard setups is expedient when
\[ C''_1 < C'_1. \]
For the example given above (automatic machines 1112–1118), with five parts secured in one setup ($n=5$), we have:
\[ C'_1 = 6.3,4 \cdot 313 + 3000 = 9390 \text{ kopecks,} \]
\[ C''_1 = \frac{6[3,4 \cdot 313 + (5 - 1)1 \cdot 313] + 3000}{5} = 3380 \text{ kopecks.} \]
Consequently, the size of the production program $P_g$, determined by formula (a), will decrease by almost 3.5 times (see the graph in Fig. 2).
Fig. 2
In this connection, however, it must be borne in mind that the variable costs $V_t$ in the denominator of (a) must be calculated for the largest and most complex part in the standard setup.