April 2021

Parallel machine scheduling

20 April 2021 (166 words)

Parallel machine scheduling

Yet Another Math Programming Consultant (YAMPC) has a couple of interesting articles exploring different model formulations for machine scheduling problems:

The situation involves scheduling 50 jobs on 4 parallel machines, with precedence relationships between jobs and multiple weighted objectives.

Five different formulations are analyzed:

  • Model 1. Jobs are scheduled in discrete time slots.
  • Model 2. Jobs are scheduled in continuous time.
  • Model 3. A variation of Model 1.
  • Model 4. A more complex variation of Model 2.
  • Model 5. A positional, rather than time-based, model.

In this situation, Model 1 is the simplest and it performs the best – by a substantial margin.

YAMPC concludes that choosing the right formulation can pay off (though often we need to do numerical tests to determine which formulation is best), and having different formulations is an excellent debugging tool as they give us confidence that the results are correct.

Allocate people to balanced teams

17 April 2021 (1,804 words)

Balanced teams

Allocating people to teams is a common task in both sport and business. Often we want the teams to be as balanced as possible. But making the allocation can be a difficult problem, especially if there are many people or we need to form several teams.

In this article we build and analyze a model that allocates 32 people to four teams, with the objective of each team having an aggregate rating that is as balanced as possible. The task is complicated by having three types of position in the teams, with a diversity of ratings across the available people.

The model is built in Excel and solved using either Solver or OpenSolver.

Optimization 101

5 April 2021 (75 words)

Optimization 101

To learn about optimization modelling, the Optimization 101 website is a great place to start.

The website aims to provide "a complete but compact introduction to the major topics in optimization". The content is divided into chapters, like a book, covering topics that include:

  • Linear Programming.
  • Sensitivity Analysis.
  • Networks.
  • PERT for Project Planning and Scheduling.
  • Integer / Discrete Programming.
  • Binary and Mixed-Integer Programming.
  • Dynamic Programming.
  • Nonlinear Programming (NLP).

Are you a maximizer or a satisficer?

1 April 2021 (173 words)

Which way?

The BBC has an interesting article: Do 'maximisers' or 'satisficers' make better decisions?

According to the article, there are two main types of decision-makers:

  • 'Maximizers' weigh choices carefully to assess which is the best one.
  • 'Satisficers' make decisions quickly and accept a 'good enough' outcome.

Each approach comes with benefits and drawbacks. Being a maximizer tends to be very time-consuming and can lead to post-decision regret and counterfactual thinking. Conversely, satisficers may not necessarily get the best outcome. As a general rule, maximizers do better but feel worse.

Of course, at SolverMax we focus on optimization modelling, so obviously we prefer the maximizer approach. But even then, often it can take a solver a very long time to find an optimal solution. In such situations we may have to accept a near-optimal solution as the best practical trade-off between outcome and timeliness.

As the article suggests, perhaps the best way to make decisions may be by combining maximizer and satisficer tendencies.

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