This study aims to investigate the multi-item inventory model in a production/rework system with multiple production setups. Rework can be depicted as the transformation of production rejects, failed, or non-conforming items into re-usable products of the same or lower quality during or after inspection. Rework is very valuable and profitable, especially if materials are limited in availability and also pricey. Moreover, rework can be a good contribution to a ‘green image environment’. In this paper, we establish a multi-item inventory model to determine the optimal inventory replenishment policy for the economic production quantity (EPQ) model for imperfect, deteriorating items with multiple productions and rework under inflation and learning environment. In inventory modelling, Inflation plays a very important role. In one cycle, production system produces items in n production setups and one rework setup, i.e. system follows (n, 1) policy. To reduce the deterioration of products preservation technology investment is also considered in this model. Holding cost is taken as time dependent. We develop expressions for the average profit per time unit, including procurement of input materials, costs for production, rework, deterioration cost and storage of serviceable and reworkable lots. Using those expressions, the proposed model is demonstrated numerically and the sensitivity analysis is also performed to study the behaviour of the model.

In this study, we develop a three echelon supply chain model for items to determine the optimal reliability and production rate, which achieves the biggest total integrated profit for an imperfect manufacturing process. Here, we have taken a supplier, a manufacturer and a retailer in which supplier supplies raw materials to manufacturer, manufacturer produces perfect and imperfect quality items because practically it happens and manufacturer supplies perfect quality items to the retailers. In production system, production facility may shift from an in-control state to an out-of-control state at any random time. The basic assumption of classical economic manufacturing quantity model is that all manufacturing items are of perfect quality but the assumption is not true in practice. The proposed study is formulated assuming that a certain percent of total product is defective. This percentage also varies with production rate and production run time. The defective items are restored in original quality by reworked at some costs to maintain the quality of products in a competitive market. Finally, numerical example and its graphical representation are given to illustrate the proposed model. Sensitivity analysis is also provided to test feasibility of the model.

Trade credit is the most succeeding economic phenomenon which is used by the supplier for encouraging the retailers to buy more quantity. In this article, a mathematical model with stock dependent demand and deterioration is developed to investigate the retailer’s optimal inventory policy under the scheme of permissible delay in payment. It is assumed that defective items are produced during the production process and delay period is progressive. The objective is to minimize the total average cost of the system. To exemplify hypothesis of the proposed model numerical examples and sensitivity analysis are provided. Finally, the convexities of the cost functions and the effects of changing parameters are represented through the graphs.

A two warehouse production inventory model is developed for deteriorating items under reliability consideration. The effect of trade credit is considered under inflation. Since, formulating a suitable inventory model is one of the major concerns for an industry, the main objective of this paper is to optimize the total related cost for reliable production process. The model is illustrated through numerical example. The sensitivity analyses of the cost function are performed due to different measures and some managerial inferences are presented.

A finite time horizon inventory problem for a deteriorating item having two separate warehouses, one with an own warehouse (OW) of finite dimension and the other with a rented warehouse (RW), is developed in fuzzy environment. Due to different preserving facilities and storage environment, inventory holding cost is considered to be different in different warehouses. The demand rate of item depends on the selling price and is displayed stocked level in own warehouse. Shortages are allowed and backlogged them partially, which depends on the duration of stock out. The stocks of RW are transported to OW in continuous release pattern. Due to impreciseness in nature, total revenue and shortage cost are assumed to be imprecise in nature too. By using the fuzzy goal programming method, multi-objective problem is converted into single objective function. The model is illustrated numerically and the results are presented in tabular form.

This paper presents a unified multi items general inventory model for integrated production of new items and remanufacturing of returned and defected items for a finite planning horizon. In this paper, a production model that takes into account learning, instantaneous deterioration rate and inflation is proposed. In addition, we also consider that the holding cost is a non-negative, non-decreasing and continuous function of time. In this model, the preservation technology is used to reduce the rate of product deterioration. A theory is developed to find the optimal solution of the proposed model; it is then exemplified with the help of several numerical examples. An efficient solution procedure is also provided to find the optimal strategy. Finally, sensitivity of the optimal solution to changes in the values of different parameters of the system and the convexities of the cost functions are also studied and represented through the graphs.

The objective of this study is to develop of an inventory policy for deteriorating items, in which demand for the products is stock dependent and the retailer invests in preservation technology to reduce the rate of product deterioration. In many real-life situations, for certain types of consumer goods, the consumption rate is sometimes influenced by the stock-level. It is usually observed that a large pile of goods on a shelf in a supermarket will lead the customer to buy more and then generate higher demand. The consumption rate may go up or down with the on-hand stock level. This paper is developed with the realistic conditions of demand, allowable credit period, partial backlogging and variable ordering cost. A solution procedure is given to find the optimal preservation technology cost and total cost of the system. A numerical example and sensitivity analysis are presented to illustrate the model.