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In today's competitive and dynamic world, the importance of supplier evaluation has become more widely recognized. When considering measurement of supplier performance and supply impact the literature identifies two sets of criteria: management criteria and green criteria. Management criteria can be extended with process cost criteria, which then poses new requirements to be met by the evaluation methodologies. This paper aims to present a methodology that can handle the different characteristics of these criteria. As a solution, a green supplier selection problem is generalized.A Data Envelopment Analysis (DEA)-type supplier selection method was developed, where green factors served as the output variables of a DEA model, and management variables were the inputs. This new methodology examines, in addition to managerial and green criteria, the effect of inventory-related costs, such as the EOQ costs of inventory holding or ordering costs on the selected supplier. The parametrical linear programming of technological coefficients is used in the DEA method. This paper draws attention to a new problem, namely, the literature fails to provide solutions for how to handle the nonlinearity of the cost functions in the most commonly used methodologies.

Supplier selection is an important business decision. Beside traditional management criteria the environmental aspects are getting often recognition. In this paper the method of Data Envelopment Analysis (DEA) is used to study the extension of traditional supplier selection methods with environmental factors. The focus will be on the weight selection process which can control the selection. In this method we divide the criteria in two manners: the traditional and environmental (green) factors. Then with the help of DEA we are searching a weight system with which the environmental criteria can influence the decision with a representation of the green factors. To choose the mentioned weight system, we apply DEA (Data Envelopment Analysis) with common weights analysis (CWA) method. In this case of DEA/CWA the common weights are calculated with a linear programming problem.

We study an integrated production–inventory system that manufactures new items of a certain product and receives some of the used items back. These can be either remanufactured on the same production line or disposed of. Used items awaiting remanufacturing need to be held in stock. New and as-good-as-new items are kept in stock, from which the product demand is satisfied. Controlling such a system involves decisions with regard to disposal of used items, succession of manufacturing and remanufacturing operations, and the choice of respective lot sizes. Recent works have referred to settings assuming variation in quality of returned items and a limited number of remanufacturing cycles that an item can undergo. We seek to determine optimal lot sizing for such a system and derive sufficient conditions for an optimal policy to forego remanufacturing.

Supplier assessment is widely studied in the literature as it is an important means of managing supplier relationships. Although some evaluation methods have been proposed in the literature to measure suppliers׳ green performance, they are not developed specifically to help other than strategic purchasing situation. Based on literature results our paper examines the extension of the vendor evaluation methods with environmental, green issues. This generalization means an extension of the traditional criteria and weight system of the supplier evaluation methods. In our paper the method composite indicators (CI) is used to study the extension of traditional supplier selection methods with environmental factors. The selection of the weight system can control the result of the selection process. Our goal is to choose such weights which affect the results of the selection process. In this method we divide the criteria in two manners: the traditional (managerial) and environmental (green) factors. Then with the help of CI we are searching a weight system with which the environmental criteria can influence the decision with a representation of the green factors. In our study we look for a weight system to determine the environmental factors, as an important decision factors. To choose the mentioned weight system, we apply data envelopment analysis (DEA) with the common weights analysis (CWA) method.

The paper focuses on the development of buyer – supplier relationships over time. Although there is an ongoing debate about the nature and characteristics of relationship life cycle, the existence of some kind of life cycle is usually assumed when timely development of these relationships is investigated. The objective of our analysis is to investigate this hidden hypothesis using quantitative research methodology. The research focusing on the development of business relationships over time has mainly used qualitative research methods and to the best of our knowledge, no one have yet attempted to measure any relevant variables and the pattern of their development over time using a quantitative methodology. In order to be able to test this hypothesis the level of relation-specific investments generated in the relationship, called the explicit investment measure, was chosen. We have conceptualized and measured it and tested empirically to what extent its development over time fits the pattern of the traditional mathematical model (representation) of the life cycle, which is usually described with a logistics curve. The development of this explicit investment measure over time is a dynamic phenomenon the analysis of which is not without methodological problem. We suggest and apply a procedure developed in the field of population dynamics that makes it possible to use cross sectional data for such dynamic analysis.

We study an extended joint economic lot size problem which incorporates the return flow of remanufacturable used products. The supply chain under consideration consists of a single supplier and a single buyer. The buyer orders a single product from the supplier, uses it for her own needs, and collects the remanufacturable items after use. The ordered items are shipped from the supplier to the buyer in the lot-for-lot fashion by a vehicle which also returns the collected used items from the buyer to the supplier for remanufacturing and subsequent service of the buyer’s demand in the next order cycle. For satisfying the total demand, the supplier manufactures new items or remanufactures used ones received from the buyer. For given demand, productivity, collection rate, disposal cost, setup cost, order cost, holding cost for serviceable and nonserviceable products at the supplier as well as the buyer the lot size (order size) for the supplier (buyer) has to be found which minimizes the total cost. Furthermore, we address a decentralised decision making of the parties under a two-part tariff and determine their equilibrium strategies within the Nash framework.

An integrated production–recycling system is investigated. A constant demand can be satisfied by production and recycling. The used items might be bought back and then recycled. The not recycled products are disposed off. Two types of models are analyzed. The first model examines and minimizes the EOQ related cost. The second model generalizes the first one by introducing additionally linear waste disposal, recycling, production and buyback costs. This basic model was examined by the authors in a previous paper. The main results are that a pure strategy (either production or recycling) is optimal. This paper extends the model for the case of quality consideration: it is asked for the quality of the bought back products. In the former model we have assumed that all returned items are serviceable. One can put the following question: Who should control the quality of the returned items? If the suppliers examine the quality of the reusable products, then the buyback rate is strongly smaller than one, α

A production–recycling system is investigated. A constant demand can be satisfied with production and recycling. The used items are bought back and then recycled. The non-recycled products are disposed of. Two types of models will be analyzed. The first model examines the EOQ-related costs and minimizes the relevant costs. The second model generalizes the first model with the introduction of the cost function with linear waste disposal, recycling, production and buyback costs. It is asked whether the pure (either production or recycling) or mixed strategies are optimal and it will be shown that under these circumstances the mixed strategies are dominated by the pure strategies. The paper generalizes a former model proposed by the authors for the case of one recycling and one production batch to the case of arbitrary batch numbers.

The aim of the paper is to investigate how environmental policies affect the production-inventory decisions of a firm. Optimal control theory is applied to analyze optimal production policies. The environmental policy investigated in the paper is a combined emission charges and limits policy. The paper modifies the results of Wirl (European Journal of Operational Research 55 (1991) 191–200 [1]) for the case of this combined policy.

We investigate a supply chain with a single supplier and a single manufacturer. The manufacturer is supposed to know the demand for the final product which is produced from a raw material ordered from the supplier just in time—i.e., the manufacturer holds no raw material inventory. Her costs consist of the linear purchasing cost, quadratic production cost and the final product quadratic holding costs. It is assumed that the market price of the final product is known as well, hence the sales of the manufacturer are known in advance. Her goal is to maximize her cumulated profits. The supplier’s costs are the quadratic manufacturing and inventory holding costs; his goal is to maximize the revenues minus the relevant costs.We will not examine the bargaining process that determines the adequate price and quantity. The situation is modeled as a differential game. The decision variables of the supplier are the sales price and the production quantity, while the manufacturer chooses a production plan that minimizes her costs, so maximizing the cumulated profits. The basic problem is a Holt-Modigliani-Muth-Simon (HMMS) problem extended to linear purchasing costs. We examine two cases: the decentralized Nash-solution and a centralized Pareto-solution to optimize the behavior of the players of the game.

An extended joint economic lot size problem is studied which incorporates the return flow of repairable (remanufacturable) used products. The supply chain under consideration consists of a single supplier and a single buyer. The buyer orders a single product from the supplier, uses it for her own needs, and collects a certain fraction of used items for the subsequent remanufacturing. The product is shipped to the buyer in the lot-for-lot fashion by a vehicle which also returns the collected used items to the supplier for remanufacturing and subsequent service of the buyer’s demand in the next order cycle. To satisfy the buyer’s demand, the supplier can remanufacture used items as well as manufacture new ones. For the given demand, productivity, disposal, setup, ordering and holding costs for serviceable and nonserviceable items at the supplier and the buyer, the optimal lot sizes and collection rates are determined which minimize the joint as well as individual total costs. Further, a problem of coordinating this supply chain by a type of quantity discount is addressed.

The aim of the paper is to investigate the optimal solution of the Modigliani-Hohn inventory model with capacity and warehousing constraint, in the case of continuous time.

In this paper a general reverse logistics system to satisfy a steady demand for one product by production and recycling is studied. The model incorporates the two extreme policies of production (the pure production model) and of recycling (the pure recycling model) only. This general model, which has been introduced recently by the authors and is therefore called RD-model, examines the possibility of repurchasing and recycling or disposing used items. Since the total cost of the model contains both EOQ-related (setup cost and holding cost) and non-EOQ-related costs (waste disposal, recycling, production and repurchasing costs), first the optimal lot sizes for the EOQ-related cost function are presented. Then, the transformation of the RD-model into a special fractional optimization program follows. The optimization program for the RD-model, let us call it RD-program, includes other known EOQ recovery models as special cases and, in this sense, it can be regarded as a meta program for all of them. An analysis of the material flow in various models will be provided, and a classification of the models is suggested. Moreover, cost-minimal repurchasing rates and use rates of used items are determined. The analysis shows — as it is known for other models — that the mixed strategies of combining production and recycling are dominated by the pure strategies (either production or recycling), i. e. — if technologically feasible — either pure production or recycling is optimal.

A production-recycling system is investigated. A constant demand can be satisfied by production and recycling. The used items are bought back and then recycled. The not recycled products are disposed off. A model is examined with EOQ-type inventory holding costs and linear waste disposal, recycling, production and buyback costs. It will be shown that under these circumstances the mixed strategies are dominated by the pure strategies. The paper generalizes a former model proposed by the authors for the case of integer recycling and production batch.

The aim of the presentation is to model dynamic environmental concerns of the production. We develop an environmental model of a manufacturing firm. The firm produces a single end product. Manufacturing this product, the firm uses two factors: a homogene production factor that can be interpreted as raw material or capital good, and a natural resources e.g. water or air. The from market returned items are investigated. If a returned item is repairable, then it is repaired and the repaired product will be used as new product. If the item is not reparaible, then it is dismantled and it is used as production factor. In other words, the model contains a reverse logistics subsystem. We assume that the firm is price-taker, and will maximize its profit. The technological aspects of the production is described with two production functions: production function for the manufacturing and production function for remanufacturing. The production functions are stock-flow type function. We have chosen this type of production function, because in case of flow production function the warehouses were empty in the planning horizon. To characterize the optimal production-environment interdependences, we use a continuous time model. To solve the profit maximization problem, we use the maximum principle of Pontryagin.

In this paper we analyze a reverse logistics inventory model investigated by Teunter (2001). Demand of a product can be satisfied with newly manufactured and remanufactured products. The used products are collected and then returned to the manufacturer of the product. The returned items are inspected and some of the used products are disposed outside. The rate of reuse is decision variable in this model. The goal of the decision maker is to minimize the relevant costs. The aim of this paper is to reexamine the proposed model and to improve some small mistakes. First, we show that it is comfortable to determine the batch numbers of the manufacturing and remanufacturing activities, because these decision variables are integer, rather than the manufacturing and remanufacturing lot sizes. Secondly, we show that there exist optimal solutions for the batch numbers inside of the possible set, i.e. both manufacturing and remanufacturing batches could be higher than one. Thirdly, the above mentioned paper have not ana lyzed a case with one batch numbers both manufacturing and remanufacturing. This case can occur for some parameters.