Scheduling to Minimize the Variance of Holding Costs in Joint Production

This paper considers the case of a product consisting of several components, each of which is batch manufactured. It assumes that the product demands occur singly, and that the components are manufactured in equal-batch quantities in a reorder level-batch quantity system. The paper is concerned with the optimal phasing of the components in order to minimize the variance of holding cost for the product. It shows that the optimal policy is independent of the order of sequencing of the components and is given when the phase lag between consecutive components in the cycle is equal to [(A_i + A_j)/∑_all iA_i](q/2), where A_i, A_j are the unit values of the components, and q is the batch quantity. A specific example is included to illustrate the three-component case and the discrete practical solution for any number of components is indicated.