Economic Production Quantity Inventory Model Research Articles

Optimization of price, lot size and backordered level in an EPQ inventory model with rework process

In traditional inventory models, the demand rate normally is considered as a constant value, while in marketing and pricing, it is dependent on the selling price. The present study introduces a new type of economic production quantity (EPQ) inventory model. This production-inventory model is among the aspects that make the management of inventories more realistic and practical for managers. The pricing policy, planned backorders, and the rework process are included in the EPQ inventory model. The main contribution is that, in the EPQ inventory model, the price serves as a critical factor that affects the size of demand to maximize total long-term profit. The primarily objective is to determine the optimum selling price, discrete values for the optimal lot size, and the level of optimal backorders so that the total profit is maximized. To accomplish the optimal value for the decision variables an algorithm is developed. The proposed algorithm provides an accurate solution for production managers to jointly decide on lot size, backorder size, and selling price. In addition, a numerical example is solved using real industry data. The results affirm that the total profit obtained using the production-inventory model increases significantly in comparison with the current situation. Furthermore, sensitivity analysis is carried out in order to describe the practical application of the suggested production-inventory model.

An economic production quantity inventory model for multi-product imperfect production system with setup time/cost function

An economic production quantity inventory model for multi-product imperfect production system with setup time/cost function

An EPQ inventory model considering an imperfect production system with probabilistic demand and collaborative approach

PurposeThe purpose of this paper is to propose an economic production quantity (EPQ) inventory model considering imperfect items and probabilistic demand for a two-echelon supply chain. The production process is imperfect and the imperfect quality items are removed from the lot size. The demand rate of the inventory system is random and follows an exponential probability density function and the demand of the retailers is depending on the initiatives of the sales team.Design/methodology/approachTwo approaches are examined. In the non-collaborative approach, any member of the supply chain can be the leader and takes decisions to optimize the profits, and in the collaborative system, all members make joint decisions about the production, supply, sales and inventory to optimize the profits of the supply chain members. The calculus approach is applied to find the maximum profit related to the members of the supply chain.FindingsA numerical example is presented to illustrate the performance of the EPQ model. The results show that collaborative approach generates greater profits to the supply chain and the market’s demand represents the variable behavior and uncertainty that is generated in the replenishment of a supply chain.Originality/valueThe new and major contributions of this research are: the inventory model considers demand for products is random variable which follows an exponential probability distribution function and it also depends on the initiatives of sales teams, the imperfect production system generates defective items, different cycle time are considered in manufacturer and retailers and collaborative and non-collaborative approaches are also studied.

Note on “Multiproduct Single-Machine Production System with Stochastic Scrapped Production Rate, Partial Backordering and Service Level Constraint”

An economic production quantity (EPQ) inventory model for a multiproduct single-machine production system with stochastic scrapped production rate, partial backordering and service level constraint is proposed. This research work revisits this EPQ inventory model and identifies some technical inconsistencies in it. Additionally, some observations and corrections to the shortcomings are provided as well as the solution procedure is improved.

Deteriorating inventory with preservation technology under price- and stock-sensitive demand

In this paper, we formulate and solve an Economic Production Quantity inventory model with deteriorating items. To reduce the rate of deterioration, we apply a preservation technology and calculate the amount for preservation technology investment. The demand function is dependent on stock-level and price. We assume that the production rate is linearly dependent on time, based on customer demand. Shortages are allowed in our consideration, and the shortages amount is partially backlogged for the interested customers for the next slot. The effect of inflation is incorporated, which indicates a critical factor in modern days. Our main objective is to find the optimal cycle length and the optimal amount of preservation technology investment by adjusting the inflation rate with maximizing the profit. A numerical example is provided to illustrate the features and advances of the model. A sensitivity analysis with respect to major parameters is performed in order to assess the stability of our model. The paper ends with a conclusion and an outlook at possible future directions.

Imperfect production system with rework of regular production with sales returns by customers and buffer stock

Jamal et al. (2004) proposed a model, which dealt with the optimum batch quantity in a single-stage system in which rework is done by addressing two different operational policies to minimise the total system cost but their models do not considered sales return by customers. A portion of defective items produced are not successfully screened out internally during the production process and passed on to customers, thereby causing defect sales returns and reverse logistic from customers back to the manufacturer. In this direction, this paper develops an economic production quantity inventory model with sales return by customers for determining the economic production quantity for a single product, which is manufactured in a single-stage manufacturing system that generates imperfect quality products and all these defective products are reworked in the same cycle. Mathematical model is developed and the optimal production lot size which minimises the total cost is derived.

EPQ Inventory Model for Deteriorating Raw Materials with Two-Level Trade Credit and Limited Storage Capacity under Alternate Due Date of Payment

Economic production quantity (EPQ) research has typically focused on the cost of production processes, but has not employed accurate calculation to assess factors influencing ordering costs, because one of their assumptions is the raw materials that are product timely. However, the production and transport process of raw materials are influencing factors and increase the holding cost of raw materials, either by increasing or reducing the total relevant cost. [1] combined [2]’s concept of holding cost of raw materials and [3]’s two-level trade credit and limited storage capacity model to develop innovative and detailed EPQ model that considers the holding cost of non-deteriorating raw materials to closer to the real world. However, some raw materials have deteriorated should be considered. Therefore, this research extends [1]’s model to consider the holding cost of deteriorating raw materials. Four theorems for determining the optimal cycle time and the total relevant cost were developed using cost minimization. Finally, sensitivity analyses are used to find out the effects of the parameters to determine the ordering policies.

A comparative study on economic production quantity (EPQ) model under space constraint with different kinds of data

PurposeThe purpose of this paper is to develop a multi-item economic production quantity (EPQ) strategy under grey environment and space constraint. Since the “demand” cannot be predicted with certainty, it is assumed that data behave under grey environment and compare the proposed inventory model with other studies using crisp or fuzzy environments.Design/methodology/approachThis paper is to optimise the cycle time and total cost of the multi-item EPQ inventory model. For this purpose, the Lagrangian coefficient is used to solve the constrained optimisation problem. The grey relational analysis approach and grey data are applied in developing the EPQ inventory model.FindingsThe results are compared with the analysis using crisp and fuzzy data. Sensitivity analysis is done to illustrate the effect of parameter variations on the optimal solution. The results of the study demonstrate that crisp data outperform the other two data in all scales problems in terms of cycle time and cost; grey data perform better in all scales problems than fuzzy data.Originality/valueThe contribution of this research is the use of grey data in developing the EPQ inventory model with space constraint.

A multiproduct single machine economic production quantity (EPQ) inventory model with discrete delivery order, joint production policy and budget constraints

This paper develops a multiproduct economic production quantity inventory model for a vendor–buyer system in which several products are manufactured on a single machine. The vendor delivers the products to customer in small batches. The number of orders must be a discrete value. Moreover, benefitting from a just-in-time policy, the buyer decides the size of the delivered batches. Due to the fact that several products are manufactured on one machine, this makes that the production capacity be considered as a constraint. The aim of this study is to determine the optimal cycle length and the number of delivered batches for each product so that the total inventory cost is minimized. The problem under study is modeled as a mixed integer nonlinear programing problem considering maximum number of orders, capacity and budget constraints. Three different methods are developed and employed to solve this problem: an exact method, a heuristic algorithm and a hybrid genetic algorithm. Based on the results, the three algorithms have near efficiency with different running times. The results shows that the heuristic algorithm obtains a good solution in a short time and the hybrid genetic algorithm finds solutions with higher quality in an acceptable time. Finally, a sensitivity analysis is done to evaluate the effect of changes in the parameters of problem.

An economic production quantity inventory model with a defective production system and uncertain uptime

In this study, a fuzzy mathematical programming for an inventory system with defective items is considered. The system consists of a single machine that requires maintenance to enhance its efficiency, performance and lifespan. Due to the environmental uncertainties, uptime is estimated based on the linguistic variables, i.e., experts' opinions. So, the inherited uptime is a fuzzy number in trapezoid form, i.e., machine works certainly up to a time and it fails with an optimistic and pessimistic estimation. Moreover, machinery should go through a preventive maintenance procedure during downtime. The proposed model helps production managers to reduce system costs by improving machine efficiency and performance employing appropriate maintenance policies. To solve the proposed problem, we optimise system costs by calculating optimum production cycle using an algorithm to calculate upper and lower bounds of inherited crisp problem. Finally, a numerical example is represented to investigate the effectiveness of the proposed algorithm.

An economic production quantity inventory model with a defective production system and uncertain uptime

An economic production quantity inventory model with a defective production system and uncertain uptime

A single machine EPQ inventory model for a multi-product imperfect production system with rework process and auction

In this paper, a multi-product Economic Production Quantity (EPQ) inventory model for a defective production system by a single machine is considered. The faulty produced products are reworked or are put on auction as they are. The aim of this research is to determine the optimal cycle length and the percentage of reworking every fault product such that the total inventory cost, including setup, production, holding, reworking, and lost profit, is minimized. We have proved that this problem is a convex non-linear programming method. Therefore, we came up with the exact algorithm based on differentiation to solve it. Finally, a sensitivity analysis is performed to evaluate the effect of changes in different parameters of the problem.

An economic production quantity inventory model with backorders considering the raw material costs

The classical Economic Production Quantity (EPQ) inventory model does not consider ordering and holding costs of raw materials. In this direction, this paper considers the ordering and holding costs for both raw materials and nished product. Basically, four EPQ inventory models are developed from an easy perspective that has not been considered before. It was found that the ordering and holding costs of raw materials must be taken into account, because they signi cantly impact on the optimal production lot size of the nished product in both EPQ without shortages and EPQ with shortages inventory models. Furthermore, an EPQ inventory model that determines the optimal lot size for a product that requires more than one raw material, and an EPQ inventory model that obtains the optimal batch size for multiple products, which are manufactured with multiple raw materials, are proposed. Numerical examples are presented in order to illustrate the use of the proposed inventory models.

Pricing and lot sizing for an EPQ inventory model with rework and multiple shipments

This paper deals with an economic production quantity (EPQ) inventory model with reworkable defective items when a given multi-shipment policy is used. In this work, it is assumed that in each cycle, the rework process of all defective items starts when the regular production process finishes. After the rework process, a portion of reworked items fails. This portion becomes scrap and only the perfect finished items can be delivered to customers at the end of rework process. A profit function is derived to model the inventory problem and it is shown that the profit function is concave. Due to the complexity of the optimization problem, an algorithm is developed to determine the optimal values of manufacturing lot size and price such that the long-run average profit function is maximized. Furthermore, two special cases are identified and explained. Finally, a numerical example is given to illustrate the applicability of the proposed inventory model.

Optimal pricing and lot-sizing policies for an economic production quantity model with non-instantaneous deteriorating items, permissible delay in payments, customer returns, and inflation

This article deals with an economic production quantity inventory model for non-instantaneous deteriorating items under inflationary conditions, permissible delay in payments, customer returns, and price- and time-dependent demand. The customer returns are assumed as a function of demand and price. The effects of time value of money are studied using the Discounted Cash Flow approach. The main objective is to determine the optimal selling price, the optimal length of the production period, and the optimal length of inventory cycle simultaneously such that the present value of total profit is maximized. An efficient algorithm is presented to find the optimal solution of the developed model. Finally, a numerical example is extracted to solve the presented inventory model using our proposed algorithm, and the effects of the customer returns, inflation, and delay in payments are also discussed.

A constrained multi-products EPQ inventory model with discrete delivery order and lot size

This paper proposes an alternative heuristic algorithm for a multi-product Economic Production Quantity (EPQ) vendor–buyer integrated model with Just in Time (JIT) philosophy and a budget constraint. This type of problem is usually solved by a Mixed Integer Non Linear Problem (MINLP), which is complex and computationally expensive. The proposed heuristic algorithm involves less computation and therefore it is less expensive than the previously published algorithms. Furthermore, the heuristic algorithm is simpler as it derives the integer values for all discrete variables in a straightforward manner. Through empirical experimentation, it is demonstrated that the heuristic algorithm provides solutions closer to the lower bound in a very short time.

An inventory model with non-instantaneous receipt and exponentially deteriorating items for an integrated three layer supply chain system under two levels of trade credit

Recently, the enterprises, from a financial perspective, have been seeing that need of the integrating with others with trade credit policies as a promising issue for savings in the supply chain. In this direction, this paper establishes a new economic production quantity (EPQ) inventory model for deteriorating items under two levels of trade credit, in which the supplier offers to the retailer a permissible delay period and simultaneously the retailer in turn provides a maximal trade credit period to its customers in a supply chain system comprised of three stages. The purpose of this paper is to determine the optimal replenishment policy so that the total relevant cost is minimized. It is shown that this new EPQ inventory model forms a general framework that contains several inventory models that appear in some previous published articles.

A deterministic multi product single machine EPQ model with backordering, scraped products, rework and interruption in manufacturing process

In this paper, an economic production quantity (EPQ) inventory model with interruption in process, scrap and rework is developed and analyzed. The inventory model is for multiple products and all products are manufactured in a unique machine. Obviously, the existence of only one machine results in limited production capacity and shortages. Therefore, shortages are permitted and fully backordered. In this EPQ inventory model, the decision variables are cycle length and backordered quantities of each product and the main objective is to minimize the expected total cost. An easy to use solution procedure is developed for finding the optimal solution. Numerical examples are provided to perform a sensitivity analysis. Finally, some conclusions and future researches are included.

Optimal pricing and ordering policy for non-instantaneous deteriorating items under inflation and customer returns

This paper deals with an economic production quantity inventory model for non-instantaneous deteriorating items under inflationary conditions considering customer returns. We adopt a price- and time-dependent demand function. Also, the customer returns are considered as a function of both price and demand. The effects of time value of money are studied using the Discounted Cash Flow approach. The main objective is to determine the optimal selling price, the optimal replenishment cycles, and the optimal production quantity simultaneously such that the present value of total profit is maximized. An efficient algorithm is presented to find the optimal solution. Finally, numerical examples are provided to solve the presented inventory model using our proposed algorithm, which is further clarified through a sensitivity analysis. The results of analysing customer returns provide important suggestions to financial managers who use price as a control to match the quantity sold to inventory while maximizing revenues. The paper ends with a conclusion and an outlook to future studies.

A mathematical model on EPQ for stochastic demand in an imperfect production system

In the paper, we develop an EPQ (economic production quantity) inventory model to determine the optimal buffer inventory for stochastic demand in the market during preventive maintenance or repair of a manufacturing facility with an EPQ (economic production quantity) model in an imperfect production system. Preventive maintenance, an essential element of the just-in-time structure, may cause shortage which is reduced by buffer inventory. The products are sold with the free minimal repair warranty (FRW) policy. The production system may undergo “out-of-control” state from “in-control” state, after a certain time that follows a probability density function. The defective (non-conforming) items in “in-control” or “out-of-control” state are reworked at a cost just after the regular production time. Finally, an expected cost function regarding the inventory cost, unit production cost, preventive maintenance cost and shortage cost is minimized analytically. We develop another case where the buffer inventory as well as the production rate are decision variables and the expected unit cost considering the above cost functions is optimized also. The numerical examples are provided to illustrate the behaviour and application of the model. Sensitivity analysis of the model with respect to key parameters of the system is carried out.