A TWO-WAREHOUSE INVENTORY MODEL FOR ITEMS WITH IMPERFECT QUALITY AND QUANTITY DISCOUNTS

2011 ◽  
Vol 28 (02) ◽  
pp. 147-161 ◽  
Author(s):  
TIEN-YU LIN
Keyword(s):  
Inventory Model ◽  
The Other ◽  
Quantity Discounts ◽  
Storage Space ◽  
Lot Size ◽  
Numerical Examples ◽  
Purchasing Cost ◽  
Imperfect Quality ◽  
Lot Sizes

In this paper, a two-warehouse inventory model for items with imperfect quality and all-unit quantity discounts was developed. In practice, the supplier usually offers quantity discounts to encourage the retailer ordering larger lot sizes and thus, extra storage space is needed for the retailer. Two levels of storages, owned-warehouse and rented warehouse, are considered in this study to store bulk quantities. We develop two algorithms to determine the optimal lot size and purchasing cost: one is based on the work of Render et al. (2003) and the other is similar to the method proposed by Goyal (1995). Two numerical examples are provided for illustration, in which we show that our algorithms require fewer iterations than that of the modified procedures based on the work of Render et al. (2003).

scholarly journals A profit jump inventory model for imperfect quality items with receiving reparative batch and order overlapping in dense fuzzy environment

2021 ◽  
Vol 55 (2) ◽  
pp. 723-744
Author(s):  
Sujit Kumar De ◽  
Gour Chandra Mahata
Keyword(s):  
Deterministic Model ◽  
Classical Method ◽  
Profit Maximization ◽  
Extensive Study ◽  
Inventory Model ◽  
Purchasing Cost ◽  
Imperfect Quality ◽  
Holding Costs ◽  
Fuzzy Environment ◽  
Imperfect Items

This paper presents an economic order quantity (EOQ) inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a dense fuzzy environment Here, the imperfect items are identified by screening and are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterwards, the items are returned to the supplier to be reworked. Also, discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error free. An order overlapping scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. However, we assume the total monthly demand quantity as the dense fuzzy number because of learning effect. Moreover, first of all a profit maximization deterministic model is developed and solve by classical method. Fuzzifying the final optimized function via dense fuzzy demand quantity we have employed extended ranking index rule for its defuzzification. During the process of defuzzification we make an extensive study on the paradoxical unit square of the left and right deviations of dense fuzzy numbers. A comparative study is made after splitting the model into general fuzzy and dense fuzzy environment. Finally numerical and graphical illustrations and sensitivity analysis have been made for its global justifications.

THE EFFECT OF CREDIT PERIOD ON THE OPTIMAL LOT SIZE FOR DETERIORATING ITEMS WITH TIME VARYING DEMAND AND DETERIORATION RATES

2005 ◽  
Vol 22 (02) ◽  
pp. 211-227 ◽  
Author(s):  
HORNG-JINH CHANG ◽  
CHUNG-YUAN DYE
Keyword(s):  
Inventory Model ◽  
Deteriorating Items ◽  
Simple Solution ◽  
Future Research ◽  
Time Varying ◽  
Lot Size ◽  
Credit Period ◽  
Numerical Examples ◽  
Varying Demand ◽  
Ordering Quantity

In this paper, we present an inventory model for deteriorating items with time varying demand and deterioration rates when the credit period depends on the retailer's ordering quantity. We also provide simple solution procedures for finding the optimal replenishment period and show in a rigorous way that the policy suggested is indeed optimal. Further, we use numerical examples to illustrate the model and conclude the paper with suggestions for possible future research.

Optimization of Inventory for Optimal Replenishment Policies and Lead-Time with Time Varying Demand

2016 ◽  
pp. 201-221
Author(s):  
Kaushik Kumar ◽  
Supriyo Roy
Keyword(s):  
Inventory Management ◽  
Lead Time ◽  
Product Life Cycle ◽  
Inventory Model ◽  
Decision Variable ◽  
Time Varying ◽  
Lot Size ◽  
Solution Approach ◽  
Purchasing Cost ◽  
Increasing Demand

Considering a single period inventory management problem used in the distribution channel to represent consumer demand for marketing/sales of a product, attempt is made to develop a deterministic inventory model with time-varying increasing demand that may be used to reflect sales in different phases of a product life cycle in the competitive market. We propose inventory model assuming replenishment cost is to be linearly dependent on lot size and purchasing cost per unit item is dependent on lead time. Lead time is taken as decision variable. Shortages are allowed to backlog and to lose partly. Our objective is to cumulatively evaluate optimal replenishment lot-size, order time and lead-time for maximization of total profit. Considering the complexities of the proposed model, we propose a heuristic solution approach by developing an ERCM Genetic Algorithm based on ranking section, elitism, whole arithmetic crossover and non-uniform mutation dependent on the age of the population. This heuristics are easy to compute and practical to implement, and perform well in numerical trials.

Supply Chain Coordination under Price Competition

2011 ◽  
pp. 226-248
Author(s):  
S.P. Sarmah ◽  
Santanu Sinha
Keyword(s):  
Supply Chain ◽  
Steady State ◽  
Price Competition ◽  
Supply Chain Coordination ◽  
The Other ◽  
Coordination Mechanism ◽  
Quantity Discounts ◽  
Numerical Examples ◽  
Retail Prices ◽  
Perfect Channel

This chapter analyzes the coordination and competition issues in a two-stage supply-chain in which a vendor distributes a product to two different retailers who compete on their retail prices in the same market. The demand faced by each retailer not only depends on its own price, but also on the price set by the other retailer. Mathematical models have been developed to analyze the coordination mechanism. It is shown here that perfect channel coordination can be achieved by employing simultaneously quantity discounts, volume discounts and franchise fees. Further, it has been shown that under non-cooperative price competition, the steady state equilibrium is dynamically stable in nature under certain conditions. The model is illustrated with suitable numerical examples.

scholarly journals A Fuzzy Inventory Model Considering Imperfect Quality Items with Receiving Reparative Batch and Order

2020 ◽  
Vol 5 (10) ◽  
pp. 1179-1185
Author(s):  
Hesamoddin Tahami ◽  
Hengameh Fakhravar
Keyword(s):  
Fuzzy Model ◽  
Inventory Model ◽  
Purchasing Cost ◽  
Imperfect Quality ◽  
Holding Costs ◽  
Fuzzy Environment ◽  
Imperfect Items ◽  
Triangular Numbers ◽  
Order Scheme ◽  
Fuzzy Inventory

This paper presents an inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a fuzzy environment by employing fuzzy triangular numbers. It is assumed that the imperfect items identified by Screening are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterward, the items are returned to the supplier to be reworked. Also, a discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error-free. An overlapping order scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. In the fuzzy model, the graded mean integration method is taken to defuzzify the model and determine its approximation of a profit function and optimal policy. In doing so, numerical examples are rendered to represent the model behavior, and, eventually, the sensitivity analysis is presented.

scholarly journals An Inventory Model with Stock-Dependent Demand Rate and Maximization of the Return on Investment

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 844
Author(s):  
Valentín Pando ◽  
Luis A. San-José ◽  
Joaquín Sicilia
Keyword(s):  
Optimal Policy ◽  
Return On Investment ◽  
Global Optimum ◽  
Inventory Model ◽  
Selling Price ◽  
Fixed Costs ◽  
Lot Size ◽  
Inventory Cost ◽  
Purchasing Cost ◽  
Demand Rate

This work presents an inventory model for a single item where the demand rate is stock-dependent. Three fixed costs are considered in the model: purchasing cost, ordering cost and holding cost. A new approach focused on maximizing the return on investment (ROI) is used to determine the optimal policy. It is proved that maximizing profitability is equivalent to minimizing the average inventory cost per item. The global optimum of the objective function is obtained, proving that the zero ending policy at the final of a cycle is optimal. Closed expressions for the lot size and the maximum ROI are determined. The optimal policy for minimizing the inventory cost per unit time is also obtained with a zero-order point, but the optimal lot size is different. Both solutions are not equal to the one that provides the maximum profit per unit time. The optimal lot size for the maximum ROI policy does not change if the purchasing cost or the selling price vary. A sensitivity analysis for the optimal values regarding the initial parameters is performed by using partial derivatives. The maximum ROI is more sensitive regarding the selling price or the purchasing cost than regarding the other parameters. Some useful managerial insights are deduced for decision-makers. Numerical examples are solved to illustrate the obtained results.

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