A two-echelon production-inventory model for deteriorating items with multiple buyers

In a production-inventory system, the manufacturer produces the items at a rate, e.g. R, dispatches the order quantities to the customers in specific intervals and stores the excess inventory for subsequent deliveries. Therefore each inventory cycle of the manufacturer can be divided into two phases, first is the period of production, the second is when the manufacturer does not do any production and utilises the inventory that is in stock. One of the challenges in these models is how to obtain the inventory level of the supplier when there is deterioration. The existing literature that considers multi-echelon systems (including models with single-buyer or multi-buyer), analyses the deterioration/inventory cost of these echelons with the assumption of having huge surplus in production capacity. Then it seems acceptable to drop part of the production period which is for producing the first batch(s) for buyer(s) at the beginning of each production period. In this paper we develop a single-manufacturer, multi-buyer model for a deteriorating item with finite production rate. We also relax the assumption on the production capacity and find the average inventory of the supplier. It is shown that in case the production rate is not high, the existing models may not be sufficiently accurate. It is also illustrated that these models are more applicable to inventory systems (and not production-inventory) as they result in fairly accurate solutions when the manufacturer has much higher production capacity compared to the demand rate. Also a sensitivity analysis is conducted to show how the model reacts to changes in parameters.