scholarly journals Planning Horizon for Production Inventory Models with Production Rate Dependent on Demand and Inventory Level

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jennifer Lin ◽  
Henry C. J. Chao ◽  
Peterson Julian
Keyword(s):  
Production Rate ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Inventory Model ◽  
Inventory Level ◽  
Inventory Models ◽  
New Production ◽  
Production Inventory ◽  
Infinite Planning Horizon ◽  
Finite Planning Horizon

This paper discusses why the selection of a finite planning horizon is preferable to an infinite one for a replenishment policy of production inventory models. In a production inventory model, the production rate is dependent on both the demand rate and the inventory level. When there is an exponentially decreasing demand, the application of an infinite planning horizon model is not suitable. The emphasis of this paper is threefold. First, while pointing out questionable results from a previous study, we propose a corrected infinite planning horizon inventory model for the first replenishment cycle. Second, while investigating the optimal solution for the minimization problem, we found that the infinite planning horizon should not be applied when dealing with an exponentially decreasing demand. Third, we developed a new production inventory model under a finite planning horizon for practitioners. Numerical examples are provided to support our findings.

scholarly journals Production inventory models for deteiorative items with three levels of production and shortages

2017 ◽  
Vol 27 (4) ◽  
pp. 499-519
Author(s):  
Chickian Krishnamoorthi ◽  
C.K. Sivashankari
Keyword(s):  
Production Rate ◽  
Consumer Satisfaction ◽  
Optimal Solution ◽  
Inventory Model ◽  
Lot Size ◽  
Inventory Models ◽  
Total Cost ◽  
Initial Stage ◽  
Production Inventory ◽  
Holding Cost

In this paper, three level production inventory models for deteriorative items are considered under the variation in production rate. Namely, it is possible that production started at one rate, after some time, switches to another rate. Such a situation is desirable in the sense that by starting at a low rate of production, a large quantum stock of manufacturing items at the initial stage are avoided, leading to reduction in the holding cost. The variation in production rate results in consumer satisfaction and potential profit. Two levels of production inventory models are developed, and the optimum lot size quantity and total cost are derived when the production inventory model without shortages is studied first and a production inventory model with shortages next. An optimal production lot size, which minimizes the total cost, is developed. The optimal solution is derived and a numerical example is provided. The validation of the results in this model was coded in Microsoft Visual Basic 6.0.

An Imperfect Production Model for Breakable Multi-Item with Dynamic Demand and Learning Effect on Rework over Random Planning Horizon

2021 ◽  
Vol 14 (12) ◽  
pp. 574
Author(s):  
Amalesh Kumar Manna ◽  
Leopoldo Eduardo Cárdenas-Barrón ◽  
Barun Das ◽  
Ali Akbar Shaikh ◽  
Armando Céspedes-Mota ◽  
...  
Keyword(s):  
Learning Effect ◽  
Planning Horizon ◽  
Inventory Model ◽  
Inventory System ◽  
Production Model ◽  
Inventory Models ◽  
Imperfect Production ◽  
Production Inventory ◽  
Random Planning Horizon ◽  
Production Inventory System

In recent times, in the literature of inventory management there exists a notorious interest in production-inventory models focused on imperfect production processes with a deterministic time horizon. Nevertheless, it is well-known that there is a high influence and impact caused by the learning effect on the production-inventory models in the random planning horizon. This research work formulates a mathematical model for a re-workable multi-item production-inventory system, in which the demand of the items depends on the accessible stock and selling revenue. The production-inventory model allows shortages and these are partial backlogged over a random planning horizon. Also, the learning effect on the rework policy, inflation, and the time value of money are considered. The main aim is to determine the optimum production rates that minimize the expected total cost of the multi-item production-inventory system. A numerical example is solved and a detailed sensitivity analysis is conducted in order to study the production-inventory model.

scholarly journals An Inventory Model for Imperfect Quality Products with Rework, Distinct Holding Costs, and Nonlinear Demand Dependent on Price

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1362
Author(s):  
Leopoldo Eduardo Cárdenas-Barrón ◽  
María José Lea Plaza-Makowsky ◽  
María Alejandra Sevilla-Roca ◽  
José María Núñez-Baumert ◽  
Buddhadev Mandal
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Inventory System ◽  
Inventory Level ◽  
Selling Price ◽  
Lot Size ◽  
Inventory Models ◽  
Holding Costs ◽  
Imperfect Items ◽  
The Moment

Traditionally, the inventory models available in the literature assume that all articles in the purchased lot are perfect and the demand is constant. However, there are many causes that provoke the presence of defective goods and the demand is dependent on some factors. In this direction, this paper develops an economic order quantity (EOQ) inventory model for imperfect and perfect quality items, taking into account that the imperfect ones are sent as a single lot to a repair shop for reworking. After reparation, the items return to the inventory system and are inspected again. Depending on the moment at which the reworked lot arrives to the inventory system, two scenarios can occur: Case 1: The reworked lot enters when there still exists inventory; and Case 2: The reworked lot comes into when the inventory level is zero. Furthermore, it is considered that the holding costs of perfect and imperfect items are distinct. The demand of the products is nonlinear and dependent on price, which follows a polynomial function. The main goal is to optimize jointly the lot size and the selling price such that the expected total profit per unit of time is maximized. Some theoretic results are derived and algorithms are developed for determining the optimal solution for each modeled case. It is worth mentioning that the proposed inventory model is a general model due to the fact that this contains some published inventory models as particular cases. With the aim to illustrate the use of the proposed inventory model, some numerical examples are solved.

Integrated production inventory model with variable production rate on quality of products involving probabilistic defective under variable setup cost

2020 ◽  
Vol 54 (6) ◽  
pp. 1723-1756 ◽  
Author(s):  
S. Hemapriya ◽  
R. Uthayakumar
Keyword(s):  
Production Rate ◽  
Production Cost ◽  
Optimal Solution ◽  
Inventory Model ◽  
Setup Cost ◽  
Integrated Production ◽  
Production Inventory ◽  
Quality Of Products ◽  
Variable Production

A predetermined production rate in a supply chain model with economic production lot size is quite appropriate for this type of situations as production rate can be changed in some cases to fulfill demand of customers. This paper investigates an integrated production inventory model with variable production rate on quality of products involving probabilistic defective under variable setup cost. As a rate of production has a direct impact on system performance, the production rate is considered as a variable along with the production cost. This production process gone through a long run system as a result after some specific time the production gone out-of-control state due to different issues and produced defective items. In addition, we consider that the defective follows three types of probability distribution function such as, (i) uniform, (ii) triangular and (iii) beta distributions. Two types of lead time crashed concept considering in this model and also we consider three types of continuous probabilistic defective function to find the associated cost of the system. The main objective is to find an optimal solution for an order quantity, safety factor, production cost, setup cost and to analyze how the flexibility of the production rate affects the process quality. An efficient iterative algorithm is designed to obtain the optimal solution of the model numerically and sensitivity analysis table formulate to show the impact of different parameter.

scholarly journals A production-inventory model for a deteriorating item with shortage and time dependent demand

2011 ◽  
Vol 21 (1) ◽  
pp. 29-45
Author(s):  
S. Khanra ◽  
K.S. Chaudhuri
Keyword(s):  
Sensitivity Analysis ◽  
Minimization Problem ◽  
Planning Horizon ◽  
Inventory Model ◽  
Time Dependent ◽  
Production Inventory ◽  
Constrained Minimization Problem ◽  
The Given ◽  
Finite Planning Horizon ◽  
Dependent Demand

In the present article, a production-inventory model is developed over a finite planning horizon where the demand varies linearly with time. The machine production rate is assumed to be finite and constant. Shortages in inventory are allowed and are completely backlogged. The associated constrained minimization problem is numerically solved. Sensitivity analysis is also presented for the given model.

Study on the Bounded Inventory Model with Returning Items and Disposals

2010 ◽  
Vol 102-104 ◽  
pp. 920-925
Author(s):  
Neng Min Wang ◽  
Zheng Wen He ◽  
Lin Yan Sun
Keyword(s):  
Lot Sizing ◽  
Dynamic Programming Algorithm ◽  
Planning Horizon ◽  
Cost Functions ◽  
Programming Algorithm ◽  
Inventory Level ◽  
Lot Sizing Problem ◽  
Production Inventory ◽  
Dynamic Lot Sizing ◽  
Inventory Holding

This paper addresses a dynamic lot sizing problem with mixed returning items and disposals and bounded inventory. The returning items mean that returns are in good enough condition to re-enter the inventory supply stream. The producing, the holding, backlogging and disposals cost functions are concave cost functions. Furthermore, backlogging level and inventory level at each period is limited. The goal is to minimize the total cost of production, inventory holding/backlogging and disposal. A dynamic programming algorithm with complexity O(T3) is developed to solve this model, where T is the length of the planning horizon.

Multiple Deliveries of Two-Warehouse Deteriorating Production-Inventory Model

2013 ◽  
Vol 684 ◽  
pp. 634-638
Author(s):  
Hsiao Ching Chen ◽  
Yao Hung Hsieh
Keyword(s):  
Supply Chain ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Inventory Model ◽  
Integrated System ◽  
Discounted Cash Flow ◽  
Supply Chain System ◽  
Partial Backordering ◽  
Production Inventory ◽  
Production Inventory System

In this study we develop a two-warehouse deteriorating production-inventory model from the perspectives of both the manufacturer and the retailer. The model considered multiple deliveries, partial backordering and inflation. The discounted cash flow (DSF) and optimization technique are also used to derive the optimal solution. A numerical example is given to validate the results of the whole production-inventory system. This study shows that multiple deliveries of the integrated system results in an optimal solution for the manufacturer-retailer supply chain system.

scholarly journals Inventory Model Considering Deterioration, Stock-Dependent and Ramp-Type Demand with Reserve Money and Carbon Emission

2020 ◽  
Vol 8 (5) ◽  
pp. 5330-5337
Keyword(s):  
Carbon Emission ◽  
Trade Credit ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Life Time ◽  
Planning Horizon ◽  
Inventory Model ◽  
Ramp Type Demand ◽  
In The Beginning ◽  
Dependent Demand

Now a day, government is more concerned about the environment, so inventory model for deteriorating product for multi-product with partial backlogging is modeled here by considering carbon emission cost under the influence of inflation. It is also assumed buyer have sufficient amount of money to pay the vendor in the beginning of the business but still buyer focus to avail the offer of trade credit offered by vendor. As demand of many products such as fashionable products, cold drinks etc., get stabilized after the acceptance by the market and take the form of ramp-type. So, while developing the model, ramp-type initial stock-dependent demand is considered. As the life time of the product is finite so finite planning horizon is considered here. To obtain the optimal solution, search algorithm is provided. To illustrate and validate the model, numerical example is provided. Further, to study the effect of important parameters, sensitive analysis is also carried.

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