In the present day, focused commercial centers, offering exchange credit, have turned into a usually received strategy. Past inventory models under reasonable postponement in installments generally accepted that the request of the things was either consistent or simply relying on the retail cost. In this paper, we proposed to sum up, two distribution centers inventory model for crumbling things when the provider offers the retailer to defer period and thus the retailer gives to postpone period to their clients. The request design has been figured in a powerful example, which can be communicated in a straight or exponential shape. Shortages were not permitted. The differing criteria and lead time, smashing expenses were thought to be constant elements of unit cost and lead time, separately. From these, a basic iterative calculation to acquire the ideal renewal number and time booking was given. At last, numerical cases were introduced to show the model and investigation of different parameters was additionally performed. Likewise, the impact of changes in the diverse parameters in the ideal aggregate cost was graphically displayed and the suggestions were examined in details.

In this paper, an imperfect production inventory system with multi-production run for single vendor and single buyer is studied where the defective items are reworked after several production processes and there is no break down during the rework process. The model is considered for deteriorating items under two delivery policies in order to determine the delivery policy leading to the minimum holding cost of system. The objective of this model is to determine the optimal production setup, number of deliveries and lot size by minimizing the total relevant cost of the proposed vendor-buyer integrated system. To minimize the manufacturer’s and buyer’s holding cost, the supply of finished products are made in small quantities. The total relevant cost of the vendor and the buyer is derived and a numerical example is presented to demonstrate the utility of the model.

Many researchers focused on economic production quantity (EPQ) model for deteriorating items with rework of defective items in a single production run. Few of them proposed the model for multi-production inventory model under the assumptions (i) all the defective items can be reproduced as serviceable items and (ii) all the deteriorating items can be detached from the inventory through screening process. However, in real life manufacturing systems, due to controllable or uncontrollable factors, the defective items may not be reproduced as serviceable items and hence the generation of scrap (disposable) items is potential. It is possible that the internally deteriorating items like fruits, vegetables, eggs, pharmaceutical drugs, etc. pass on to customers which will make negative impact on corporate image in the global market. This paper presents a multi-production run inventory model for deteriorating items with scrap, defective items, failure rework and penalty cost for selling the deteriorating items to customers under finite planning horizon. Our objective is to determine the optimal production run, optimal finite planning horizon by minimizing the total cost of the system. A solution procedure with an algorithm is proposed and a numerical example is provided to demonstrate the applicability of the model. Finally, sensitivity analysis is provided to provide managerial phenomena of the system.