An Optimal Batch Size for a Production System Operating Under a Fixed-Quantity, Periodic Delivery Policy

• Published in: The Journal of the Operational Research Society 1994-08, Vol.45 (8), p.891-900
• Main Authors: Sarker, Bhaba R., Parija, Gyana R.
• Format: Article
• Language: English
• Subjects: Batch processing; Business and Management; Capital costs; Carrying costs; Case-Oriented Paper; Case-Oriented Papers; Cost functions; Economic Manufacturing Quantity; Finished goods; Fixed-Quantity Delivery; Inventories; Inventory control; Management; Manufacturing output; Mathematical models; Operations research; Operations Research/Decision Theory; Optimization techniques; Order quantity; Production; Production costs; Production planning; Raw material costs; Raw materials; Shipments; Studies
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/jors.1994.141

A manufacturing system which procures raw materials from suppliers and processes them to convert to finished products is considered here. This paper develops an ordering policy for raw materials to meet the requirements of a production facility which, in turn, must deliver finished products demanded by outside buyers at fixed interval points in time. First, a general cost model is developed considering both supplier (of raw material) and buyer (of finished products) sides. This model is used to determine an optimal ordering policy for procurement of raw materials, and the manufacturing batch size to minimize the total cost for meeting equal shipments of the finished products, at fixed intervals, to the buyers. The total cost is found to be a piece-wise convex cost function. An interval that contains the optimal solution is first determined followed by an optimization technique to identify the exact solution from this interval.