The consignment stock of inventories in coordinated model with generalized policy

• More general consignment stock policies for the vendor–buyer model are presented.
• Delivery schedules and the inventory patterns are described in different scenarios.
• Optimal solutions are found and illustrated with numerical examples.
• Solution procedures for optimal generalized CS-policies are given.

In this paper, coordination between a single vendor (or manufacturer) and a buyer (or retailer) via the delivery schedule in a production and distribution system is presented. A continuous deterministic model with centralized decision process is developed. To satisfy the buyer’s demands, the product is delivered in discrete batches from the vendor’s stock to the buyer’s stock and all shipments are realized instantaneously. A more general type of consignment stock (CS) policies for the vendor–buyer integrated production–distribution model is analyzed. Our model does not require equal in size shipments. The inventory patterns and the cost structure of production distribution cycles (PDC) are described in different scenarios. A comparative study of the results shows that the generalized CS policies perform better. Considering CS-policies Braglia and Zavanella (2003) ask about a possibility of cost reduction by delaying a number of late deliveries. Unfortunately, a negative answer was given by Zanoni and Grubbström (2004). We verify this problem to obtain a positive answer in more general setting. A solution procedure is developed to find optimal generalized CS-policy for the problems with nonequal and equal in size deliveries. Optimal solutions are found and illustrated with numerical examples.