Determining manufacturing batch sizes for a lumpy delivery system with trend demand

This paper considers a manufacturing system that procures raw materials and converts them to a finished product. The life cycle of the product usually has three distinct phases: increasing (inception), level (maturity) and declining (phasing out) demand. The finished products are supplied to the consumer at a fixed interval of deliveries with trend delivery quantities following the demand pattern, composed of piece-wise linear functions. This paper developed a decision rule for the manufacturer to determine the delivery quantities, the production start time and batch sizes with trend demands during increasing, level and declining phases of the life cycle of a product. It is found that when the demand is constant, the cost model becomes convex and a simple closed form solution can be obtained, but an algorithm is employed here under other cases to find a minimal cost of maintaining the system.