## Determination of Consistency of Set of Sentences

Determine if the following set of sentence is consistent or inconsistent: If John committed the murder, then he was in the victim’s apartment and did not leave before 11. John was in the victim’s apartment. If he left before 11, then the doorman saw him but it is not the case either that the doorman […]

## Using the Hungarian Algorithm to Find an Allocation That Maximises Profit

The Hungarian Algorithm is used to find an allocation to minimise cost, but can be adapted to find an allocation that maximises profit. This is done by making each entry in the profit matrix negative and and a fixed number to each element in the resulting table to make it non – zero. The following […]

## The Unbalanced Transportation Problem

In practice supply rarely equals demand exactly, at least in the short term. The difference may be stored or taken from the supply chain, or from some warehouse. We can model the situation where supply does not equal demand by introducing dummy suppliers or customers. The table below shows demand for and supply of bread, […]

## Using the Stepping Stone Method to Find an Improved Solution to the Transportation Problem

The stepping stone method is an algorithm for swapping the routes between sites that supply and receive goods. We start with the matrix below, representing the costs of transporting from each quarry to each site, together with the supply capacity of each quarry and the receiving capacity of each site. Site 1 Site 2 Site […]

## Dynamic Programming – Worked Example

A clockmaker makes clocks to order. His order books for clocks over the next five months is shown below. Months January February March April May Number of Clocks Scheduled for Delivery 1 5 3 3 2 The clocks are delivered at the end of each month. The clockmaker can make up to four clocks a […]

## The Dynamic Programming Labelling Procedure

Labelling dynamic programming networks is a real problem. There are many different notations, starting from the left hand side of a diagram or the right hand side, using coordinate (x,y) notation, or just numbering the states. I will explain the coordinate notation starting from the right. This notation takes the form (x,y) with x equal […]

## Optimal Strategies in Games That Are Not Stable When Players Have Two Possible Strategies Each

If a player uses the same strategy in every game, he is using a ‘pure strategy’. Pure strategies provide the best results for both players in a game which has a stable solution. If no stable solution exists, each player will maximise his winnings by adopting a mixed strategy in which each available strategy is […]

## Dummies

Dummies are used in critical path analysis to indicate which activities must be finished before other activities can start. Sometimes it happens that some activities have some preceding activities that need to be finished before they can start. If activities depend on other activities – not all the same activities – then dummies are need […]

## Critical Path Analysis – A Brief Explanation

Critical path analysis is algorithm that allows large projects to be planned. Each projects consists of a series of activities that must be completed. Before an activity can be started, certain other activities must be completed. The algorithm allows the ordering of activities, maybe doing several activities at the same time, so that the project […]