Planning/ Scheduling Problem. This scheduling solution was designed in order to allocate the items of a product over the painting line conveyor. This environment scenario (introduced by Xxxxxx Xxxxxx pilot-case) describes the class of resources that contain a batch machine with discrete sequential material input. This problem could not be handled through the other optimization solutions, as each resource was defined to take one task/ job at a time, leaving no capability in handling multiple items at once. What is more, the need for giving the ability to create combinations of items over the conveyor’s positions, the problem gets event more complex. In a simplistic approach, methodologies of previous sections could be used with the assumption that one item is a task and one position on the conveyor is a resource. Although this is an adequate solution in cases that one item takes one position on the conveyor, it performs poorly in cases where combination of items is required. This planning solution models the paint shop environment of a production system. The paint shop can be considered as a sequence of carriers moving in a conveyor line. Each carrier can take a specific quantity of items which is related to the size of the items. The following considerations are involved within the mathematical modelling of this research: (i) each item occupies a specific percentage of the carrier’s capacity which can be even up to two carriers; (ii) the conveyor moves at a constant speed and contains a static number of carriers distributed across the line in equal distances; (iii) two items with different colours need to have at least the gap of empty carriers given by the setup delay for these colours. Figure 39 Basic problem illustration for the proposed environment
