Optimal buffer space for a periodic review production/inventory system with inventory-dependent production rate

This paper considers the problem of designing a feeding buffer included in a manufacturing system, in combination with a manufacturing shop equipped with multiple pallets where items (raw material) are periodically delivered in batches, according to the “order up to R” inventory policy from a central warehouse to the local feeding buffer and then loaded by pallet for processing at the manufacturing shop whenever pallets are available. The objective is to determine the optimal storage capacity of the feeding buffer, for which the problem analysis is made in a periodic-review inventory model approach under the assumptions that demand rates at the manufacturing shop are dependent on on-hand raw-item inventory (state-dependent) and the periodic review interval is given. In the problem analysis, a sufficient condition for the total cost function to be convex is derived. Therewith, the problem solution is found so as to minimize the sum of the expected inventory holding costs and the expected production loss (due to raw-item shortage) costs.