#minizinc

[mooptcom]

Learn Constraints Optimization with Minizinc Online: Moopt School

Moopt School equips operational researchers with the skills to analyze, model and solve real-world optimization problems through simple terms, plenty of real-world examples and helpful illustrations.

Our analysts are working with commercial-quality products, rather than educational-level optimisation software. We believe that if we could teach them on the same technologies that they will be using in workspace, we would be doing a better job of preparing the next generation for a successful Optimization or Operations Research career.

Introduction

Traditionally businesses will focus on efficiency to differentiate themselves from competitors. This includes waste reduction, faster throughput time and better customer service. While efficiency is still important in today’s environment, it is no longer sufficient for differentiation.

Today’s buzzwords include Big Data and Analytics. We have huge IT infrastructure for data collection and storage, better skills in processing data with advanced statistical software like SAS or R and friendlier data visualisation dashboard. Provided that data is available and usable, companies will have personnel and tools for reporting and prediction.

However, we still has to make decisions based on gut feel. There is no actionable recommendation provided by the systems and reports or what-if analyses to quantify what will happen if different course of actions are taken.

There are 3 types of analytics: descriptive (what has happened), predictive (what will happen), and prescriptive (what should happen).

Refer Descriptive, Predictive & Prescriptive Analytics: Port Operations Case Study, a nonfiction that explains the three stages of advanced analytics: Descriptive, Predictive & Prescriptive Analytics from the view of a port operator.

Prescriptive analytics, the third level analytics, which sits at the top of analytics evolution diagram above. It uses advanced analytical methods from Operations Research (OR), Management Science (MS) or Decision Science for quantitative decision making to help make better decisions.

It recommends one or more courses of action and showing the likely outcome of each decision so that the business decision makers can take this information and act. No more gut feel or crystal ball in decision making.

OR/MS is not new as it started during World War II. Optimization problems need to be formulated as mathematical models and solved with the optimization engine to get the solutions/recommendations.

Today’s computing capability has enabled very large and complex practical problems to be solved very quickly. Unfortunately OR/MS applications are not widespread in Malaysia compared to USA, Europe, South Korea, Taiwan and Singapore. Asia’s economy and competition require optimization of the business operations.

A decision-support environment is essential for business people to review their options and make confident decisions. Optimization technology has long been used to find the best solutions to complex planning and scheduling problems. It helps businesses make complex decisions and trade-offs about limited resources, better and faster.

Barriers to Learning & Modeling

Do you want to increase your salary exponentially? Constraints Programming with Minizinc is a very niche skill, but it is highly valued by the critical industries, like Oil and Gas, Supply Chain and Manufacturing.

Let’s face it. Learning Minizinc can be a nightmare. It is hard, boring and expensive.

Hard: People gave up. Beginners to modelling languages often find it difficult to get started.

Bad Tutor: They don’t have a good teacher. They tend to ignore the computer science aspects of writing robust models.

Boring: The learning resources are too boring. They assume a base level of knowledge of modelling languages or a deep familiarity with some certain optimisation problems.

Expensive: Almost all optimization training courses are mainly for big corporations. Our standard training is just way too expensive for individuals, starting at USD 2000, per day.

We have many training requests from individual operational scientists and planners, to improve their skills and increase their salaries.

Solution

We're experimenting a standardized Minizinc e-learning course that lets you learn how to start from nothing and get models up and running.

Different from other courses, we focus more on practical lessons, less on theory. We stick with one general problem and expand on that model in simple steps.

Instead of meeting a real person expert trainer, you can learn Minizinc modeling at any time, any place, by reading through our bite-sized lessons.

Think of Codecademy for Minizinc. A 8 minutes lesson is superior than a 2-hour class or lecture.

For whom is this e-course for?

The objective of this e-Course is to teach those aspiring IT analysts with varying degrees of Operations Research knowledge, about how to use the most important features of Minizinc IDE.

1) Developers who want to leverage mathematical optimization or constraint programming engine into real-world applications. Business Analysts, Modelers, IT developers and managers working with OR professionals derive maximum value out of the course.

2) Managers and executives who are involved in what-if analyses and recommendations / decision making of investment, pricing and revenue management, portfolio management, risk analysis, strategic planning, facility site location, production planning and scheduling, resource allocation, assets optimization, cost reduction, etc.

3) University students of Mathematics or Engineering Schools (MSc. or PhD). This course will equip you with the necessary skills and knowledge to provide effective solutions to complex organizational challenges in a business environment.

Ideal Profiles

In the early stage of your career

Want to enhance your career

Changing career to Operations Research industry as a planner or scheduler

Employed under critical industries

Operations research / Mathematics / Engineering background

Self-learning

Don’t have big budget for self-development

Benefits

Upon a successful completion of this course, we want you to be able to:

Understand where Operations Research fits in the analytics big picture and how it helps decision making

Understand Mathematical Programming and Constraint Optimization concepts and modelling techniques

Formulate decision-making problems as different models and solve with Minizinc IDE

Build production planning models and scheduling models

Course Content

A 8 minutes bite-sized lesson is superior than a 2-hour class or lecture for learning Minizinc.

1. Linear Programming Model with Minizinc Introduction

2. Why Minizinc? and its Components

3. Minizinc Desktop IDE Setup & MooptDev Cloud IDE

4. Simple Minizinc Model Explanation

5. Comments for Minizinc Model

6. Debugging Minizinc Model

7. Minizinc Decision Variable Expressions

8. Non-negativity Constraints

9. Minizinc Output Statement

10. Separate Parameters from Minizinc Model

11. Separate Data from Miniznc Model

12. Modelling Range with Sets, Arrays & Indices

13. Forall Loop to Output Result

14. Modelling with Summation Function

15. Naming with Strings Array

16. Compact Modelling with Enumerated Type

More ...

Participants who complete our Minizinc Optimization e-course, can take an online 35 questions multiple choice free assessment exam. Upon successful completion of the exam, you will receive Course Completion Certificate.

Learn Minizinc like your career depends on it. Your one-time investment will make an exponential 40% increase in your annual salary!

Access to all courses and lessons

Education in the most relevant tools and skills

Increased coding knowledge and understanding

More career opportunities

Track your progress: points / experience = ranking

Gain confidence and expertise

Direct contribution to open-source software

I HAVE A NEW ADDICTION. IT’S POWERFUL. IT’S DISTURBING. IT’S MOOPT SCHOOL.

Minizinc is one of the best option in the market, highly valued by the critical industries. Beginners often find it difficult to get started and gave up early. Are you ready to learn Minizinc and upgrade your career?

[mooptcom]

Linear Programming with Minizinc Introduction

Introducing Linear Programming, a mathematical programming method to solve a simple truck loading optimization puzzle with Minizinc.

Consider this problem: 300 boxes need to be loaded and shipped to a supermarket from a warehouse. We may rent lorries that can accommodate 30 boxes and 40 boxes, costing us RM 400 and ​RM 500 respectively. How many lorries of each type to load all boxes while minimizing the cost?

How many lorries of each type do we need?

The term "lorry" is more common in the United Kingdom while "truck" is often used in American contexts. Both terms can be used interchangeably. Our goal is to minimize the cost of loading these boxes by selecting the right amount of the different lorries.

At first glance this seems a simple task. A box costs RM 12.50 for 40-boxes-lorry (RM 500 / 40 boxes) and RM 13.33 for 30-boxes-lorry. So we would prefer the 40-boxes-lorry over 30-boxes-lorry, for cheaper unit price. However, what complicates matters are the resources needed.

We first put 280 boxes into 7 lorries of 40-boxes for RM 3500 (7 x ​RM 500). Then we add an eighth 30-boxes-lorry for RM 400 for the remaining 20 boxes. Total cost is RM 3900 for 8 lorries. This looks fine. But this is not the best solution.

Better Solution - Saving extra RM 100!

With 6 lorries of 40 boxes (240 boxes @ RM 3000) and 2 lorries with 30 seats (60 boxes @ ​RM 800), we can load all the boxes and pay only ​RM 3800. We can save RM 100! The best decision is not that obvious.

Solving puzzle with Minizinc

Mathematical Formulation:

$\begin{aligned} \min 400 * nLorry30 + 500 * nLorry40 \quad (0) \\\ 30 * nLorry30 + 40 * nLorry40 \geq 300 \quad (1) \\\ nLorry30, nLorry40 \geq 0 \quad (2) \end{aligned}$

We can easily solve the puzzle above with Minizinc code:

var int: nLorry30; var int: nLorry40; constraint 30 * nLorry30 + 40 * nLorry40 >= 300; constraint nLorry30 > 0; constraint nLorry40 > 0; solve minimize 400 * nLorry30 + 500 * nLorry40;

You can try at Moopt Dev, a web-based optimization modeling platform and get the result:

nLorry30 = 9; nLorry40 = 1; ---------- nLorry30 = 6; nLorry40 = 3; ---------- nLorry30 = 2; nLorry40 = 6;

Solving Real World Problems for Millions of ROI

This problem is a very simple example with only 2 variables, which are 2 types of lorries. In reality, real business problems in real companies can contain up to thousands or more variables. Solving it using our brain purely or graphically is totally impossible.

With modern tools, like Minizinc, companies can tackle more complex real-world problems and the return of investment would not be just RM 100 as in our toy lorry problem but millions of dollars. Other practical applications are production planning, resource allocation, investment decisions, military operations, inventory management, transportation scheduling, ... etc.

In the coming lessons, we will be revisiting how to code in Minizinc to solve this puzzle in details!

[kyagrd]

n-Queens using MiniZinc

MiniZinc is a high level Constraint Programming (CP) language (or a frontend for constraint programming solvers). Being distributed with its own IDE, it is a most friendly enviornment to have a taste on what constraint programming is. Here is the n-Queens problem, which is like a hello world for CP, in MiniZinc.

include "globals.mzn"; int: n; % fixed integer parameter % (xs[y],y), is a coordiate for a queen array[1..n] of var 1..n: xs; % constraint for the n queens problem on nxn borard constraint alldifferent(xs); constraint forall (i,j in 1..n where i<j) ( j-i != abs(xs[i]-xs[j]) ); solve satisfy; % find satisfying solution output ["Solution:\n", "xs = \(xs) \n", "To pretty-print the chessboard config, use ghci to run:\n", "let xs = \(xs) in putStrLn $ concat $ Data.List.intersperse \"\\n\" [ [if i==k then 'Q' else '#' | k <- ys ] | i<-[1..length xs] ]"];

Note that fixed parameters, which should be initialized before runnning the solver, are declared witout the var keyword and the variables that are to be searched for solutions are declared with the var keyword. This var is in fact part of the type.

And in the IDE it looks like this.

Since we have not initizlied the fixed paramenter n, the IDE will prompt for its value when you run it with Ctrl-R.

The output looks like this for n = 8.

Solution: xs = [3, 6, 4, 2, 8, 5, 7, 1] To pretty-print the chessboard config, use ghci to run: let xs = [3, 6, 4, 2, 8, 5, 7, 1] in putStrLn $ concat $ Data.List.intersperse "\n" [ [if i==k then 'Q' else '#' | k <- ys ] | i<-[1..length xs] ]

Try to pretty-print the result in 2D chessboard configuration using your favorite programming langauge, which is in my case Haskell.

Seems like MiniZinc got a correct solution :)

You actually have to use an external mechanism to print this last step because you cannot use var types where normal types are required. var int is differet from int. The output command only prints strings not var strings. Var is like a stage annotation that contaminates the result once you use it. For instance if you try to print out something that relies on any var value MiniZinc will complain that it is var string not string. If a high level constraint programming lanaguage supported multi-staged computation we could actualy do those kind of things at the last step of printing out a result depending on the solution value.