Estimating cost for shaping processes 429

18.7 Estimating cost for shaping processes 429

. into C oh , as we shall do here. Finally, there is the cost of information, meaning

that of research and development, royalty or license fees; this, too, we view as

a cost per unit time and lump it into the overhead. Consider now the manufacture of a component (the ‘unit of output’) weigh-

ing m kg, and made of a material costing C m $/kg. The first contribution to the unit cost is that of the material mC m . Processes rarely use exactly the right amount of material but generate a scrap fraction f, which ends up in runners, risers, machining swarf and rejects. Some is recycled, but the material cost per unit needs to be magnified by the factor 1/(1 ⫺ f ) to account for the fraction that is lost. Hence the material contribution per unit is:

mC

The cost C t of a set of tooling—dies, molds, fixtures and jigs—is what is called

a dedicated cost: one that must be wholly assigned to the production run of this single component. It is written off against the numerical size n of the produc- tion run. However, tooling wears out at a rate which depends on the number of items processed. We define the tool life n t as the number of units that a set of tooling can make before it has to be replaced. We have to use one tooling set even if the production run is only one unit. But each time the tooling is replaced there is a step up in the total cost to be spread over the whole batch. To capture this with a smooth function, we multiply the cost of a tooling set C t by (1 ⫹ n/n t ). Thus, the tooling cost per unit takes the form:

n t   The capital cost of equipment, C c , by contrast, is rarely dedicated. A given

n  

piece of equipment—a powder press, for example—can be used to make many different components by installing different die-sets or tooling. It is usual to convert the capital cost of non-dedicated equipment and the cost of borrowing the capital itself into an overhead by dividing it by a capital write-off time, t wo ,

(5 years, say) over which it is to be recovered. The quantity C c /t wo is then a cost per hour—provided the equipment is used continuously. That is rarely the case, so the term is modified by dividing it by a load factor, L—the fraction of time for which the equipment is productive. This gives an effective hourly cost of the equipment, like a rental charge, even though it is your own piece of kit. The capital contribution to the cost per unit is then this hourly cost divided by the

. production rate/hour n at which units are produced:

C ⫽  3 c 

n ɺ   Lt wo  

430 Chapter 18 Heat, beat, stick and polish: manufacturing processes

. Finally, there is the general background hourly overhead rate C oh for labor,

energy and so on. This is again converted to a cost per unit by dividing by the

production rate n units per hour:

C oh

The total shaping cost per part, C s , is the sum of these four terms, C 1 –C 4 , taking the form:

mC m

 1 ⫹  1 C ⫹ c  ⫹ ⫹ɺ C  (18.6)

  To emphasize the simple form of this equation, it can be written:

C capital ⫹ C overhe aad

s ⫽ material ⫹

C C dedicated

ɺn

This equation shows that the cost has three essential contributions—a material cost per unit of production that is independent of batch size and rate, a dedicated cost per unit of production that varies as the reciprocal of the production volume (1/n), and a gross overhead per unit of production that varies as the reciprocal of the production rate (1/n . ). The dedicated cost, the effective hourly rate of capital write-off and the production rate can all be defined by a representative range for . each process; target batch size n, the overhead rate C oh , the load factor L and the capital write-off time t wo must be defined by the user.

Figure 18.16 uses equation (18.6). It is a plot of cost, C s , against batch size, n, comparing the cost of casting a small aluminum component by three alter-