3D Printing Precision Parts

Problem Definition

You work for a company that manufactures high quality polymer parts for OrgoCorp, a galactic bioengineering company. The quality requirements are so high that you need to use very sophisticated 3D printing machines. You need to develop a mathematical programming model to organize monthly production considering:

• Fixed operational costs (euros): Each 3D printing machine \(m\) has a different fixed operational costs \(Fm\) that needs to be considered when a printing machine is used to print any units.

• Unitary production costs (euros): Each 3D printing machine \(m\) produces parts of product type \(p\) at a different unitary costs \(C_{mp}\)

• Capacity (minutes): Each 3D printing machine \(m\) has a different capacity \(S_m\) (minutes)

• Speed (minutes/part): Each 3D printing machine \(m\) prints a unit of product type \(p\) at a different unitary speed

• Demand (units): OrgoCorp has confirmed a demand for \(d_p\) units of every product type \(p\) Build a model that takes into account these requirements, identifying indices, decision variables, objective function and constraints.

The CEO of OrgoCorp, The High Evolutionary, would like to set up a new contract allowing more flexibility in the delivery of units, such that:

• Demand per period (units): Now you need to consider that the demand for every product type \(p\) is not constant and depends on the planning period \(t\), \(D_{pt}\)

• Delayed demand (units): You may delay the production for one period. For every unit of product type \(p\) that is delayed, OrgoCorp will charge an extra delayed demand cost of \(B_{pt}\) Modify the model to take into account this new contract