Lecture 4 - Case Study: Smart Manufacturing and the Job Shop Scheduling Problem

Question 1

What is smart manufacturing?

Answer 1

• has the goal of optimizing development, production, and logistics.
• employs computer control and high levels of adaptability in the multi-phase process of creating a product from raw material.
• utilizes advanced information and manufacturing technologies to enable flexibility in production processes to address a dynamic market.
• requires increased workforce training for flexibility and use of the technology instead

Question 2

What are some of the technologies involved in smart manufacturing?

Answer 2

• Cyber-Physical Systems: deep connection between physical and software systems, often networks of interacting elements.
• Internet of Things: network enabling physical things to exchange data or being controlled, allowing a computer system to directly interact with the physical world.
• Cloud Computing: move data and computation into the cloud (not just storage, but also computational resources, applications).
• # Big Data: Collection, processing, and evaluation of huge amounts of data.These are known as technology enablers as the do not make the product intelligent yet

Question 3

In business wha can be optimised?

Answer 3

Given the business structure is: delivery, production, management, products/services and sales, in each category there are things that can optimised
REFER TO SLIDES FOR THAT LIST

Question 4

Define optimisation from an economical point of view

Answer 4

An optimization problem is a situation which requires deciding for one choice (candidate solution) from a set of possible alternatives (hyptothesis space) in order to reach a predefined/required benefit at minimal costs. (metric)
NOTE: everything in brackets is just telling you what it is and is not part of the definition

Question 5

Define optimisation from a mathematical point of view

Answer 5

Solving an optimization problem requires finding an input value (candidate solution) y! → Y from a set Y (hyptothesis space) of allowed values for which a mathematical function f : Y “→ R takes on the smallest possible value. (metric)
NOTE: everything in brackets is just telling you what it is and is not part of the definition

Question 6

Why are benchmarks used?

Answer 6

• Many questions in the real world are optimization problems, so benchmarks are used to compare and understanding how something is optimised and how it is optimised

Question 7

Define optimisation from a programming point of view

Answer 7

• From the perspective of a programmer, we can say that an optimization problem has the following components:
• 1 the input data which specifies the problem specification I to be solved
• 2 a data type Y (language representation) for the candidate solutions y → Y, and
• 3 an objective function f : Y “→ R, which rates “how good” a candidate solution y → Y is. (metric)

Question 8

What is the Job Shop problem?

Answer 8

• The Job Shop Scheduling Problem (JSSP) [5–9] is a classical optimization problem.
• We have a factory with m machines.
• We need to fulfill n production requests, the jobs.
• Each job will need to be processed by some or all of the machines in a job-specific order.
• Also, each job will require a job-specific time at a given machine.
• The goal is to fulfill all tasks as quickly as possible.

Question 9

Exponential growth vs polynomial growth

Answer 9

Something that is exponential will grow faster than something that is polynomial

Question 10

What is the input (problem instance) of the job shop problem?

Answer 10

• A concrete scenario, with a specific number of machines and with specific jobs (the instance)
• Where the instance has the number of jobs, the number of machines and rows and columns of the values needed (REFER TO SLIDES)

Question 11

What is the output (solution space) of the job shop problem?

Answer 11

Using a Gantt chart to layout the jobs and when they should be done. REFER TO SLIDES
* The solution space Y is the set of all possible feasible Gantt charts for one problem.

Question 12

What is the quality of the solution (Gantt chart) of the job shop problem?

Answer 12

• A Gantt chart y1 element of Y is a better solution to our problem than another chart y2 element of Y if it allows us to complete our work faster. (COMPARING TWO CHARTS IN SLIDES)
• Where the objective function f : Y “→ R is the makespan (time it takes to make something), the time when the last sub-job is completed, the right-most edge of any bar in the Gantt chart

Question 13

In general why should there be at least one globally optimal solution?

Answer 13

As we can find an upper and lower bound.
For example using the Job shop problem:
Upper bound: take all the jobs and line them all up and add up the times
Lower bound: taking an average or a better solution is to find the longest sub job
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As well as we know the problem is N P-hard [10], so any algorithm that guarantees to find this solution may take time exponential in m or n in the worst case
Therefore we cannot guarantee to find the best possible solution for a normal-sized JSSP in reasonable time, we just do a search in Y and hope to get as close as possible to y within reasonable time.
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If we can find a solution with a slightly larger makespan than the best possible solution, but we can get it within a few minutes, that would also be nice