# Product/Production Relationships

Companies organize their manufacturing operations and production systems as a function of the particular products they make. It is instructive to recognize that there are certain product parameters that are influential in determining how the products are manufactured. Let us consider four key parameters: (1) production quantity, (2) product variety, (3) complexity of assembled products, and (4) complexity of individual parts.

PRODUCT/PRODUCTION RELATIONSHIPS

Companies organize their manufacturing operations and production systems as a function of the particular products they make. It is instructive to recognize that there are certain product parameters that are influential in determining how the products are manufactured. Let us consider four key parameters: (1) production quantity, (2) product variety, (3) complexity of assembled products, and (4) complexity of individual parts.

1     Production Quantity and Product Variety

We previously discussed production quantity and product variety in Chapter 1 (Section 1.1). Let us develop a set of symbols to represent these important parameters. First, let Q=production quantity and P=product variety. Thus we can discuss product variety and production quantity relationships as PQ relationships.

Q refers to the number of units of a given part or product that are produced annually by a plant. Our interest includes both the quantities of each individual part or product style and the total quantity of all styles. Let us identify each part or product style by using the subscript j, so that Qj=annual quantity of style j. Then let Qf=total quantity of all parts or products made in the factory. Qj and Qf are related as follows:

where P=total number of different part or product styles, and j is a subscript to identify products, j=1, 2, p , P.

P refers to the different product designs or types that are produced in a plant. It is a parameter that can be counted, and yet we recognize that the difference between products can be great or small. In Chapter 1, we distinguished between hard product variety and soft product variety. Hard product variety is when the products differ substantially. Soft product variety is when there are only small differences between products. Let us divide the parameter P into two levels, as in a tree structure. Call them P1 and P2. P1 refers to the number of distinct product lines produced by the factory, and P2 refers to the number of models in a product line. P1 represents hard product variety, and P2 is for soft variety.

2     Product and Part Complexity

How complex is each product made in the plant? Product complexity is a complicated issue. It has both qualitative and quantitative aspects. Let us deal with it using quantitative measures. For an assembled product, one possible indicator of product complexity is its number of components—the more parts, the more complex the product is. This is easily demonstrated by comparing the numbers of components in various assembled products, as in Table 2.4. Our list demonstrates that the more components a product has, the more complex it tends to be.

For a fabricated component, a possible measure of part complexity is the number of processing steps required to produce it. An integrated circuit, which is technically a monolithic silicon chip with localized alterations in its surface chemistry, requires hundreds of processing steps in its fabrication. Although it may measure only 9 mm (3 8 inch) on a side and is 0.5 mm (0.020 inch) thick, its complexity is orders of magnitude greater than a round washer of 9 mm (3 8 inch) outside diameter, stamped out of 0.80mm (1 32inch) thick stainless steel in one step. In Table 2.5, we have compiled a list of manufactured parts with the typical number of processing operations that would be required for each.

So, we have complexity of an assembled product defined as the number of distinct components; let np= the number of parts per product. And we have processing complexity of each part as the number of operations required to make it; let no= the number of operations or processing steps to make a part.We can draw some distinctions among production plants on the basis of np and no.As defined in Table 2.6, three different types of plant can be identified: parts producers, pure assembly plants, and vertically integrated plants.

TABLE 2.4       Typical Number of Separate Components in Various Assembled Products (Compiled from [2], [4], and Other Sources)

Let us develop some simple relationships among the parameters P, Q, np, and no that indicate the level of activity in a manufacturing plant.We will ignore the differences between P1 and P2 here. The total number of products made annually in a plant is the sum of the quantities of the individual product designs, as expressed in previous Eq. (2.1). Assuming that the products are all assembled and that all component parts used in these products are made in the plant (no purchased components), then the total number of parts manufactured by the plant per year is given by:

where npf=total number of parts made in the factory (pc yr), Qj=annual quantity of product style j (products yr), and npj=number of parts in product j (pc product).

Finally, if all parts are manufactured in the plant, then the total number of processing operations performed by the plant is given by:

where nof=total number of operation cycles performed in the factory (ops yr), and nojk=number of processing operations for each part k, summed over the number of parts in product j, npj. Parameter nof provides a numerical value for the total activity level in the factory.

We might try to simplify this to better conceptualize the situation by assuming that the number of product designs P are produced in equal quantities Q, all products have the same number of components np, and all components require an equal number of processing steps no. In this case, the total number of product units produced by the factory is given by:

The total number of parts produced by the factory is given by:

And the total number of manufacturing operation cycles performed by the factory is given by:

Using these simplified equations, consider the following example.

EXAMPLE 2.2        A Manufacturing Operations (and Production Systems) Problem

Suppose a company has designed a new product line and is planning to build a new plant to manufacture this product line. The new line consists of 100 different product types, and for each product type the company wants to produce 10,000 units annually. The products average 1000 components each, and the average number of processing steps required for each component is 10. All parts will be made in the factory. Each processing step takes an average of 1 min. Determine: (a) how many products, (b) how many parts, and (c) how many production operations will be required each year, and (d) how many workers will be needed for the plant, if it operates one shift for 250 day yr?

Solution:           The total number of units to be produced by the factory is given by Eq (2.5):

Q=PQ=100*10,000=1,000,000 products annually.

The total number of parts produced is:

npf=PQnp=1,000,000*1000=1,000,000,000 parts annually.

The number of distinct production operations is:

nof=PQnpno=1,000,000,000*10=10,000,000,000 operations.

Let us try to estimate the number of workers required. First consider the total time to perform these operations. If each operation takes 1 min (1 60 hr),

Total time=10,000,000,000*1 60=166,666,667 hr

If each worker works 2000 hr yr (40 hr wk*50 wk yr), then the total number of workers required is:

The factory in our example is a fully integrated factory. It would be a big factory. The number of workers we have calculated only includes direct labor. Add indirect labor, staff, and management, and the number increases to well over 100,000 employees. Imagine the parking lot. And inside the factory, the logistics problems of dealing with all of the products, parts, and operations would be overwhelming. No organization in its right mind would consider building or operating such a plant today—not even the federal government.

3     Limitations and Capabilities of a Manufacturing Plant

Companies do not attempt the kind of factory in our example. Instead, today’s factory is designed with a much more specific mission. Referred to as a focused factory [5], it is a plant which concentrates “on a limited, concise, manageable set of products, technologies, volumes, and markets.” It is a recognition that a manufacturing plant cannot do everything. It must limit its mission only to a certain scope of products and activities in which it can best compete. Its size is typically limited to about 500 workers, although that number may vary widely for different types of products and manufacturing operations.

Let us consider how a plant, or its parent company, limits the scope of its manufacturing operations and production systems. In limiting its scope, the plant in effect makes a set of deliberate decisions about what it will not try to do. Certainly one way to limit a plant’s scope is by avoiding being a fully integrated factory, at least to the extent of our Example 2.2. Instead, it specializes in being either a parts producer or an assembly plant. Just as it decides what it will not do, the plant must also decide on the specific technologies, products, and volumes in which it will specialize. These decisions define the plant’s intended manufacturing capability. Manufacturing capability refers to the technical and physical limitations of a manufacturing firm and each of its plants. We can identify several dimensions of this capability: (1) technological processing capability, (2) physical size and weight of product, and (3) production capacity.

Technological Processing Capability. The technological processing capability of a plant (or company) is its available set of manufacturing processes. Certain plants perform machining operations, others roll steel billets into sheet stock, and others build automobiles. A machine shop cannot roll steel, and a rolling mill cannot build cars. The underlying feature that distinguishes these plants is the set of processes they can perform. Technological processing capability is closely related to the material being processed. Certain manufacturing processes are suited to certain materials, while other processes are suited to other materials. By specializing in a certain process or group of processes, the plant is simultaneously specializing in a certain material type or range of materials.

Technological processing capability includes not only the physical processes, but also the expertise possessed by plant personnel in these processing technologies. Companies are limited by their available processes. They must focus on designing and manufacturing products for which their technological processing capability provides a competitive advantage.

Physical Product Limitations. A second aspect of manufacturing capability is imposed by the physical product. Given a plant with a certain set of processes, there are size and weight limitations on the products that can be accommodated in the plant. Big, heavy products are difficult to move. To move products about, the plant must be equipped with cranes of large load capacity. Smaller parts and products made in large quantities can be moved by conveyor or fork lift truck.The limitation on product size and weight extends to the physical capacity of the manufacturing equipment as well. Production machines come in different sizes. Larger machines can be used to process larger parts. Smaller machines limit the size of the work that can be processed. The set of production equipment, material handling, storage capability, and plant size must be planned for products that lie within a certain size and weight range.

Production Capacity. A third limitation on a plant’s manufacturing capability is the production quantity that can be produced in a given time period (e.g., month or year). This quantity limitation is commonly called plant capacity, or production capacity, which is defined as the maximum rate of production per period that a plant can achieve under assumed operating conditions. The operating conditions refer to number of shifts per week, hours per shift, direct labor manning levels in the plant, and similar conditions under which the plant has been designed to operate. These factors represent inputs to the manufacturing plant. Given these inputs, how much output can the factory produce?

Plant capacity is often measured in terms of output units, such as annual tons of steel produced by a steel mill, or number of cars produced by a final assembly plant. In these cases, the outputs are homogeneous, more or less. In cases where the output units are not homogeneous, other factors may be more appropriate measures, such as available labor hours of productive capacity in a machine shop that produces a variety of parts.

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