Economic Production Lot Size Model Research Articles

Cloudy fuzzy inventory model under imperfect production process with demand dependent production rate

The aim of this article is an effort to initiate the cloudy fuzzy number in developing classical economic production lot-size model of an item produced in scrappy production process with fixed ordering cost and without shortages. Here, the market value of an item is cloudy fuzzy number and the production rate is demand dependent. In general, fuzziness of any parameter remains fixed over time, but in practice, fuzziness of parameter begins to reduce as time progresses because of collected experience and knowledge that motivates to take cloudy fuzzy number. The model is solved in a crisp, general fuzzy and cloudy fuzzy environment using Yager’s index method and De and Beg’s ranking index method and comparisons are made for all cases and better results obtained in the cloudy fuzzy model. The model is solved by dominance based Particle Swarm Optimization algorithm to obtain optimal decision and numerical examples and sensitivity analyses are presented to justify the notion.

An economic production lot size model for randomly imperfect production system with stock-dependent demand and rework

This paper considers a single item, imperfect economic production lot-size (EPL) model with stock-dependent demand and partial rework. In real life EPL models, defective production commences from the out-of-control state, after the passage of some time from production commencement. Its occurrence is random after the lapse of certain time and imposed here through a chance constraint. The set-up cost is partly production dependent. Unit production cost is also production dependent and a part of it is taken as environment protection cost. Defective rate is also assumed to be random and production dependent. The model is formulated as an average cost minimisation problem subject to a chance constraint and solved using a nonlinear optimisation technique - generalised reduced gradient (GRG) method through LINGO 11.0. Several special cases are derived and more specifically, the present investigation the works of Sana (2010) and Khouja and Mehrez (1994). Numerical experiments are performed to illustrate the general and particular models. Some sensitivity analyses are presented against few model parameters.

An economic production lot size model for randomly imperfect production system with stock-dependent demand and rework

This paper considers a single item, imperfect economic production lot-size (EPL) model with stock-dependent demand and partial rework. In real life EPL models, defective production commences from the out-of-control state, after the passage of some time from production commencement. Its occurrence is random after the lapse of certain time and imposed here through a chance constraint. The set-up cost is partly production dependent. Unit production cost is also production dependent and a part of it is taken as environment protection cost. Defective rate is also assumed to be random and production dependent. The model is formulated as an average cost minimisation problem subject to a chance constraint and solved using a nonlinear optimisation technique - generalised reduced gradient (GRG) method through LINGO 11.0. Several special cases are derived and more specifically, the present investigation the works of Sana (2010) and Khouja and Mehrez (1994). Numerical experiments are performed to illustrate the general and particular models. Some sensitivity analyses are presented against few model parameters.

An EPQ (economic production lot size) model for product life cycle (maturity stage) of deteriorating items with increasing demand rate and shortages

A product life cycle is the life span of a product which the period begins with initial product specification and ends with the withdrawal from the market of both the product and its support. A product life cycle can be divided into several stages characterised by the revenue generated by the product. The purpose of this paper is to investigate the optimal production lot size and total cost during the product life cycle which consists of introduction, growth, maturity and decline stages. The defective rate is considered as a variable of known proportions. The relevant model is built and it is also solved. Necessary and sufficient conditions for a unique and optimal solution are derived. A numerical example is provided using LINGO software.

An iterative learning method for multi-cycle flexible production/inventory control under random demands

Proposed in this paper is a new economic production lot size (EPLS) model, i.e., a multi-cycle flexible production/inventory model under random demands, which considers the holding and shortage costs of finished products as well as the setup costs of production, and employs an (s,Q) policy for production/inventory control. We have theoretically proved that the total expected cost of the model is a convex function with respect to variables s andQ. On this basis, an iterative learning algorithm is designed to speed up the process by using the model convexity, which enables us to obtain the optimal production preparation point and the optimal production quantity. Results from the comparison between the proposed algorithm and the genetic algorithm (GA) show that the control quantities secured by the two algorithms are consistent but the former has higher solution speed, which verifies the accuracy and effectiveness of the proposed model and algorithm.

An economic production lot size model for defective items with stochastic demand, backlogging and rework

An economic production lot size model for defective items with stochastic demand, backlogging and rework

An economic production lot size model for product life cycle (maturity stage) with defective items with shortages

A product life cycle is the life span of a product which the period begins with initial product specification and ends with the withdrawal from the market of both the product and its support. A product life cycle can be divided into several stages characterized by the revenue generated by the product. The purpose of this paper is to investigate the optimal production lot size and total cost during the Product Life Cycle which consists of introduction, growth, maturity and decline stages. The defective rate is considered as a variable of known proportions. The relevant model is built and it is also solved. Necessary and sufficient conditions for a unique and global optimal solution are derived. A numerical example is provided and numerically verified. The validation of result in this model was coded in Microsoft Visual Basic 6.0.

Optimal production schedule in declining market for an imperfect production system

This is a study about economic production in an imperfect production system. The imperfect production system means is a system in which the machine shifts from an ‘in-control’ state to an ‘out-of-control’ state. This may happen at any random time during the production period. The classical economic production lot size model is based on the assumption that the produced items are of perfect quality. However, this is not observed during the production phase. In the long run, the process shifts from the ‘in-control’ state to the ‘out-of-control’ state after certain time due to continuous usage of the machine. The proposed model is developed to study the optimal production when a certain percent of total product is of imperfect quality. These items are reworked to maintain the quality of the products. The production cost per unit item is convex function of production rate. The demand is assumed to be decreasing function of time. The total cost of inventory system per time unit is minimized. The development of the model is validated by numerical examples and its sensitivity analysis is carried out too.

An economic production lot size model in an imperfect production system

The paper investigates an EPL ( Economic Production Lotsize ) model in an imperfect production system in which the production facility may shift from an ‘ in-control ’ state to an ‘ out-of-control ’ state at any random time. The basic assumption of the classical EPL model is that 100% of produced items are perfect quality. This assumption may not be valid for most of the production environments. More specifically, the paper extends the article of Khouja and Mehrez [Khouja, M., Mehrez, A., 1994. An economic production lot size model with imperfect quality and variable production rate. Journal of the Operational Research Society 45, 1405–1417]. Generally, the manufacturing process is ‘ in-control ’ state at the starting of the production and produced items are of conforming quality. In long-run process, the process shifts from the ‘ in-control ’ state to the ‘ out-of-control ’ state after certain time due to higher production rate and production-run-time.The proposed model is formulated assuming that a certain percent of total product is defective ( imperfect ), in ‘ out-of-control ’ state. This percentage also varies with production rate and production-run time. The defective items are restored in original quality by reworked at some costs to maintain the quality of products in a competitive market. The production cost per unit item is convex function of production rate. The total costs in this investment model include manufacturing cost, setup cost, holding cost and reworking cost of imperfect quality products. The associated profit maximization problem is illustrated by numerical examples and also its sensitivity analysis is carried out.

A stochastic EPLS model with random price sensitive demand

In real estate businesses, the price fluctuates due to the variation of a number of factors such as brokerage, inflation and time value of money etc. In this article we consider an stochastic EPLS (economic production lot size) model with price sensitive demand when the price is random in character. The model investigates a self manufacturing/finite replenishment rate with profit maximization problem for a single item over finite time horizon, allowing shortages. A general model is built up by taking production cost, holding cost, shortage cost and selling price into consideration. The general model is analyzed by considering three different distributions of selling price: uniform distribution, exponential distribution and linear distribution for showing the flexibility and utility of the model. Numerical examples are illustrated to test the proposed model. Sensitivity analysis is carried out. A comparative study between these three distributions has also been done.

A finite horizon EPQ model for deteriorating items with shortages under permissible delay in payments

This paper discusses a deterministic finite horizon economic production lot size (EPLS) model for deteriorating items under permissible delay in payments. Shortages are allowed and backlogged partially. Three models are developed over a finite planning horizon. The existence and uniqueness of the optimal solutions of the proposed models are examined. Here, production cycle time, the time at which the shortage begins, production stopping time, shortage ending time and total number of production cycles are taken as decision variables. Numerical examples are given to illustrate the model.

An application of tournament genetic algorithm in a marketing oriented economic production lot-size model for deteriorating items

The goal of this research is to discuss an application of tournament genetic algorithm (TGA) for solving an economic production lot-size (EPL) model. In this model, the production rate of the item is finite and it is assumed to be a decision variable. The demand rate is also a deterministic function of selling price and the marketing cost. The selling price per unit item is determined by a mark-up over the unit production cost. The deterioration rate at any instant is a linear increasing/decreasing function of time. Partial backlogging shortages are allowed with a variable rate dependent on the length of the waiting time up to the starting of next production. This model is formulated as a highly non-linear constrained optimization problem. To solve this problem, a TGA with steady-state selection, whole arithmetic crossover and non-uniform mutation has been developed and applied. The model has been illustrated with three numerical examples. Finally, sensitivity analyses have been shown graphically to study the variations of the average profit with respect to the different parameters.

An economic production lot size model with deteriorating items, stock-dependent demand, inflation, and partial backlogging

In this paper, we present an optimization framework to derive optimal production over a fixed planning horizon for items with a stock-dependent demand rate and under inflationary conditions. We consider a perishable item that follows a two-parameter Weibull distribution. Shortage is allowed and partially backlogged at a fixed rate. A numerical example is taken up to illustrate the solution procedure and sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.

The economic production lot size model extended to include more than one production rate

AbstractWe study an extension of the economic production lot size model, where more than one production rate can be used during a cycle. Moreover, the production rates, as well as their corresponding runtimes are decision variables. We decompose the problem into two subproblems. First, we show that all production rates should be chosen in the interval between the demand rate and the production rate which minimizes unit production costs, and should be used in an increasing order. Then, given the production rates, we derive closed‐form expressions for all optimal runtimes as well as the minimum average cost. This analysis reveals that it is the size of the setup cost that determines the need for being able to use several production rates. We also show how to derive a near‐optimal solution of the general problem.

An economic production lot size model with increasing demand, shortages and partial backlogging

In this paper, an economic production quantity model is developed for a production–inventory system where the demand rate increases with time, the production rate is finite and adjustable in each cycle over an infinite planning horizon and shortages are permitted. The cost of adjusting the production rate depends linearly on the magnitude of the change in the production rate. During the stock-out period, a known fraction of the unsatisfied demands is backordered while the remaining fraction is lost. The model is formulated taking the demand rate as a general increasing function of time and the optimal production policy is obtained for the special case of a linearly increasing demand rate. The proposed model is also shown to be suitable for a prescribed time horizon. A procedure to find approximately the minimum total cost of the system over a finite time horizon is suggested. A numerical example is taken to illustrate the solution procedure of the developed model.

A decision-making model for optimal production rate in economic volume-flexibility production system

The classical economic production lot size (EPL) model assumes a predetermined and inflexible production rate and a continuous demand of customers, and does not take raw materials inventory cost into account. In this paper, a production system with volume flexibility is considered which procures raw materials from suppliers and processes them to convert to finished products. We develop a decision-making model for optimal production rate selection in a volume-flexible production system, where finished products are delivered periodically at a fixed quantity with a fixed interval of time. In this model, production rate is perceived as a decision variable and unit production cost becomes a function of production rate. We develop a pragmatic computation approach to solve the proposed model for special unit production cost functions. Some observations are made for optimal production rate analysis. Finally, we conduct a numerical study to illustrate the solution. Also, a set of data with ten problems is tested and compared.

Lot streaming in multistage production systems

Lot streaming is a procedure in which a production lot is split into smaller sub-lots and moved to the next processing stage so that operations at successive stages of a multistage manufacturing system can be overlapped in time. Lot streaming reduces the manufacturing lead time and thereby provides an opportunity to lower the costs of holding work-in-process inventories. In this paper, we present an economic production lot size model that minimizes the total relevant cost when lot streaming is used. Using illustrative numerical examples, we show that our model can yield significant cost economies compared to the traditional approaches.

An economic production lot-size model with shortages and time-dependent demand

An economic production lot-size model with shortages and time-dependent demand

Using a variable production rate as a response mechanism in the economic production lot size model

Using a variable production rate as a response mechanism in the economic production lot size model

Using a variable production rate as a response mechanism in the economic production lot size model

In this paper we consider a variant of the well known EPL model where the production rate is a decision variable. We show that the following response mechanism can be optimal, namely as a response to an increased demand rate to decrease the production rate.