Own Warehouse Research Articles

A Two-Warehouse Inventory System with Time-Dependent Demand and Preservation Technology

Because of rapid environmental changes in current worldwide society, preserving technique is becoming increasingly crucial. With the aim to examine this idea, we created a model for two-warehouse inventory system that incorporates preservation technique investments. The model considers time as a linear function representing the rate of demand. Time-dependent demand is a common feature in many industries, where demand fluctuates over time due to various factors such as seasonality and market trends. The stock is kept in the restricted storage area (OW) and other warehouse (rented) is utilized for keep any excess stock that exceeds the OW's storage limit. The stock in RW is consumed first, followed by the stock in OW, as the cost of holding of the rented warehouse (RW) is more than that of the owned warehouse (OW). This paper does not allow for shortages. We use numerical simulations to illustrate the effectiveness of our proposed model under various parameters.

Three warehouse inventory model for non-instantaneous deteriorating items with quadratic demand, time-varying holding costs and backlogging over finite time horizon

This paper presents a novel sustainable inventory model tailored for non-instantaneous deteriorating items, incorporating quadratic demand and time-dependent holding costs. Notably, the model accounts for shortages over a finite time horizon, simulating real-world scenarios. The inventory management the strategy involves distributing products across three warehouses: the Own Warehouse (OW) and two Rental Warehouses (RW), with applications spanning supermarkets, bakeries, malls, and floral businesses. The primary objective is minimizing total costs to enhance consumer satisfaction and bolster profits. The theoretical framework is substantiated through numerical examples, focusing on the critical finding regarding optimal total cost. A special methodology is employed to balance inventory dynamics amidst various warehouses, optimizing resource allocation and mitigating shortages. Furthermore, a comprehensive sensitivity analysis using MATLAB Software unveils the repercussions of parameter modifications, providing valuable insights for decision-makers in diverse industrial settings.

A Study on Two-Warehouse Inventory Systems with Integrated Multi-Purpose Production Unit and Partitioned Rental Warehouse

A study of two warehouse inventory systems with a production unit is developed in this article with some constraints which are of practical applicability to optimize the total production cycle and its cost. A production unit evolves in three different states to retain its quality and prolong its lifetime: the state of producing items, the state of reworking the identified defective items, and the state of being idle. It processes the items up to a certain time point. The screening process starts immediately after a product comes out of the production unit. The classified non-defective items are first stored in own warehouse (OW), after filling to its maximum capacity, and the remaining items fill in the first block RW1 of the rental warehouse RW. All identified defective items are stored in the second block RW2 of RW. The holding cost of an item is higher in RW than OW. All defective items are sent to the production unit for re-do processes as a single lot immediately after the stop of the production and re-do items are stored in RW1 to satisfy the demand. The items in the RW1 are of higher priority in satisfying the demands after the stop of the production unit in producing new items as to deduce the total cost. Demand is assumed as both time and advertisement dependent and is encouraged once production starts. The deterioration rate differs in both warehouses. No backlog is entertained. The study is directed to achieve optimum total cycle cost towards the attainment of the optimum production time slot and the entire cycle of the system. We have arrived at explicit expressions for the total cost function of the entire production cycle. An analytic optimization process of the discriminant method is employed in the form of an algorithm to arrive at the optimum total cost. It provides a numerical illustration of a specific environment. The implications of the current research work are as follows. The optimum utility of production units in three different states in arriving at the optimum total cost is extensively studied with respect to deterioration, demand, and production rates. It also examined the influence of fluctuating deterioration, demand, and production parameters in arriving at optimum deterioration cost, holding cost, and total cycle cost, as they have important managerial insights. The effect of rental charges on the optimum total cost is examined as the system is used for multi-purpose storage.

A Study of a Two Storage Single Product Inventory System with Ramp Type Demand, N-Phase Prepayment and Purchase for Exigency

This model considers a two-warehouse inventory system of deteriorated items with ramp-type demand and a constant rate of deterioration. It is maintained a rental warehouse (RW) of infinite capacity to load the excess items of replenished goods after filling the items of finite capacity in the own warehouse (OW). Retailers are encouraged to opt for the prepayment option of paying their purchase cost in equal installments prior to the delivery of the ordered items with a considerable discount, which will ensure the purchase guarantee of their orders. The slotted backlog interval of the stock out period is handled in two different ways to retain the customers and ease their impatience. Customers in the first slot of the stock out period are satisfied by the emergency purchases from local suppliers with high purchasing costs to avoid losing customers. Customers in the next slot are satisfied immediately after the next replenishment point. Essential measures of the system are derived: optimal ordering quantities from both regular and local suppliers; replenishment cycle length; and a partitioned backlog interval. A numerical example is given along with the optimal solutions for a particular environment with sensitive analysis in order to validate the model’s efficacy.

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.

A Green Approach—Cost Optimization for a Manufacturing Supply Chain with MFIFO Warehouse Dispatching Policy and Inspection Policy

The present paper considers a manufacturing supply chain of deteriorating type inventories. The problem addresses the extra rented warehouse (RW) to store extra inventories if the manufacturer is producing more inventories than their owned warehouse (OW) capacity. Now, the problem is which inventories should be used first with minimum cost and minimum deterioration. To solve this problem, we have assumed a MFIFO (mixed first in first out) dispatching policy and constant demand rate over a finite time horizon. Along with these we have also assumed an inspection policy during the supply chain to separate deteriorated items and a carbon tax policy is also considered to control carbon emissions. The rate of deterioration depends on the number of inspections. If the number of inspections increases, it minimizes the rate of the decaying process. Due to the adoption of the inspection policy, the supply chain moves toward a green supply chain as it removes deteriorated inventories that minimize further decay by contact, and simultaneously separated deteriorated products can be utilized for other purposes that solve the problem of the disposal of deteriorating inventories and reduce emission generation. We have also established the uniqueness of the established model. The motto of solving the mathematical model is to find the values of the optimum value of N, the number of cycles, and n, the number of inspections that helps to minimize total cost. At last, we illustrate the result with the help of a numerical example.

Effect of Inflation and Permitted Three-Slot Payment on Two-Warehouse Inventory System with Stock-Dependent Demand and Partial Backlogging

This study examines the effect of monetary inflation for a two-warehouse single-product inventory system, in which items are stored in a limited capacity Own Warehouse (OW) and an unlimited capacity Rental Warehouse (RW). Demand for an item is considered stock dependent. Items may deteriorate at a different constant rate in both warehouses. Shortages are allowed in the stock-out period and are partially backlogged and satisfied in the next replenishment point. The supplier permits flexible payment options for the retailer to pay the amount in three equal payments at different time points. The retailers’ preferred payment option is as follows: the first payment is prior to the replenishment point with some discount; the second payment is one-third of the total purchasing cost, which is paid at the time of the replenishment epoch; and the third payment is after the replenishment point and before the start of the next cycle, with some penalty. The influence of inflation on the cost calculation is considered, and an analytic expression for optimal minimal cost is explicitly derived from this. We performed arrived sensitivity analysis to discern the effects of the inflation and backlogging rates, as well as the effects of the discount rate on purchasing cost, and the effects of penalties upon the late payment of purchasing costs in optimizing the total cost.

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.

An integrated inventory model with capacity constraint under order-size dependent trade credit, all-unit discount and partial backordering

In today’s competitive business situation, the supplier frequently offers his or her retailers a permissible delay period (i.e., trade credit) to stimulate sales. In addition, the capacity of any warehouse is limited in practice, thus the retailer needs an additional rented warehouse (RW) to store the excess units when the order quantity exceeds the capacity of the own warehouse (OW). Furthermore, with the globalization of the marketing policy, the supplier may provide the retailer with a discounted price if the quantity of purchase is large enough. Considering all of the factors mentioned above, in this paper we study an integrated inventory model with capacity constraint under order-size dependent trade credit and all-units discount. Shortages are allowed and partially backordered. In addition, the unit production cost, which is a function of the production rate, is considered. An algorithm is developed to determine the optimal production and replenishment policies for both the supplier and the retailer. Finally, numerical examples are presented to illustrate theoretical results. Sensitivity analysis of the major parameters are performed and some insights are obtained.

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.

An inventory model under linked-to-order hybrid partial advance payment, partial credit policy, all-units discount and partial backlogging with capacity constraint

A profit maximizing economic order quantity (EOQ) model is studied under linked-to-order hybrid prepayment and delay payment scheme considering the practical scenario that the capacity of the retailer's own warehouse (OW) is limited. Shortages are allowed which are accumulated partially during the stock out period. The main objective is to decide whether a rented warehouse (RW) is needed to obtain the optimal ordering and replenishment policies for a retailer. The closed-form optimal solutions are found examining all possible cases and an algorithm is constructed to achieve the global optimal solutions for the retailer. Finally, some management insights are drawn by observing the applicability of the developed algorithm and also by performing sensitivity analyses on different parameters.

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

Impact of Imperfect Quality Items on Inventory Management for Two Warehouses with Shortages

Generally, the majority of the inventory models work on the concept that overall units produced must be perfect in terms of quality and that the storage capacity of the warehouse is unlimited. In fact, under realistic conditions, it is not possible to manufacture products with complete perfection. Furthermore, there are always some limits associated with storage capacity of the warehouse. This paper formulates an inventory model that considers the impact of imperfect quality items and shortages. The cost of storage in rented warehouse (RW) is greater than own warehouse (OW) due to fact there are better preservation facilities in RW. This work considers that defective items are completely withdrawn after the inspection process. The purpose of this inventory model is to establish the optimal order quantity and backorder size that maximize the total profit. Some numerical examples are solved, and a sensitivity analysis is included.

Inclusion of two-warehouse production prototype for deteriorating inventory items in payments

In this study an inventory model is proposed for deteriorating items considering two separate warehouses, as own warehouse (OW) of finite dimension and the rented warehouse (RW) for keeping the extra elements higher than the specified accommodation of the OW in practice. A lower deterioration rate is provided by the RW compared to OW due to its better preserving amenity. Also, the holding cost per unit in OW is lower compared to RW. In this paper an inventory model is considered for deteriorating items with inclusion of a two-warehouse management with linear demand rate and delay in payment. The objective of this work is to obtain the best fit replenishment strategies with minimisation of the total inventory cost. Numerical experiments are conducted with the developed mathematical model considering various parameters such as order, units and year. A sensitivity analysis is made to obtain optimal solutions with the change of parametric values with time.

Multi-item two warehouse inventory model for deteriorating item under partial credit period via Contractive Mapping Genetic Algorithm and PSO

Present study proposes a two warehouse ordering policy for multi-product, deteriorating items when demand is stock and selling price dependent. It is assumed that the supplier offers a full and partial trade credit for a certain fixed period to entice more customers. A retailer has its own warehouse (OW) W1 of finite capacity at the central location in the city and a rented warehouse (RW) W2 of infinite capacity situated just outside the city. Units are continuously transferred from warehouse W2 to warehouse W1 and sold from warehouse W1. The objective of this work is to maximise the profit for different models by using contractive mapping genetic algorithm (CMGA) and particle swarm optimisation (PSO). The order quantity, selling price and refilling point at the first warehouse are considered as the decision variables to maximise the objective. Mathematical models are formulated by using two heuristic techniques and illustrated with a numerical example.

A supply chain of deteriorating items with variable demand

Here two-level supply chain model is considered for a deteriorating item where the retailer’s warehouse in the market place has a limited capacity. Therefore the retailer can rent a warehouse (RW) if needed with a higher cost compared to own warehouse (OW). This model includes one wholesaler and on e retailer and our aim is to maximize the total profit. The demand rate in retailer is stock-dependent and in case of any shortages, the demand is partially backlogged. Retailer also introduces some promotional cost to boost the base demand of the item. It is established that if the wholesaler shares a part of promotional cost then channel profit as well as individual profit increase. The supply chain model is also considered for imprecise environment when different inventory parameters are fuzzy/rough in nature. In this case individual profits as well as channel profit become fuzzy/rough in nature. As optimization of fuzzy/rough objective is not well defined, following credibility/trust measure of fuzzy/rough event, an approach is proposed for comparison of fuzzy/rough objectives and a Particle Swarm Optimization (PSO) algorithm is used to find marketing decisions. Models are illustrated with numerical examples.

An inventory model for non-instantaneous deteriorating items with variable holding cost under two-storage

This paper presents a two warehouse inventory model for non-instantaneous deteriorating items under assumption that the inventory cost (including holding cost and deterioration cost) in rented warehouse (RW) is higher than those in owned warehouse (OW) due to better preservation facilities in RW. The demand and holding cost, both are taken variable and as linear increasing function of time. Shortages are allowed in the OW and completely backlogged at the next replenishment cycle. This paper mainly dealt with non-instantaneous deteriorating items with linear time dependent holding cost and demand where transportation cost from RW to OW has been incurred and is depended upon the amount of goods transported irrespective of time, distance from RW to OW and the capacity of vehicle used for transporting commodities.

A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy

It is impossible in this competitive era to assess the demand for items in advance. So, it is essential to refer to a stochastic demand function. In this paper, a probabilistic inventory model for deteriorating items is unfolded. Here, the supplier as well as the retailer adopt the trade-credit policy for their customers with the aim of promoting the market competition. Shortages are included into the model, and when stock on hand is zero, the retailer offers a price discount to those customers who are willing to back-order their demands. We consider two different warehouses in which the first one is an Own Warehouse (OW) where the deterioration is constant over time and the other is a Rented Warehouse (RW), and where the deterioration rate follows a Weibull distribution. An algorithm is provided for finding the solutions of the formulated model.Global convexity of the cost function is established which shows that our proposed model is very helpful for any supplier or retailer to finalize the optimal ordering policy. Beside of this, we target to increase the total profit for retailer by reducing the corresponding total inventory cost. The theoretical concept is justified with the help of some numerical examples. A sensitivity analysis of the optimal solution with respect to the major parameters is also provided in order to stabilize our model. We finalize the paper through a conclusion and a preview onto possible future studies.

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.

Two-warehouse partial backlogging inventory model with ramp type demand rate, three-parameter Weibull distribution deterioration under inflation and permissible delay in payments

Abstract Decay or deterioration of physical goods while in stock is a natural phenomenon in many inventory systems. The three-parameter Weibull distribution is an excellent generalization of exponential decay, which can be used for items with any initial value of the rate of deterioration and for items which starts deteriorating only after a certain period of time. To reduce the amount of deterioration and the limited storage facility in own warehouse (OW) the retailer’s is moving their excess items to store in a rented warehouse (RW). Generally it is seen that for any new brand of consumer goods coming to the market, the demand rate increases with time up to a certain period and then ultimately stabilize and becomes constant. This kind of stabilization has been termed as ’ramp-type’ demand rate. So, in this paper, we have developed two warehouse inventory models with ramp type demand rate and three-parameter Weibull distribution deterioration (ThPWD) under inflationary conditions, where permissible delay in payment is available for retailer if outstanding amount is compensated within the given credit period. Since, not all customers are willing to wait for backlogged during the shortage period, in this investigation shortages are also allowed and partially backlogged. The purpose of this study is not only to find retailer’s optimal replenishment policies but also to minimize the total average cost. Finally, a numerical example is presented to illustrate the proposed model and sensitivity analysis of the optimal solutions with respect to major parameters is carried out using the Mathematica-8.0 software.