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This research work develops a two-warehouse inventory model for non-instantaneous deteriorating items with interval-valued inventory costs and stock-dependent demand under inflationary conditions. The proposed inventory model permits shortages, and the backlogging rate is variable and dependent on the waiting time for the next order, and inventory parameters are interval-valued. The main aim of this research is to obtain the retailer’s optimal replenishment policy that minimizes the present worth of total cost per unit time. The optimization problems of the inventory model have been formulated and solved using two variants of particle swarm optimization (PSO) and interval order relations. The efficiency and effectiveness of the inventory model are validated with numerical examples and a sensitivity analysis. The proposed inventory model can assist a decision maker in making important replenishment decisions.

In supply chain management, the location of facilities, inventory control, and vehicle routing are three key components. This paper incorporates a two-warehouse inventory system into the location- inventory-routing problems (LIRPs) and develops LIRP models with two warehouses in one-level, two-level, and three-level supply chain networks. This study aims to minimize the average total costs of the models by reducing their average costs. To handle these models, two innovative hybrid algorithms, viz. Clarke and Wright—genetic algorithm (CW-GA) and Clarke and Wright—firefly algorithm (CW-FA) are put forward. Computational experiments and sensitivity analyses are conducted to compare the proposed two algorithms with Baron and test the algorithms’ effectiveness and the models’ feasibility. The management implications of this study are presented from two dimensions: model and method. Finally, future research directions and the gap between models and reality are discussed.

Generally, most of the inventory costs are not always fixed due to uncertainty of competitive market. In the existing literature, it is found that several researchers have worked on uncertainty considering inventory parameters as fuzzy valued. In this work, we have represented the inventory parameters as interval. Using this concept, we have developed a two-warehouse inventory model with advanced payment, partial backlogged shortages. Due to uncertainty, this problem cannot be solved by existing direct/indirect optimization technique. For this purpose, different variants of particle swarm optimization techniques (viz. PSO-CO, WQPSO and GQPSO) have been developed to solve the problem of the proposed inventory model by using interval arithmetic and interval order relations. Finally, to illustrate and also to validate the proposed model, a numerical example has been solved and the best found solutions (which is either optimal solution or near optimal solution) obtained from different variants of PSO have been compared. Then, a sensitivity analysis has been performed to study the effect of changes of different parameters of the model on the optimal policy.

The process of deterioration may not start immediately after the consignment reaches the go down; there generally occurs a delay. In certain cases, deterioration might begin after a certain period which may further prolong due to the introduction of better methods of inventory management. To take into cognizance of these situations, in contrast to the ordinary assumption in the existing models, we have considered that the decay in owned warehouse begins earlier than that in case of rented warehouse as the latter always provides for better inventory management and facilities. Applying these phenomena, a two-storage inventory model has been formulated with advance payment under three different situations according to different possibilities of starting times of deterioration in both warehouses. In this model, demand depends upon the selling price wherein shortages are considered partially with fixed backlogging rate. Analyzing and investigating the proposed problem, three different optimization problems are formulated and the optimality of these problems is proved theoretically. To solve the model, an algorithm is proposed. Then, to illustrate the model numerically, an example is considered and solved. Finally, post optimality is performed in order to investigate the effects of changes of different system parameters.

The formulation of classical deteriorating inventory models is done with the common unrealistic assumption that all the items start deteriorating as soon as they arrive in the warehouse. On the contrary, in a realistic environment, it has been observed that there are several items that do not deteriorate immediately. Items such as dry fruits, potatoes, yams and even some fruits and vegetables have a shelf life and deteriorate only after a time lag. Apart from this, in today’s competitive business world, the supplier usually offers a trade credit period to his retailers to attract more sales and the retailer considers it as an alternative to price discount. The present research proposes a two warehouse inventory model for non-instantaneous deteriorating items under trade credit based on the above phenomena, where the demand rate is assumed to be a function of the selling price. Further, shortages are completely backlogged and the interest on shortages at the beginning of the cycle has also been considered. The objective of the study is to determine the retailer’s optimal replenishment policies that maximize the average profit per unit time. Conclusively, a numerical example is presented to illustrate the applicability of the proposed model. Sensitivity analysis on key parameters is provided to reveal the managerial insights.

With the convergence of innovation, technology, and supply chain, the world has been shrinking, and the retail industry is one of the largest spread across the globe in the past few decades. Consumer expectations are on priority for the retailers. Most of the retail sector deals with the items whose usefulness declines with time and reaches the expiration date, resulting in a decrease in sales and eventually diminishing revenues for the retailers. In such cases, effective replenishment decisions and ordering policies may yield a significant increase in revenues. Further, with emerging retail trends, providing trade credit is considered a price reduction tool and an alternative to price discounts. Motivated by this, an inventory model developed and analyzed for items exhibiting time-varying deterioration with partially backlogged shortages and permissible delay in payment in the two-warehouse environment. The primary objective is to obtain the optimal ordering and backlogging policies for the retailer by minimizing the relevant cost. The optimal solution is obtained, solved analytically, and the inventory model validated with the help of numerical illustrations. The sensitivity analysis of the optimal solution with respect to key parameters and the managerial implications are also provided. The model is applicable to perishable items such as baked products, fruits, vegetables, groceries, meat, and seafood, where the deterioration is time-dependent and is perceived by its expiration date.

Application of freshness preservation technologies in case of perishable inventory management can play a vital role in mitigating the losses that occur due to deterioration of perishable inventory, typical perishable inventory includes Agri-fresh products like fresh fruits, fresh meat, fresh vegetables, seafood and packed foods. In case of perishable inventory price as well as freshness both decide the demand, so supplying a fresh product at a competitive price creates more customer satisfaction and makes a firm profitable. This paper develops two warehouse dispatching policies, first in, first out (FIFO) and last in, first out (LIFO) for perishable items taking deterioration into account. Demand varies as a function of price and freshness keeping effort. As the price increases and freshness keeping efforts decreases, demand decreases, and vice versa. Stockout is allowed, and during the stockout period as the waiting time increases backlogging rate decreases exponentially. Inflation is considered while calculating different costs. The objective of this paper is to determine the optimum price per unit item and lot size to maximize the profit. The sensitivity of the models is examined through the design of experiment. The present models are applicable for perishable items that start losing their quality immediately after arriving into the system.

Abstract-Depending on demand, the selling price is the price at which the goods are offered for sale in response to their demand level. It is a pricing strategy that considers the relationship between supply and demand. The two-warehouse inventory model in the proposed model deals with perishable goods. The demands for the goods are time- and pricedependent, taking inflationary impacts into account. To improve operational effectiveness and customer happiness, the model allows for partial backlogs of shortages. The proposed model uses a positive definite Hessian matrix condition to get the best quantity and cycle length while minimising the nonlinear average total cost. This research paper conducts a numerical evaluation of the highly nonlinear average total cost using MATLAB software. Additionally, the study includes an analysis of the robustness of the results through sensitivity analysis. The conclusion drawn from the study helps summarise the essential findings and highlights the efficiency of the proposed model.

Establishing warehouses is necessary in societies where commercial activities have grown to the extent that efficient storage becomes a prerequisite for seamless exchange. Variable holding cost is a pivotal factor influencing warehouse costs, as is the dynamic nature of holding expenses, which tend to increase over time. This study focuses on an inventory model designed for goods subject to degradation, stored across two distinct warehouses (rented and owned) within a partial backlogging and inflationary economic environment. The cost associated with holding these goods is linearly dependent on time. The demand pattern in the inventory model for goods follows an exponential trajectory over time. The primary objective of the proposed model is to forecast the optimal quantity and the corresponding timeframe, thereby minimizing the overall cost. Rigorous validation of the model's outcomes is undertaken through sensitivity analysis utilizing MATLAB R2017b software, ensuring the robustness and reliability of the findings.