Optimizing total safety inventory for large transfer lines

Serial production lines are widely used in production systems. Balancing the capacities of a group of machines and connecting them by a common transfer mechanism constitutes a transfer line. Generally, the term transfer line represents a synchronized serial production line where the output from each production stage is equal to the output of the line. Because the stages are tightly linked together, loss of production due to breakdowns or defective items at any stage can temporarily stop the entire line. Consequently, transfer lines often have low efficiences. However, efficiency can be increased by adding safety inventories to decouple the stages. This paper presents a model and procedures for determining the safety inventories needed at each stage to assure that a prespecified transfer line efficiency is met and that the minimum amount of safety inventory is used. To reduce inventory carrying costs, larger inventories are arranged near the beginning of the line where the unit costs are lower than at the end of the line. Examples illustrate a solution procedure which is applicable to large transfer lines and can accommodate any theoretical or empirical probability distribution for breakdowns and production of defective items.