Manufacturing and Production Economics Numerical Model Old Non-FMS versus Modern FMS Plants

Flexible Manufacturing System (FMS) is a modern innovation in manufacturing technology that allows a factory to switch at no cost between manufacturing different products. This paper presents a simple numerical model of manufacturing and production economics with illustrated demand and cost curves. The model shows industry long-run equilibrium ( ( ) 0 E π = ) for manufacturing and production to supply hypothetical demand schedules for two products: 1 and 2. The model has two plant types: old non-FMS Plant 2L that can produce only product 2 and modern FMS Plant K that can switch easily between manufacturing products 1 and 2. The model assumes linear total cost curves with absolute capacity limits for the two plant types.


Percent Capacity Utilization: Generally Low
Today we experience world-wide technological revolutions, political upheavals, trade wars, and financial crises. World economies generally operate today below long-run average rates for capacity utilization.
US reports on capacity utilization for manufacturing are shown in Table 1

The Flexible Manufacturing System: Surviving Trade Wars and Technology Revolutions
A flexible manufacturing system allows the system to react to changes, whether predicted or unpredicted. This flexibility falls into two categories. The first category, routing flexibility, covers the system's ability to produce new product types and change the order of operations executed on a part. The second category is called machine flexibility, which is the ability to use multiple machines to perform the same operation on a part, as well as the system's ability to absorb large-scale changes, such as in volume or capability. In my simple numerical example of flexible versus inflexible manufacturing system, K versus L, K is the flexible manufacturing system that can easily switch from making Product 1 to making Product 2 and visa versa. L is the inflexible manufacturing system that manufactures only Product 2. The flexible manufacturing system is an exciting new development in manufacturing technology, allowing switching easily between products manufactured.
Researchers in production and manufacturing praise the flexible manufacturing system 3 . My numerical example convincingly demonstrates the superiority of the flexible manufacturing system.

A World of Globalization
I wrote recently about today's world of globalization. I write 4 : Globalization is a process of interaction and integration among the people, companies, and governments of different nations, a process driven by international trade and investment and aided by information technology.

Old Non-FMS Plant2L versus Modern FMS PlantK
In my numerical example, for simplification, I assume the demand schedules for product 1 and for product 2 are identical except for the frequency of the occurrence, w. At times of w 1 there is demand only for product 1 and no demand for product 2. At times of w 2 there is demand for product 2 and no demand for product 1. assets with low FC and operate as standby capacity to meet peak demand periods. The model assumes, for simplicity, that the modern FMS plant has the same VC and FC, for products 1 and 2. The assumption is that products 1 and 2 use raw materials that cost the same and that the production process is the same or similar.

The Industry of Manufacturing Product 1 and Product 2
Investors seeking to invest in manufacturing and production of product 1 and product 2 can choose between two hypothetical plants, modern FMS plant K and Old non-FMS plant 2L . Both plants have durable specific assets and linear short-run total costs curves with absolute capacity limits. The plants differ in per-unit variable cost, (b), per-unit fixed cost, ( β ), and capacity per plant, (q). My notation is that b is the constant per-unit variable operating cost. β is the per-unit fixed capacity cost where the numerator is the constant fixed costs per week and the denominator is the maximum the plant can produce in a week. I assume periods of a week. I assume q is the operating rate in a week. Let n be the number of plants, a continuous variable.
> , and L K q q > 5 . In my model, investors can order any number of plants K or plants L . Plant K has the lean accounting system which lowers its b. Plant K requires more fixed assets for the same output which raises its β and lowers its q for the same investment amount, say $1,000,000. Investors cannot choose a mixture of plant K and plant L .
For simplification, the industry will be comprised of only plants K or only plants L . If investors could choose a mixture of plant K and plant L , then plant K would dominate.
Demand fluctuates between 1 P with frequency 1 w and 2 P with frequency 2 w .

A Quantum Leap Forward in Manufacturing
Flexible manufacturing systems are a quantum leap forward in manufacturing.
My earlier work on output-flexibility 6 presumes old-fashioned factories as in John M. Clark's 7 days. Investors will want to invest in plant capacity that has a flexible manufacturing system that will enable the factory to operate at a higher rate of utilization.

Automobile Manufacturing Facing Uncertainty
A recent WSJ article highlights uncertainty for automobile manufacturing 8 .

More Complex Computer Models Needed
My simple numerical example can help companies make complex computer models of proposed plant expansion, construction, or renovation. Today, with globalization and intense worldwide competition, and technological developments, there is much uncertainty on exactly which products a company should make. Computer models will aid decision making. The flexible manufacturing system may justify capital expenditures where an inflexible manufacturing system could not be justified. Companies must have a flexible manufacturing system to prosper.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.