In today’s era of higher competition in the business, there are many conditions such as offered concession in bulk purchasing, seasonality, higher ordering cost, etc., which force a retailer to purchase more quantities than needed or exceed the storage capacity. So in this situation the retailer has to purchase an extra warehouse named as rented warehouse to stock the extra quantity. In this paper an inventory model for deteriorating products with selling price dependent rate is developed. The occurring shortages are assumed to be partially backlogged and cycle time is also variable. The purpose of the development of this model is to compute the amount and time of order which can optimize the total average cost of the system. A solution procedure and numerical example are presented to illustrate the implementation of the proposed study. Sensitivity analysis concerning with distinct system parameters is also presented to demonstrate the model.

This paper derives a production inventory model over infinite planning horizon with flexible but unreliable manufacturing process and the stochastic repair time. Demand is stock dependent and during the period of sale it depends on reduction on selling price. Production rate is a function of demand and reliability of the production equipment is assumed to be exponentially decreasing function of time. Repair time is estimated using uniform probability density function. The objective of the study is to determine the optimal policy for production system, which maximizes the total profit subject to some constraints under consideration. The results are discussed with a numerical example to illustrate the theory.

The objective of this work is to generalize the three echelon supply chain model proposed by Jaber and Goyal (2008) [Jaber, M. Y., & Goyal, S. K. (2008). Coordinating a three-level supply chain with multiple suppliers, a vendor and multiple buyers. International Journal Production Economics, 116, 95-103.] for multi-items where single item was considered in production and distribution. This paper develops the coordination amongst different parties in a three-echelon supply chain with a centralized decision process. Producer, suppliers and retailers are the parties of the supply chain where multiple suppliers deliver various types of raw materials to a producer; producer produces different types of items, multi-items, in different units of the factory and supplies the items to multiple retailers. Different deterioration rates for finished items and raw materials are also considered. The model developed of this paper guarantees that the local costs for the members either remain the same as before coordination, or decrease as a result of coordination. A numerical example along with graphical illustrations is considered and the sensitivity analysis is provided to test the feasibility of the proposed model.

In this paper, an attempt is made to characterize the preservation technology for deteriorating items to reduce the deterioration rate. This model assumes a single producer and single supplier and formulates a production model with a time varying rate of deterioration rate. Here production and demand are treated as a fuzzy variables and total cost is minimized for both the crisp and fuzzy model. Shortage is allowed on the supplier’s part, which is partially backlogged. A solution procedure is presented to determine an optimal replenishment cycle and total cost per unit time, which is a convex function of preservation technology cost. Results have been validated with relevant example. In a way, the proposed model provides a unique theory to reduce the deterioration rate for the production model.

Quantity discount is a usual term in business and has been a topic of interest for a long time, but have received very little attention. Many vendors offer different schemes to their customers to increase the existing size of order, which results in higher annual sale for the vendor and a lower purchasing price for the retailer. Therefore, the buyer adjusts his/her selling price, which influences the demand for the product. The objective of this paper is to develop an inventory model for deteriorating products with quantity discount and partial backlogging to determine the optimal ordering quantity for the retailer optimizing the total cost or profit of the associated model. A numerical example is also given to illustrate the model and its significant features.

In this paper, we present a model for time dependent demand with multiple productions and rework setups. Production is demand dependent and greater than the demand rate. Production facility produces items in m production setups and one rework setup (m, 1) policy. The major reason of reverse logistic and green supply chain is rework, so it reduces the cost of production and other ecological problems. Most of the researchers developed a rework model without deteriorating items. A numerical example and sensitivity analysis is shown to describe the model.

In this paper we develop an inventory model for deteriorating items with price sensitive demand. Generally the vendor offers a cash discount or fix time period to the retailer to pay all the dues. According to the availability of money the retailer chooses his/her option. In this paper we discuss the possible cases of permissible delay and cash discount. The shortages are allowed in this model and are partially backlogged. Holding cost is considered as varying function of time, which reflects a more realistic concept. The purpose of this study is to optimize the overall cost of the system and to compute optimal ordering quantity. Numerical examples for different cases are also presented to illustrate the study. A sensitivity analysis with regard to distinct associated parameters is shown to make sure the constancy of the model.

In this paper, we explored an economic production quantity model (EPQ) model for finite production rate and deteriorating items with time-dependent trapezoidal demand. The objective of the model under study is to determine the optimal production run-time as well as the number of production cycle in order to maximize the profit. Numerical example is also given to illustrate the model and sensitivity analyses regarding various parameters are performed to study their effects on the optimal policy.

This paper addresses a multi items volume flexible system for time dependent decaying items with the concept of machine breakdown and imprecise environment. In this study, partially backlogged shortages have been discussed. All the costs are fuzzified with signed distance method. Numerical examples are given to illustrate the theoretical results and sensitivity analysis is given to validate the results for various parameters.

In this paper, we develop a two-warehouse imperfect production model under two cases: (i) model starts with shortages (ii) model ends with shortages. Most of the researchers proposed the models for perfect items but we develop for imperfect quality items, which is very realistic. Demand is taken as time dependent and dependent on the production. Holding cost in rented warehouse (RW) is greater than own warehouse (OW). Deterioration is taken as Weibull distribution in both OW and RW. Shortages are allowed and partially backlogged. The effect of learning on production cost is also considered. Learning from one cycle to other cycle, improve the efficiency of the organization. A numerical example including the sensitivity analysis is given to validate the results of the production-inventory model.