Assembly Line Scheduling Problem

Keisha recently started a clothing company that uses two assembly lines to produce articles of clothing. She has separated the the process of manufacturing an item of clothing into n steps, so each assembly line is separated into n different stations, with each station performing a specific task (So for example station three's job may be to add a right sleeve to shirts). The task of a specific station is independent of which line the station occurs on (so if station three's job is to add a right sleeve to shirts, this will be true in both assembly line 1 and assembly line 2). Lets denote the jth station (with j = 1, 2, ..., n) on line i (where i is 1 or 2) by Si, j. Although they're doing the same jobs the time it takes the employee at station S1, j may be different from the time it takes the employee at station S2, j. We will denote the time required at station Si, j by ai, j. For each line, there is also an amount of time required for the article of clothing to enter assembly line i, ei; and an amount of time required for the article of clothing to exit assembly line i, xi.

One of the reasons that assembly lines are very productive is that stations on the same assembly line are generally in close proximity to one another, resulting in a very low cost of transferring an item from one station to the next on the same assembly line. When we have multiple lines in place, as Keisha has, there is a (possibly beneficial) cost of transferring an item from one line to another. Lets denote this cost by ti, j which represents the cost of transferring a partially completed item of clothing from line i after having gone through station Si, j (again, i is 1 or 2 and j = 1, 2, ..., n).

your browser does not support the canvas tag

Recent Updates

  • 08-10-2017 Floyd-Warshall Shortest Paths
  • 08-01-2017 Degree Centrality of a Graph
  • 06-03-2017 Tarjan's Strongly Connected Components Algorithm
  • 03-20-2017 Longest Common Subsequence
  • 10-27-2016 Independent Set Puzzles
  • 06-28-2016 Lets Learn About XOR Encryption
  • 06-15-2016 Discrete-time Markov Chains
  • 03-01-2016 Topological Sort
  • 01-21-2016 The RSA Algorithm
  • 11-20-2015 How To Take Notes in Math Class
  • 10-28-2015 The Depth-First-Search Algorithm
  • 10-28-2015 The Breadth-First-Search Algorithm
  • 09-23-2015 ID3 Algorithm Decision Trees
  • 07-08-2015 Clique Problem Puzzles
  • 06-25-2015 Unidirectional TSP Puzzles
  • 04-04-2015 Learn About Descriptive Statistics
  • 02-19-2015 Slope Formula
  • 01-15-2015 Interactive Midpoint Formula
  • 12-18-2014 Triangle Sum Puzzle
  • 12-02-2014 The Bridge Crossing Problem