Modelling a Mixed Linear Programming Model

Tax is a company involved in steel industry. Within this, one of the critical stages is to process custom plates according to the needs of customer, where depending on the dimensions, thickness and characteristics of the material, certain amount of time will be required for such processing.

You are hired by Tax as a plant planner who handles the requirements, where you have the following information.

The company has a machine to process (J) jobs (or orders). Each processing of the works, considering the characteristics of the aforementioned requirements, has an estimated time known in days (pj) . In addition, the company has a policy where it engages customers to deliver their orders to them on a known date (dj). Consequently, if that date is not fulfilled the company must make a discount on the final price, fining the lack of commitment, which is measured in $ (pesos) per day of delay. It should be noted that this fine (rj) will clearly depend on the work.

As an additional consideration, keep in mind that delivery dates are measured from reference zero, which is the assumed start time of the first job.

OBJECTIVE: Formulate a mixed linear programming model that determines the minimum sequence of penalty for delay when processing (J) jobs.

(This means establishing the Variables, constraints and Target Function, this in addition to the Sets and Parameters already mentioned. No software implementation is necessary, unless you want to compare the outputs with mine.)

Some clarifications:

1.- The machine can do only one job at a time.

2.- The order of how the work is performed must be delivered by the program to use (not required part), that is, it is not a parameter.

3.- The work is delivered instantly, that is, as soon as it is finished it is delivered.

4.- The (j+1) job starts immediately when the (j) job is finished.

Matemáticas Programación lineal Operations Research

Nº del proyecto: #22998595

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