This paper deals with developing an inventory model for two warehouses. In today’s business era, there are various types of conditions such as discounts, bulk storage and seasonal products forcing the buyer to purchase the order more than owned warehouse capacity. To store the excess unit of purchase order, buyer arrange additional storage space called as rented warehouse. It is known that the demand of the seasonal products (as woolen garments) increases at the beginning of the season up to a certain time and then stabilizes to a constant rate for the remaining time of the season. The ramp type demand rate forces the buyer to store a higher quantity of the product at the beginning of the season. Most of the physical goods undergo decay or deterioration over time so we study deteriorating seasonal products in this paper. This two warehouse inventory model is developed with inflation and shortages. The model starts with rent warehouse, in first rent warehouse’s inventory level is depleted due to demand and deterioration. At this time own warehouse is depleted due to deterioration only. But after that the inventory level of owned warehouse is depleted due to both demand and deterioration. The shortages are considered in owned warehouse, which is partially backlogged. Numerical solution of the model is obtained to verify the optimal solution. Comprehensive sensitivity analysis has been carried out for showing the effect of variations in the parameters. The model is solved analytically by minimizing the total cost.

This study deals with an economic order quantity model to find out the optimal selling price and optimal ordering quantity for the products which deteriorates over time. The demand for the products depends on available stock level and selling price of the products. The shortages are allowed, and it is assumed that the occurring shortages are partially backlogged. Depending on the rate of backlogging two models are presented in this study. The first model assumes a constant rate of backlogging, while in second model the backlogging rate is assumed to be dependent on waiting time. Numerical example and sensitivity analysis are presented to illustrate the results of the proposed model.

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.

This paper formulates a multi-level supply chain network with a single producer, multi distributors and multi retailers during a finite planning horizon. The demand rate is assumed to be exponential function of time; shortages are allowed and completely backlogged. The stock is assumed to undergo deterioration as soon as it is produced. The production rate is dependent on demand rate and greater than the demand rate. Optimal solution for the proposed model is derived and using a numerical example, the behavior of the model is analyzed.

The purpose of these comments is to serve as a revision to the article by Khan et al. (2016) [Khan, M., Jaber, M.Y., Zanoni, S., & Zavanella, L. (2016). Vendor managed inventory with consignment stock agreement for a supply chain with defective items. Applied Mathematical Modelling, 40(15–16), 7102–7114.]. This commenting paper suggests that the expected total cost function derived in Khan et al. (2016) was incorrect, and then offers revisions to complement the shortcomings.

Today, distributing high quality perishable foods is one of the challenging issues in food industry. This paper introduces a deterministic vehicle routing problem model with multiple middle depots and proposes the freshness of perishable foods as a new concept to obtain optimal delivery routes. For the proposed mathematical model, profit maximization of delivering the product, minimization of the transportation costs and vehicle traveling time, and maximum level of delivered product perishability (loss of freshness) are considered. GAMS software is implemented to show the authority of the model. Furthermore, genetic algorithm (GA) has been developed to solve the model for large size instances. Several problems are tested in order to compare the exact and the GA solutions.

In this paper, an alternative version of the fuzzy PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) method is proposed. Differently from other studies, preference functions used in PROMETHEE method are handled in terms of fuzzy distances between alternatives with respect to each criterion. In order to indicate the applicability of this method, the method is applied for a supplier selection problem in the literature. Ranking results are similar obtained by TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and fuzzy ELECTRE (ELimination Et Choix Traduisant la REalité) methods. The implementation of the proposed method indicates that the amount of computations is decreased and decision makers can easily reach to desirable solution.

Nowadays, selecting the most appropriate location for hub is one of the most significant issues not only in road, rail and air transportations, but also in maritime. Transshipment is the fastest growing segment of the marine container market; it increases traffic flow of marine container and scope of this type of marine carriage, accordingly. In this way, determining a movement loop for the voyages of a shipping company, probes identification of container hub ports by considering different operational factors including distance to the destinations. The focus of this paper is to locate the best location for container transshipment hub in southern seas of Iran. In this paper, an MCDM model is proposed for evaluating and selecting the marine container transshipment hub port. Finally, the utilization of the proposed model is demonstrated with a real case study of Iranian main ports. The results show that the MCDM model can be used to explain the evaluation and decision-making procedures of a proper marine container hub location selection.

This paper deals with the co-ordination of a single producer, multi distributors and multi retailers for a supply chain management to get the maximum profit at minimum investment when shortages is permitted at the retailer‘s end and they are the partially backlogged. Most previous studies on supply chain have dealt with a moderately simpler chain with a single producer and a single buyer. The requirement of the producer is directly proportional to demand of the distributor, while the demand of the distributor is dependent on retailers’ requirement. This passes on rationally to the whole supply chain. The proposed model of this paper considers deteriorating items where the deterioration rate is considered as constant.

Traditional economic production quantity (EPQ) model assumes that the production products are perfect. However, this assumption does not hold for many real production systems due to several weaknesses. This paper considers production inventory model with defective items for deteriorating items. In this paper, production rate is considered to be greater than demand rate. Mathematical model is developed for finding optimal order quantity, cycle time and total profit. Moreover, a numerical example is provided to illustrate the proposed model. Next, sensitivity analysis is established to demonstrate the model developed. Finally, some conclusions and future research directions are proposed.