A Simple Numerical Example Illustrating Flexible versus Inflexible Manufacturing Systems

Flexible manufacturing system is a wonderful development in manufacturing technology that permits a modern factory to switch easily to making different products. I present a simple numerical example to illustrate flexible manufacturing system (K) and inflexible manufacturing system (L). K can produce product 1 or product 2 with the same machinery and with zero setup costs in changing output from product 1 to 2 or from product 2 to 1. L can produce only one product, product 2. I assume large numbers of producers and buyers of products 1 and 2, open market systems, each acting to his/her interest to secure profits and consumer welfare with minimal government interference/ regulation. I assume both K and L have linear total costs with absolute capacity limits. If prices are above SRMC then plants produce at capacity. Producers are price takers only. If price equals or below SRMC plants shutdown. I assume demand for products 1 and 2 are random and alternate, meaning never at the same. I assume ease of entry/exit of producers. Long-run equilibrium requires zero expected profits for all producers.

DOI: 10.4236/me.2018. 91015 242 Modern Economy change the order of operations executed on a part. The second category is called machine flexibility, which consists of 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 a flexible manufacturing system because it can it easily switch from making product 1 to making 2 and visa versa. L is an inflexible manufacturing system because it can manufacture only product 2.
The flexible manufacturing system is an exciting new development in manufacturing technology: to increase manufacturing flexibility, to easily switch from between products manufactured. My numerical example demonstrates convincingly the superiority of the flexible manufacturing system. Researchers in production and manufacturing praise the flexible manufacturing system 1 .

My Numerical Example
In my numerical example, for simplification, I assume demand schedules for product 1 and 2 are identical. I assume that flexible manufacturing system has lower variable costs, VC, per unit and higher fixed costs, FC, per period than the inflexible manufacturing system. I assume the flexible manufacturing system has the same VC and FC, for products 1 and 2.

A World of Globalization
Today we live in a world of globalization. I write 2 : Globalization is a process of interaction and integration among the people, Countries under open-market systems have large numbers of producers and buyers of goods and services each acting to his/her interest to secure profits and consumer welfare with minimal government interferrence/regulation.
In a world of globalization, there is an urgent need for the flexible manufacturing system, whereby a factory can easily switch making product 1 to making product 2 to making product 3 etc.  3456 P Q w = Plant K illustrates flexible manufacturing system because it can switch between making product 1 and 2 with infinite ease. Plant L illustrates inflexible manufacturing system because it can make only product 2. Fractional plants are permitted. No long-run economies of scale are assumed for each plant. Figure 1 shows inflexibile manufacturing system with only plants L manufacturing product 2. The industry capacity is 84.7 tons 2 per week from 94.11 plants 2L . Long run equilibrium exists because industry demand for product 2 is satisfied and expected profits over the cycle are 0. Figure 2 shows flexible manufacturing system with industry capacity, if plants K choose to make only product 1 is 36.9 tons 1 week using 51.28 plants 1K . Industry capacity, if plants K choose to make only product 2 is 84.7 tons 2 per week using 117.65 plants 2K . Figure 3 shows the numerical example plant K flexible manufacturing system which can switch instantly with no setup cost from making one product to making another product, versus plant L which can manufacture only product 2. Plant L shuts down in 1 w when there is no demand for product 2. The flexible manufacturing system will dominate, especially as in real cases, flexible manufacturing systems can switch among more than two products.

A Quantum Leap Forward in Manufacturing
Flexible manufacturing system is quantum leap forward in manufacturing. My earlier work on output-flexibility 5 presumes old-fashioned factories as in John

Steel Makers Adopting Flexible Manufacturing System
Recent WSJ article 6 .
"Steel makers are betting on the US again, building mills they hope will help them compete against cheap imports as demand rises... The company says the mill can be adapted to produce different flat-rolled steel products, potentially leaving it less vulnerable to supply gluts than mills making just one or two products."

More Complex Computer Models Needed
My simple numerical example can help companies making complex computer models of proposed plant expansion, construction, or renovation. Today, with globalization, 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.