scholarly journals Determining the Optimum Ordering Policy in Multi-Item Joint Replenishment Problem Using a Novel Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wen-Tsung Ho
Keyword(s):  
Cycle Time ◽  
Heuristic Algorithms ◽  
Optimal Solution ◽  
Lead Times ◽  
Joint Replenishment ◽  
Joint Replenishment Problem ◽  
Ordering Policy ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Time Division

This work investigates the joint replenishment problem (JRP) involving multiple items where economies exist for replenishing several items simultaneously. The demand rate for each item is known and constant. Shortages are not permitted and lead times are negligible. Many heuristic algorithms have been proposed to find quality solutions for the JRP. In this paper, cycle time division and recursive tightening methods are developed to calculate an efficient and optimal replenishment policy for JRP. Two theorems are demonstrated to guarantee that an optimal solution to the problem can be derived using cycle time division and recursive tightening methods. Restated, cycle time division and recursive tightening methods theoretically yield the optimal solution in 100% of instances. The complexity of cycle time division and recursive tightening methods is justO(NlogN), whereNrepresents the number of items involved in the problem. Numerical examples are included to demonstrate the algorithmic procedures.

Ordering Policy in a Two-Warehouse Environment for Deteriorating Items under Inflationary Conditions

2014 ◽  
pp. 320-338
Author(s):  
Chandra K. Jaggi ◽  
Sarla Pareek ◽  
Aditi Khanna ◽  
Ritu Sharma
Keyword(s):  
Global Economy ◽  
Aggregate Demand ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Inventory Problem ◽  
Inventory Costs ◽  
Ordering Policy ◽  
Demand Rate ◽  
Warehousing Systems ◽  
The Cost

In this chapter, the two-warehouse inventory problem is considered for deteriorating items with constant demand rate and shortages under inflationary conditions. In today’s unstable global economy, the effects of inflation and time value of money cannot be ignored as it increases the cost of goods. To safeguard from the rising prices, during the inflation regime, the organization prefers to keep a higher inventory, thereby increasing the aggregate demand. This additional inventory needs additional storage space that is facilitated by a rented warehouse. Further ahead, in the real business world, to retain the freshness of the commodity, most of the organizations adopt the First-In-First-Out (FIFO) dispatching policy. FIFO policy yields fresh and good conditioned stock thereby resulting in customer satisfaction, especially when items are deteriorating in nature. However, the two warehousing systems usually assume that the holding cost of items is more in Rental Warehouse (RW) than the Owned Warehouse (OW) due to modern preserving techniques. Therefore, to reduce the inventory costs, it is economical to consume the goods of RW at the earliest. This approach is termed the Last-In-First-Out (LIFO) approach. The objective of the present chapter is to develop a two warehouse inventory model with FIFO and LIFO dispatching policies under inflationary conditions. Further, comparison between FIFO and LIFO policies has been exhibited with the help of a numerical example. Sensitivity analysis has also been performed to study the impact of various parameters on the optimal solution.

scholarly journals An Inventory System for Deteriorating Products with Ramp-Type Demand Rate under Two-Level Trade Credit Financing

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
G. Darzanou ◽  
K. Skouri
Keyword(s):  
Existence And Uniqueness ◽  
Trade Credit ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Inventory System ◽  
Credit Policy ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Credit Financing ◽  
Ramp Type Demand

An inventory system for deteriorating products, with ramp-type demand rate, under two-level trade credit policy is considered. Shortages are allowed and partially backlogged. Sufficient conditions of the existence and uniqueness of the optimal replenishment policy are provided, and an algorithm, for its determination, is proposed. Numerical examples highlight the obtained results, and sensitivity analysis of the optimal solution with respect to major parameters of the system is carried out.

scholarly journals Discounted costs and obsolescence with the Joint replenishment problem

2022 ◽  
Vol 13 (1) ◽  
pp. 51-66 ◽  
Author(s):  
Ricardo Afonso ◽  
Pedro Godinho ◽  
João Paulo Costa
Keyword(s):  
Lot Sizing ◽  
Real Life ◽  
Progressive Increase ◽  
Sensitivity Analyses ◽  
Joint Replenishment ◽  
Total Cost ◽  
Joint Replenishment Problem ◽  
Ordering Policy ◽  
The Impact ◽  
Item Types

Real life inventory lot sizing problems are frequently challenged with the need to order different types of items within the same batch. The Joint Replenishment Problem (JRP) addresses this setting of coordinated ordering by minimizing the total cost, composed of ordering (or setup) costs and holding costs, while satisfying the demand. The complexity of this problem increases when some or all item types are prone to obsolescence. In fact, the items may experience an abrupt decline in demand because they are no longer needed, due to rapid advancements in technology, going out of fashion, or ceasing to be economically viable. This article proposes an extension of the Joint Replenishment Problem (JRP) where the items may suddenly become obsolete at some time in the future. The model assumes constant demand and the items’ lifetimes follow independent negative exponential distributions. The optimization process considers the time value of money by using the expected discounted total cost as the minimization criterion. The proposed model was applied to some test cases, and sensitivity analyses were performed, in order to assess the impact of obsolescence on the ordering policy. The increase in the obsolescence risk, through the progressive increase of the obsolescence rates of the item types, determines smaller lot sizes on the ordering policy. The increase in the discount rate causes smaller quantities to be ordered as well.

scholarly journals A study of inflation effects on an EOQ model for Weibull deteriorating/ameliorating items with ramp type of demand and shortages

2013 ◽  
Vol 23 (3) ◽  
pp. 441-455 ◽  
Author(s):  
M. Valliathal ◽  
R. Uthayakumar
Keyword(s):  
Computer Software ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Inventory Level ◽  
Decision Variable ◽  
Deterioration Rate ◽  
Eoq Model ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Ramp Type Demand

This paper deals with the effects of inflation and time discounting on an inventory model with general ramp type demand rate, time dependent (Weibull) deterioration rate and partial backlogging of unsatisfied demand. The model is studied under the replenishment policy, starting with shortages under two different types of backlogging rates, and their comparative study is also provided. We then use the computer software, MATLto find the optimal replenishment policies. Duration of positive inventory level is taken as the decision variable to minimize the total cost of the proposed system. Numerical examples are then taken to illustrate the solution procedure. Finally, sensitivity of the optimal solution to changes of the values of different system parameters is also studied.

scholarly journals A Global Optimizing Policy for Decaying Items with Ramp-Type Demand Rate under Two-Level Trade Credit Financing Taking Account of Preservation Technology

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
S. R. Singh ◽  
Swati Sharma
Keyword(s):  
Trade Credit ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Credit Policy ◽  
Preservation Technology ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Credit Financing ◽  
Delay In Payments ◽  
Ramp Type Demand

An inventory system for deteriorating items, with ramp-type demand rate, under two-level trade credit policy taking account of preservation technology is considered. The objective of this study is to develop a deteriorating inventory policy when the supplier provides to the retailer a permissible delay in payments, and during this credit period, the retailer accumulates the revenue and earns interest on that revenue; also the retailer invests on the preservation technology to reduce the rate of product deterioration. Shortages are allowed and partially backlogged. Sufficient conditions of the existence and uniqueness of the optimal replenishment policy are provided, and an algorithm, for its determination, is proposed. Numerical examples draw attention to the obtained results, and the sensitivity analysis of the optimal solution with respect to leading parameters of the system is carried out.

scholarly journals Optimal Replenishment Policy for Weibull-Distributed Deteriorating Items with Trapezoidal Demand Rate and Partial Backlogging

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Lianxia Zhao
Keyword(s):  
Optimal Solution ◽  
Solution Procedure ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Partial Backlogging ◽  
Total Cost ◽  
Replenishment Policy ◽  
Demand Rate ◽  
The Stability ◽  
Theoretical Results

An inventory model for Weibull-distributed deteriorating items is considered so as to minimize the total cost per unit time in this paper. The model starts with shortage, allowed partial backlogging, and trapezoidal demand rate. By analyzing the model, an efficient solution procedure is proposed to determine the optimal replenishment and the optimal order quantity and the average total costs are also obtained. Finally, numerical examples are provided to illustrate the theoretical results and a sensitivity analysis of the major parameters with respect to the stability of optimal solution is also carried out.

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