Levelling product mix in a Heijunka Board with shortest path algorithms


A Heijunka Board is a Lean Production technique that helps to communicate a timed production plan to the factory floor. Lean advocates that production plans should be generated to level the volume and to level the mix. It is the mix levelling aspect of the Heijunka Board that we are concerned with. In particular, given that a number of products have to be produced on a production line, the order or sequence of production is of importance. This is because changing from one product to the next in the sequence incurs a setup or changeover cost. If the setups are different for each pair of products in a changeover, the question arises which is the optimal sequence that minimises the total setup costs as we go round the Product Wheel? It is this question that we answer here. We show that this mixed model production schedule problem can be represented as a Directed Acyclic Graph (DAG) where the edges of the graph represent the changeover costs. This allows us to apply various Shortest Path Algorithms to minimise the total changeover associated with going through one complete cycle of the product range. We show how the Product Wheel can be formulated as a DAG and solved by hand for small cases when all the changeover over costs are non-negative. Here we use the intuitive, logarithmic time, Dijkstra’a Shortest Path Algorithm (DSPA). For larger problems we have developed both a User Defined Function in Excel and a Java application based on both Topological Sort Algorithm operating in linear time and DSPA. Numerical examples are provided to test the solution methods and computational results illustrate the effectiveness of both approaches to randomly generated problem instances.

Pre-prints of the 18th International Working Seminar of Production Economics, Innsbruck, Austria, 24th-28th Feburary, Vol. 4, 75–87