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In any organization, the information relevant to the problem area is essential in making decisions. The top management makes decisions like expansion of the plant, automation, recruitment of senior personnel and diversification of products, etc. There are many kinds of tools or methods available to analyse these problem areas. Among these, turnover rate is useful for many purposes, especially in evaluating the performance of an organization. Here, the turnover rate is considered in order to identify the effect of the number of types of products or product mix on the performance of a manufacturing system. It can be defined as the ratio of average demand to average inventory level. The model presented discusses the effect of the number of products/product mix on the turnover rate of a production system when the appropriate market value of the products is considered. The turnover rate discussed is based on the economic production quantity (EPQ) and the manufacturing cycle time of each product. An example is presented to explain the application of the model.

The economy has recently gone through a period of industrial expansion coupled with high inflation where industry has tended to grow out of its problems by a combination of increases in output and higher prices. These policies, however, at a certain stage in the development will approach the limits to economic growth, and industry will find that a number of severe problems appear simultaneously. This leads to a period of concentration and economic decline where traditionally industry looks to the Government for relief and assistance; but it could be argued that instead they should consider a critical look at their own patterns of operation. If industry could eliminate the inefficient and ineffective elements in the structure, and concentrate upon improving the quality of their operation, then it is possible that policies adopted for economic survival will lead to growth and expansion. One way in which improvements could be made in the industrial structure is by streamlining the logistics system.

The purpose of this paper is to develop an extensive economic production quantity (EPQ) model on the basis of previous research. Considering an imperfect three‐state production process, this paper makes contributions to an integrated model combining conceptions of quality loss and design of control chart based on EPQ model. The objective is to minimize the total production cost with the determination of EPQ and design parameters of control chart subjected to quality loss and other process costs.

In this paper, imperfect process is defined as a three‐state process, and the quality cost corresponding to each state contributes to the eventual total expected cost formulation. Control chart is used to monitor the shift from the target value within whole process and its control limits are set to be related to the quality cost.

The proposed integrated model conforms more closely to the real situation of production process considering the process shift as a random variable.

Numerical computation and sensitivity analysis through a case study are presented to demonstrate the applications of the model.

Few research efforts investigate an integrated model considering EPQ, control chart and quality loss simultaneously. In particular, compared with the former researches, the process shift, due to which the quality cost incurs, is considered as a random variable in this paper.

Presents a mathematical model for determining Economic Production Quantity (EPQ) in a multistage flow‐shop production system for the case where the demand for items per unit time is deterministic and the planning horizon is finite. Solves an example problem to illustrate the model.

The 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.

This 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.

The 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.

The contribution of this research is the use of grey data in developing the EPQ inventory model with space constraint.

The purpose of this paper is to study the interaction of economics of production with process quality, when multiple key quality characteristics are present. Specifically, the paper aims to analyse the possibility of investing in a production process to reduce its variances and the impact on a multivariate quality loss function.

A bivariate inventory‐planning model is developed, in which the optimal investment for reducing process variances and the optimal lot size are jointly determined. A case study with industrial data is presented to illustrate the possible solution procedures and the potential advantages of the proposed model.

It is found that by using the previous approaches to analyse the interaction between the economics of production and process quality, a company will underestimate the cost of quality, especially the expected external failure cost (quality loss), and ultimately invest less into the prevention activities to improve the process.

The proposed model can help managers to compare different production processes and also guide the managers towards better choices for process improvement. To the best of our knowledge, this paper is the first to integrate the economic production quantity (EPQ) problem with the process quality consideration for products with multiple quality characteristics.

The purpose of this study is to investigate a joint economic lot-size model with the possibility of cofinancing between members of a three-echelon supply chain (SC) including one supplier, one manufacture and one retailer. Given the differences in credit as well as differences in access to capital markets, SC members will be able to create a financial alliance to maximize the profits of each member. This study proposed a model to maximize the annuity stream of the SC by considering the financial interaction between SC members.

This joint economic lot-sizing problem was described and modeled mathematically. To evaluate the mathematical model, different scenarios were considered with (and without) the possibility of financial interaction.

It is suggested that, in addition to the goods and information flow among SC members, proper financial flow can also have an impact on the improvement of SC performance.

While previous studies consider cofinancing between members of a two-echelon SC, this paper considers a three-echelon SC including one supplier, one manufacturer and one retailer where financial cooperation between different levels of the SC in both upstream and reverse directions will be possible.

Intermediary firms are economic agents that purchase from mostly small and numerous independent producers and sell to other firms or to the public. This article investigated how intermediary firms can optimally determine both selling quantity and purchasing price of a product. By incorporating the special structure of intermediary firms′ environments and by modifying the conventional economic order quantity (EOQ) model accordingly, we provide optimal decision rules regarding the selling quantity and purchasing price for intermediary firms under profit maximisation.

The purpose of this paper is to study integrated inventory system and pricing and ordering strategy for vendor‐buyer supply chain system. Here, the vendor offers a trade credit to the buyer when the buyer's order quantity exceeds a given pre‐specified quantity. Therefore, to incorporate the concept of vendor‐buyer integration and trade credit linked, the authors analyze the model to determine the optimal strategy for an integrated vendor‐buyer inventory system under the condition of credit linked to the order quantity when demand is quadratic.

A mathematical model for integrated inventory system is developed when demand rate is increasing function of the time and decreasing function of the retail price. By analyzing the total channel profit function, the authors developed some useful results to characterize the optimal solution and provide an iterative algorithm to find the retail price, buyer's order quantity and the number of shipments per production run from the vendor to the buyer.

By developing a solution algorithm, the optimal retail price, order quantity and number of shipments from the vendor to the buyer are provided. Numerical examples and sensitivity analyses are presented to validate the proposed model. Through extensive numerical analyses, it is observed that a longer credit term increases profits of the player for the entire supply chain. The vendor should establish the threshold for allowing trade credit comprehensively to ensure the greatest benefit for both players.

Most of the research articles available in the literature considered the constant demand or linearly changing demand. In this paper, a mathematical model is developed considering time dependent quadratic demand. Very few researchers have investigated joint optimal policy in vendor‐buyer supply chain system, considering trade credit is linked to order quantity, and still there are not many findings on the benefit of integrated policy and trade credit.

Due to uncertainty in supply chains caused by the coronavirus disease 2019 (COVID-19), organizations are adjusting their supply chain design to address challenges faced during the pandemic. To safeguard their operations against disruption in order quantities, supply chain members have been looking for alternate suppliers. This paper considers a two-level supply chain consisting of a manufacturer and two suppliers of a certain type of components required for the production of a finished product. The primary supplier (supplier A) is unreliable, in the sense that the quantity delivered is usually less than the ordered quantity. The proportion of the ordered quantity delivered by supplier A is a random variable with a known probability distribution. The secondary supplier (supplier B) always delivers the order in its entirety at a higher cost and can respond instantaneously. In order for supplier B to respond instantaneously, the manufacturer is required to reserve a certain quantity at an additional cost. Once the quantity received from the main supplier is observed, the manufacturer may place an order not exceeding the reserved quantity.

A mathematical model describing the production/inventory situation of the supply chain is formulated. The model allows the determination of the manufacturer's optimal ordering policy.

An expression for the expected total cost per unit time function is derived. The optimal solution is determined by solving a system of nonlinear equations obtained by minimizing the expected total cost function.

The proposed model can be used by supply chain managers aiming at identifying various ways of handling the uncertainty in the flow of supplies across the chain.

This proposed model addresses a gap in the production/inventory literature.