Cyclic machine loading, product allocation and lot sizing in an asbestos cement sheet factory

In an asbestos cement sheet factory a number of products can be produced on certain non-identical alternative machines. The cyclic planning problem considered deals with the case of constant product demand rates and the determination of (i) the fraction of demand of any item to be allocated to any machine, and (ii) a reorder interval between two batch productions of an item on a machine, restricted to 1, 2 or 4 months, so as to minimize the cost per unit time due to setups, inventories, and variable costs of production. Machine capacities are limited. This problem is partly akin to Caie and Maxwell’s hierarchical machine load planning in their first level of cycle planning. However, the present problem is not a particular case of theirs because product splitting among machines must be allowed, especially because the number of products in the present case is not large. Consequently, the approach to the problem is quite different altogether in terms of both bounding and branching schemes in a branch and bound approach proposed in this paper. On the other hand, the present approach concerns single stage production and does not deal with a production flow network as considered by Caie and Maxwell. Numerical results on real data are presented. This cyclic planning is helpful in determining the sequence of setup decisions over time on each machine in a four monthly cycle. The batch quantities can then be adjusted to take care of dynamic variations in demand to a reasonable extent, as in the previous work of Caie and Maxwell. The use of LP in this context can be valid to a certain extent, which is indicated.