Two-warehouse Inventory Model Research Articles

A two-warehouse inventory model for deteriorating items with partially backlogged demand rate under trade credit policies

A two-warehouse inventory model for deteriorating items with partially backlogged demand rate under trade credit policies

A two-warehouse inventory model with credit policy and inflation effect

This study investigates a non-instantaneous deteriorating two-warehouse inventory problem with allowable delay payments under inflation. The objective is to maximize the total profit per unit of time by determining the optimal order quantity, the product’s selling price, and the business cycle length. We developed a mathematical model to address this inventory optimization problem. Built on top of the available literature, we comprehensively considered credit policy, inflation, price- and time-dependent demand, and partial backlogged shortage in this study. By changing some parameters, we demonstrated that our model is a generalized version of several specific inventory models presented in the literature. We performed numerical examples to validate our model. Additionally, we carried out a sensitivity analysis to examine the impact of several parameters on the optimal solutions. The results highlight that if the fixed part of the demand decreases, the product’s selling price and the total profit decrease. In addition, if the setup cost decreases, the total profit increases, and vice versa. The results also demonstrate that the unit purchase cost and inflation significantly affect the average profit. To conclude, our study can potentially help firms (i) reduce the total inventory system’s setup cost, (ii) optimize unit purchase cost, and (ii) understand the influence of inflation.

Preservation technology investment: a catalyst for sustainable two-warehouse inventory model and SDG achievement

Preservation technology investment: a catalyst for sustainable two-warehouse inventory model and SDG achievement

A TWO-WAREHOUSE INVENTORY MODEL WITH REWORK PROCESS AND TIME-VARYING DEMAND

A two-warehouse inventory model with deteriorating items and rework process with time varying demand rate is presented. The Last-In-First-Out (LIFO) and First-In-First-Out (FIFO) policies are considered with the assumption that the holding cost is higher in the rented warehouse (RW) compared to the owned warehouse (OW). The aim of the proposed model is to determine the optimum values of time in a production cycle that will minimise the total relevant cost, TRC*. We have utilised Microsoft Excel Solver as a solution tool, in which the generalised reduced gradient (GRG Nonlinear) method has been chosen as the solving method. The result is further verified using the built-in function in the Mathematica software. We observed that given same changes are made to the parameters in both the LIFO and FIFO systems, a lower total relevant cost, TRC* is obtained in the LIFO system. This shall mean that the LIFO system is less expensive than the FIFO system, provided that the holding cost in RW is higher than the holding cost in OW. The flow of inventory in the LIFO system suggests that items stored last in the owned warehouse will be dispatched first. This is an important factor for manufacturers in ensuring that items are distributed at optimal freshness.

Preservation Technology Investment: A Catalyst for Sustainable Two-Warehouse Inventory Model and SDG Achievement

Preservation Technology Investment: A Catalyst for Sustainable Two-Warehouse Inventory Model and SDG Achievement

Pythagorean Fuzzy Storage Capacity with Controllable Carbon Emission Incorporating Green Technology Investment on a Two-Depository System

Global warming is mainly caused by carbon emissions. Currently, fewer countries are concentrating on reducing carbon emissions. The primary strategy utilized by numerous countries to achieve carbon emissions reduction is the carbon tax policy. With this in mind, a sustainable two-warehouse inventory model was taken carbon tax into account for a controllable carbon emissions rate by investing in green technology initiatives under uncertain emission and cost parameters. The globe is currently experiencing an eco-friendly period. Many individuals are interested in purchasing natural or herbal items since they are made from natural sources and do not affect the environment. The demand for products made with herbal or natural ingredients is considered eco-friendly demand. This study examines a two-warehouse inventory model of deteriorating commodities with price and marketing-dependent eco-friendly demand. The inventory system is presented to handle the inventory in the depository with last-in-first-out and first-in-first-out strategies. After comparing both the policies under deterioration rate and holding cost, this study recommended a suitable dispatch policy. Interval-valued numbers and fuzzy numbers are the mathematical techniques that deal with uncertainties, so this model’s emission and cost parameters are taken as interval-valued numbers, and the storage capacity of the owned warehouse is a Pythagorean fuzzy number. The optimal solution for the two-warehouse inventory system is evaluated by taking the parametric form of interval-valued cost parameters and the new concept of the ranking function of triangular Pythagorean fuzzy numbers. Numerical results prove that emissions are reduced by 87% under green technology investment in both policies. As a consequence, in the FIFO policy, the total cost of the two-warehouse inventory system decreases by 34.45% and cycle length increases by 5.72%, and in the LIFO policy, the total cost of the two-warehouse inventory system decreases by 34.42% and cycle length increases by 11.19%. Sensitivity analysis of the key parameters has been performed to study the effect of various parameters on the optimal solution.

Quality and selling price dependent sustainable perishable inventory policy: Lessons from Covid-19 pandemic

This paper addresses the impact of the Covid-19 lockdown on the warehousing of perishable items facing demand-side shocks, mainly those with selling price and product quality dependent demand, for example, fresh fruits, meats, vegetables, packed foods, etc. Along with demand-side issues, such an inventory system consumes a significant amount of energy in terms of freshness, increasing carbon tax and dwindling the firm's total profit. We formulate two-warehouse inventory models of perishables items using the first-in-first-out (FIFO) dispatching policy under two different Covid-19 lockdown scenarios. The two-warehouse system primarily consists of an owned warehouse (OW) and a rented warehouse (RW). Two different lockdown scenarios are considered as; (i) the lockdown during the consumption of goods in OW and (ii) the lockdown during the consumption of goods in RW. The demand rate is assumed to decline and surge by a finite volume as lockdown is forced and relaxed. The proposed models help in assessing the impact of lockdown on (i) product quality, (ii) product cost, (iii) inventory level, (iv) freshness keeping efforts, (v) investment in green technologies, and (vi) carbon cap and trade policy. We determine the above six parameters to maximize the firm's total profit. The key findings of this model suggest that yield is primarily affected due to carbon cap and trade policy, lockdown period, item price, backlogging, and variation in the holding costs in OW and RW. These models may assist the small, medium, and large firms involved in perishable or cold supply chains to assess the effect of Covid-19 like disruption and take corrective measures to maximize their profit.

Impact of Green Design and inflation on a two-warehouse inventory model

Deterioration becomes a major problem in inventory modeling which increases the carbon emission and effect the climate change. The retailer will store their excess items in a rented warehouse (RW) in order to reduce deterioration and storage space limitations in their own warehouse (OW). During this investigation, shortages are also permitted. By implementing green design and product stewardship, manufactures can reduce their recycling costs. Through green design and product stewardship, a manufacturer can maintain both profit as well as an environmental concern. In this model I determined for maximizing the average profit under the influence of inflation. Numerical example is carried out by using the software Mathematica 12.0 which used to illustrate the proposed model and a sensitivity analysis is carried out to study the effect of different parameters.

Pharmaceutical drug two-warehouse inventory model under FIFO dispatching policy using ant colony optimization for travelling salesman problem

In this paper a deterministic Pharmaceutical drug inventory model for deteriorating items with two level of storage system and time dependent demand with partial backlogged shortages is developed. Stock is transferred RW to OW under bulk release pattern and the transportation cost is taken to be negligibleUnder FIFO dispatching policy Using Ant Colony Optimization for travelling salesman problem. The deterioration rates in both the warehouses are constant but different due to the different preservation proceduresUnder FIFO dispatching policy Using Ant Colony Optimization for travelling salesman problem. Holding cost is considered to be constant up to a definite time and is increases. Ant Colony Optimization for travelling salesman problemwith varying population size is used to solve the model. In this Ant Colony Optimization for travelling salesman problem a subset of better children is included with the parent population for next generation and size of this subset is a percentage of the size of its parent set.The numerical example is presented to demonstrate the development of mode land to validate it. Sensitivity analysis is performed separately for each parameter and Ant Colony Optimization for travelling salesman problem.

A Completely Backlogged Two-Warehouse Inventory Model for Non-Instantaneous Deteriorating Items with Time and Selling Price Dependent Demand

A Completely Backlogged Two-Warehouse Inventory Model for Non-Instantaneous Deteriorating Items with Time and Selling Price Dependent Demand

Supply-chain two-warehouse inventory model for deteriorating items on exponential time function with shortage and partial backlogging in inflationary environment

In this paper, we have developed two-warehouse problem of supply chain system for deteriorating items, where demand is taken as the function of stock with the exponent function of time. The Practical situation of shortage also include due to the shortage of inventory occur so frequently in daily life in the inventory problem of supply chain system. Backlogging case of shortage is also taken into consideration to make the model more concerned with real life situation. Role of inflation cannot be avoided, so we have included an inflation factor in our model too. A sensitivity analysis is given by the suitable example. To justify our result graph between various parameters is also shown in analysis part. Keywords: term, term, term.

Green design and product stewardship approach for two-warehouse inventory model

Background/Objectives: To trim down the recycling cost of any manufactured goods with the help of green design and product stewardship. Methods/Statistical analysis: For the planned EPQ (economic production quantity model) model, all costs are calculated to find total cost and this total cost is optimized with the help of the Hessian matrix. Sensitivity analysis is also carried w.r.t. different parameters, to illustrate the impact of these parameters on the proposed model. The convexity of the total cost function is also checked with the help of mathematical software Mathematica 9.0. Findings: Major finding of the proposed model are as follows: (i) Increase in the number of recycles results in the reduction of the total cost. (ii) Product stewardship parameter has a negative effect on total cost as the PS increases from 1 to 4 units, total cost decreases from 5926.00 to 5918.96 units (see Table 9 ) (similar findings can be written for numeric example 1 after correcting it). (iii) Green design costs have a positive effect on total cost, as the green design cost increases from 3 to 6 units, total cost also increases from 5918.49 to 5920.37 units (see Table 10 ). (iv) increase in the number of recycles results in the reduction of the total cost, as the number of recycles increases from 20 to 50 units total cost decreases from 5922.87 to 5919.12 units (see Table 11 ). Novelty/Applications: The Study of the effects of recycling by this green design and product stewardship approach makes the proposed model distinctive from the existing methods. The proposed model applies to eco-friendly manufacturing items with green design and product stewardship. Keywords: Green design; product stewardship; production model; own warehouse (OW); rented warehouse (RW); shortage; deterioration

Retailer’s ordering policy for demand depending on the expiration date with limited storage capacity under supplier credits linked to order quantity and discounted cash flow

ABSTRACT Many products deteriorate with time and have a maximum lifetime. An expiration date will be marked. And then the product will no longer be sold after the expiration date. Thereafter, the demand rate for the deteriorated item will near zero as its expiration date is due. Thus, to consider the demand rate incorporates with the expiration date is practical. Furthermore, as the storage capacity is limited, the retailer needs to rent a warehouse to store the excess quantities than can be stored. Consequently, to consider a two-warehouse inventory model is necessary. Nowadays, the supplier often provides a cash discount or permissible delay in payments to its retailers, if the order quantity attains a certain amount. Likewise, the retailer also provides a downstream trade credit period to his customers. In addition, the cost is usually affected by the present value of time. For these reasons considered, a supplier-retailer-customer chain model here is established. The main task of this research is to find the optimal replenishment cycle and order quantity to keep the present value of the total relevant cost per unit time as minimum as possible. Numerical examples are performed for illustration and sensitivity analysis on the expiration date is conducted.

Two-warehouse inventory model for deteriorating items with partial backlogging and advance payment scheme

Advance payment has a great influence on making the optimal decision in an inventory system. Two-warehouse inventory system is another imperative factor in inventory analysis. Due to competitive marketing situation, the position of a warehouse performs a significant role in business strategy. Generally, retailers want to find a shop in a popular marketing place. So, they need an additional store room due to insufficient space in a popular marketplace. Also, we have considered the advance payment scheme which is made by equal installment up tontimes before receiving the products. Using all of these concepts in together, we have developed a two-warehouse inventory model for deteriorating items with advanced payment scheme. Shortages are allowed with a constant partial backlogging rate. Demand of the product is dependent on selling price. We have presented this physical problem in mathematically and solved. Also, we proved the optimality mathematically as well as graphically and proposed one theorem in order to show the optimality in theoretically. We have supplied a numerical example to illustrate the proposed inventory model. To validate the numerical result of the proposed model, we have plotted 2D and 3D graphs by using MATLAB and observed these satisfy the numerical result. Finally, we have performed sensitivity analysis changing one parameter and keeping others the same.

A two-warehouse EOQ model with interval-valued inventory cost and advance payment for deteriorating item under particle swarm optimization

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.

Optimal Ordering Policy for Deteriorating Items with Limited Storage Capacity under Two-Level Trade Credit Linked to Order Quantity by a Discounted Cash-Flow Analysis

Nowadays, the supplier often provides cash discount or permissible delay in payments to its retailers, if the order quantity attains a certain amount. Likewise, the retailer also provides a downstream trade credit period to his customers. In practice, as the supplier provides price discounts for bulk purchases, the retailer may purchase more goods than can be stored in its owned warehouse and store the excess quantities in a rented warehouse. Thus, a two-warehouse inventory model is needed to be considered. Further, the cost is usually affected by the present value of time and products deteriorate as time increases. Therefore, this paper develops a supplier-retailer-customer chain inventory model in which 1) two-level trade credit linked to order quantity is considered; 2) storage capacity is limited; 3) the effect of inflation and time value of money by a discounted cash-flow analysis is taken into account. The demand rate is linearly increasing with time and the deterioration rate is constant. Based on the viewpoint of cost minimization, the objective is to find the optimal replenishment cycle and order quantity to keep the present value of the total relevant cost per unit time as minimum as possible. The research shows that in each case discussed, the optimal solution for each case exists uniquely. Finally, numerical examples are provided for illustration and some managerial insights based on the numerical results are also presented.

A volume flexible two-warehouse model with fluctuating demand and holding cost under inflation

This article develops a two-warehouse inventory model for decaying items under a volume flexible production system. The variable demand rate is taken into consideration. Unit production cost is considered to be dependent on production rate, tool cost and dye cost. The own warehouse is taken of fixed capacity. The objective of this study is to determine the optimal schedule, for this purpose solution procedure is provided. A numerical assessment with sensitivity of different system parameters is also given to illustrate the concept of the model.

Beyond LIFO and FIFO: Exploring an Allocation-In-Fraction-Out (AIFO) policy in a two-warehouse inventory model

The classical formulation of a two-warehouse inventory model is often based on the Last-In-First-Out (LIFO) or First-In-First-Out (FIFO) dispatching policy. The LIFO policy relies upon inventory stored in a rented warehouse (RW), with an ample capacity, being consumed first, before depleting inventory of an owned warehouse (OW) that has a limited capacity. Consumption works the other way around for the FIFO policy. In this paper, a new policy entitled “Allocation-In-Fraction-Out (AIFO)” is proposed. Unlike LIFO and FIFO, AIFO implies simultaneous consumption fractions associated with RW and OW. That said, the goods at both warehouses are depleted by the end of the same cycle. This necessitates the introduction of a key performance indicator to trade-off the costs associated with AIFO, LIFO and FIFO. Consequently, three general two-warehouse inventory models for items that are subject to inspection for imperfect quality are developed and compared – each underlying one of the dispatching policies considered. Each sub-replenishment that is delivered to OW and RW incurs a distinct transportation cost and undertakes a 100 per cent screening. The mathematical formulation reflects a diverse range of time-varying forms. The paper provides illustrative examples that analyse the behaviour of deterioration, value of information and perishability in different settings. For perishable products, we demonstrate that LIFO and FIFO may not be the right dispatching policies. Further, relaxing the inherent determinism of the maximum capacity associated with OW, not only produces better results and implies comprehensive learning, but may also suggest outsourcing the inventory holding through vendor managed inventory.

A credit policy approach in a two-warehouse inventory model for deteriorating items with price- and stock-dependent demand under partial backlogging

Advertisement of the product is an important factor in inventory analysis. Also, price and stock have an important role to attract more customers in the competitive business situations. Trade credit policy is another important role in inventory analysis. We have combined these three factors together in a two-warehouse inventory model and represented it mathematically. In addition, we have added deteriorating factor of our proposed problem with price- and stock-dependent demand under partial backlogged shortage and solved. The frequency of advertisement is considered constant for a year in this paper. The proposed model is highly nonlinear in nature. Due to highly nonlinearity, we could not find the closed form solution. In this paper, trade credit facility is taken in the perspective of retailer, and all the possible cases and subcases of the model are discussed and solved using lingo 10.0 software. The results of sensitivity analysis prove the effectiveness of the proposed model.

Two-warehouse inventory model for deteriorating items with demand influenced by innovation criterion in growing technology market

One of the major concerns for the technology market is the demand volatility and its impact on inventory policies. Demand volatility in the technology sector may arise due to many factors namely customer choices, competition, growing market size, and so on. Often companies use rented warehouses to absorb any fluctuations in demand. Unfortunately, warehouse and inventory researches ignore the phenomenon of growing market size to formulate policy decisions. In this paper, we proposed a two-warehouse inventory model with deterioration for technology products with linearly increasing market size where demand follows innovation diffusion criterion. The model is based on the assumption that the holding costs in the rented warehouse are more than the own warehouse. A simple solution procedure also discussed to solve nonlinear cost function. Numerical example and sensitivity analysis are also used to describe the utility of the model.