Getting started with LpProblem()

You have been given the role of scheduler for a job shop. A job shop is a type of manufacturing process in which small batches of a variety of custom products are made. A poorly scheduled job shop will increase working capital and reduce the total number of jobs completed. These situations negatively affect a company's overall operations. You are looking to optimize the schedule.

How could you model this in PuLP?

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Linear Programming (LP) is a key technique for Supply Chain Optimization. The PuLP framework is an easy to use tool for working with LP problems and allows the programmer to focus on modeling. In this chapter we learn the basics of LP problems and start to learn how to use the PuLP framework to solve them.

Exercise 1: Basics of optimization Exercise 2: To LP, or to not IP?Exercise 3: Choosing exercise routine Exercise 4: Basics of PuLP modeling Exercise 5: Getting started with LpProblem()

Aktuelle Übung

Exercise 6: Simple resource scheduling exercise Exercise 7: Using lpSum Exercise 8: Trying out lpSum Exercise 9: Logistics planning problem

In this chapter we continue to learn how to model LP and IP problems in PuLP. We touch on how to use PuLP for large scale problems. Additionally, we begin our case study example on how to solve the Capacitated Plant location model.

Exercise 1: LpVariable dictionary function Exercise 2: Logistics planning problem 2 Exercise 3: Traveling salesman problem (TSP)Exercise 4: Example of a scheduling problem Exercise 5: Scheduling workers problem Exercise 6: Preventative maintenance scheduling Exercise 7: Capacitated plant location - case study P1 Exercise 8: Review data for case study Exercise 9: Decision variables of case study Exercise 10: Objective function of case study Exercise 11: Logical constraints Exercise 12: Logical constraint exercise Exercise 13: Logical constraints exercise 2

This chapter reviews some common mistakes made when creating constraints, and step through the process of solving the model. Once we have a solution to our LP model, how do we know if it is correct? In this chapter we also review a process for reasonableness checking or sanity checking the results. Furthermore, we continue working through our case study example on the Capacitated Plant location model by completing all the needed constraints.

Exercise 1: Common constraint mistakes Exercise 2: Dependent demand constraint exercise Exercise 3: Constraint combination exercise Exercise 4: Capacitated plant location - case study P2 Exercise 5: Constraints of case study exercise Exercise 6: Adding logical constraint in case study exercise Exercise 7: Solve the PuLP model Exercise 8: Choose the model status exercise Exercise 9: Solving production plan exercise Exercise 10: Sanity checking the solution Exercise 11: Reviewing model specification exercise Exercise 12: Sanity checking exercise

In our final chapter we review sensitivity analysis of constraints through shadow prices and slack. Additionally, we look at simulation testing our LP models. These different techniques allow us to answer different business-related questions about our models, such as available capacity and incremental costs. Finally, we complete our case study exercise and focus on using sensitivity analysis and simulation testing to answer questions about our model.

Exercise 1: Shadow price sensitivity analysis Exercise 2: Sensitivity analysis exercise Exercise 3: Shadow price and slack exercise pt1 Exercise 4: Shadow price and slack exercise pt2 Exercise 5: Capacitated plant location - case study P3 Exercise 6: Solving the model case study exercise Exercise 7: Sensitivity case study exercise Exercise 8: Simulation testing solution Exercise 9: Simulation testing solution exercise Exercise 10: What is the risk exercise Exercise 11: Capacitated plant location - case study P4 Exercise 12: Simulation testing capacitated model Exercise 13: Interpreting simulation results exercise Exercise 14: Final summary