### Two-warehouse inventory model of deteriorating items with three-component demand rate and time-proportional backlogging rate in fuzzy environment

, 2013

"... A finite time horizon inventory problem for a deteriorating item having two separate warehouses, one with an own warehouse (OW) of finite dimension and the other with a rented warehouse (RW), is developed in fuzzy environment. Due to different preserving facilities and storage environment, inventor ..."

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A finite time horizon inventory problem for a deteriorating item having two separate warehouses, one with an own warehouse (OW) of finite dimension and the other with a rented warehouse (RW), is developed in fuzzy environment. Due to different preserving facilities and storage environment, inventory holding cost is considered to be different in different warehouses. The demand rate of item depends on the selling price and is displayed stocked level in own warehouse. Shortages are allowed and backlogged them partially, which depends on the duration of stock out. The stocks of RW are transported to OW in continuous release pattern. Due to impreciseness in nature, total revenue and shortage cost are assumed to be imprecise in nature too. By using the fuzzy goal programming method, multi-objective problem is converted into single objective function. The model is illustrated numerically and the results are presented in tabular form.

### Demand of Level Dependent Linear Trend

, 2016

"... Abstract The proposed model considers the products with finite shelf-life which causes a small amount of decay. The market demand is assumed to be level dependent and in a linear form. The model has also considered the constant production rate which stops attaining a desired level of inventories an ..."

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Abstract The proposed model considers the products with finite shelf-life which causes a small amount of decay. The market demand is assumed to be level dependent and in a linear form. The model has also considered the constant production rate which stops attaining a desired level of inventories and that is the highest level of inventories. Production starts with a buffer stock and without any sort of backlogs. Due to the market demand and product's decay, the inventory reduces to the level of buffer stock where again the production cycle starts. With a numerical search procedure the proof of the proposed model has been shown. The objective of the model is to obtain the total average optimum inventory cost and optimum ordering cycle.

### Inventory control with deteriorating items: . . .

- INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING COMPUTATIONS
, 2014

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### An inventory model of two-warehouse . . .

- INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING COMPUTATIONS
, 2011

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### Optimal Procurement Policy With Trade Credit Financing, Capacity Constraints and Stock-dependent Demand

, 2012

"... Abstract ⎯ In this paper, optimum procurement policy is worked out when trade credit is offered to the retailer by the supplier and demand is stock-dependent. The own warehouse (OW) capacity is limited and excess inventory is stored in rented warehouse (RW). The rented warehouse has modern infra-str ..."

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Abstract ⎯ In this paper, optimum procurement policy is worked out when trade credit is offered to the retailer by the supplier and demand is stock-dependent. The own warehouse (OW) capacity is limited and excess inventory is stored in rented warehouse (RW). The rented warehouse has modern infra-structure facility. Hence, the unit holding cost in rented warehouse is assumed to be higher than that in the owned warehouse. A decision rule is constructed to hire a rented warehouse or not. The uniqueness of the optimal solution is discussed. The numerical examples are presented to validate the proposed problem. The managerial insights are deduced using sensitivity analysis. It is observed that the retailer should stock more and increase time for a higher ordering cost. On the other hand, lower ordering cost facilitates the retailer to go for owned warehouse only.

### Anupam Swami

"... In this paper a two warehouse inventory model for deteriorating items is considered under assumption that the Inventory cost (including holding cost and deterioration cost) in RW (Rented Warehouse) is higher than those in OW (Owned Warehouse) due to better preservation facilities in RW. The demand a ..."

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In this paper a two warehouse inventory model for deteriorating items is considered under assumption that the Inventory cost (including holding cost and deterioration cost) in RW (Rented Warehouse) is higher than those in OW (Owned Warehouse) due to better preservation facilities in RW. The demand and holding cost, both are taken variable. Shortages are allowed in the OW and a fraction of shortages backlogged at the next replenishment cycle.This paper mainly dealt with deteriorating items with time dependent demand and variable holding cost which is constant for a definite time period and after that it increases according to length of ordering cycle in RW and remains constant in OW. Transportation cost is taken to be negligible and goods are transported on the basis of bulk release pattern. A genetic algorithm with varying population size is used to solve the model. In this GA 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. A numerical example is presented to illustrate the model and sensitivity is performed for a parameter keeping rest unchanged.

### Two Warehouse Inventory Model for Deteriorating Items with Time Dependent Demand under Inflation

"... In recent years, various researchers have discussed a two warehouse inventory system. This kind of system was first discussed by Hartely (1976) [10]. Hartely presented a basic two-warehouse model, in which the cost of transporting a unit from rented warehouse (RW) to own warehouse (OW) was not consi ..."

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In recent years, various researchers have discussed a two warehouse inventory system. This kind of system was first discussed by Hartely (1976) [10]. Hartely presented a basic two-warehouse model, in which the cost of transporting a unit from rented warehouse (RW) to own warehouse (OW) was not considered. Sarma (1983)[20] developed a deterministic inventory model with infinite replenishment rate and two levels of storage. In that model, he extended Hartely’s model by introducing the transportation cost. Murdeshwar and Sathe (1985) [16] extended this model to the case of finite replenishment rate. Dave (1988) [5] further discussed the cases of bulk release pattern for both finite and infinite replenishment rates. He rectified the errors in Murdeshwar and Sathe (1985) [16] and gave a complete solution for the model given by Sarma (1983) [20]. In the above literature, deterioration phenomenon was not taken into account. In this paper, an inventory model is developed for deteriorating items with two- warehouse, permitting shortage under inflation and time-value of money. Holding costs and deterioration costs are different in OW and RW due to different preservation environments. The inventory costs (including holding cost and deterioration cost) in RW are assumed to be higher than those in OW. To reduce the inventory costs, it will be economical for firms to store goods in OW before RW, but clear the stocks in RW before OW. The stock is transferred from the RW to the OW following a bulk release rule.

### Stock Dependent Demand

"... Abstract—This paper deals with a two warehouse inventory system under the effect of stock, price and deterioration on demand. Items stored in rented warehouse RW and owned warehouse OW, deteriorates with two different rates. A fraction of discount on the selling price is offered to enhance the deman ..."

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Abstract—This paper deals with a two warehouse inventory system under the effect of stock, price and deterioration on demand. Items stored in rented warehouse RW and owned warehouse OW, deteriorates with two different rates. A fraction of discount on the selling price is offered to enhance the demand and to reduce the loss due to deterioration in owned warehouse. The objective of this study is to determine the optimal discount policy and to deduce the optimal order quantity to maximize the profit of the system. Numerical examples have been illustrated to explore the solution of the proposed model.

### OPTIMAL REPLENISHMENT POLICY FOR DETERIORATING INVENTORY WITH TRADE CREDIT FINANCING, CAPACITY CONSTRAINTS AND STOCK-DEPENDENT DEMAND

"... This research aims at optimizing the replenishment cycle time when units in inventory deteriorate at a constant rate under a permissible delay in payments when demand is stock-dependent. It is assumed that own warehouse capacity is limited and excess inventory is stored in rented warehouse. The unit ..."

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This research aims at optimizing the replenishment cycle time when units in inventory deteriorate at a constant rate under a permissible delay in payments when demand is stock-dependent. It is assumed that own warehouse capacity is limited and excess inventory is stored in rented warehouse. The unit holding cost in rented warehouse is higher than that in the owned warehouse. The deterioration rates of items in owned warehouse and rented warehouse are different. A decision policy is worked out to make a choice of own warehouse or hire the rented warehouse. The uniqueness of the optimal solution is derived. Finally, numerical examples are presented to validate the proposed problem. Sensitivity analysis is carried out to derive managerial insights. KEYWORDS:

### A Fuzzy based Two Warehouse Inventory model for deteriorating items with Cubic Demand and different fuzzy cost parameters

"... Abstract — This paper deals with a fuzzy based two warehouse inventory model for decaying items in which demand is taken to be cubic function of time, holding cost, ordering cost, backorder costs which are fuzzy in nature. Shortages are allowed in the owned warehouse. Due to lack of historical data ..."

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Abstract — This paper deals with a fuzzy based two warehouse inventory model for decaying items in which demand is taken to be cubic function of time, holding cost, ordering cost, backorder costs which are fuzzy in nature. Shortages are allowed in the owned warehouse. Due to lack of historical data and information the probability of certain new products are not known and in that case to remove certain uncertainty fuzzy concept is used. In this context we have used triangular fuzzy numbers to represent the fuzzy parameters. Finally the model is solved mathematically and profit maximization technique is used to illustrate the system using Signed Distance method.