Imre Dobos

Optimal production–inventory strategies for a HMMS-type reverse logistics system

Abstract The aim of the paper is to find optimal inventory policies in a reverse logistics system with special structure. It is assumed that demand is a known continuous function in a given planning horizon and return rate of used items is a given function. There is a constant delay between the using and return process. We investigate two stores. The demand is satisfied from the first store, where the manufactured and remanufactured items are stored. The returned products are collected in the second store and then remanufactured or disposed. The costs of this system consist of the quadratic holding costs for these two stores and the quadratic manufacturing, remanufacturing and disposal costs. The model is represented as an optimal control problem with two state variables (inventory status in the first and second store) and with three control variables (rate of manufacturing, remanufacturing and disposal). The objective is to minimize the sum of the quadratic deviation from described inventory levels in stores and from described manufacturing, remanufacturing and disposal rates. In this form, the model can be considered as a generalization of the well-known Holt et al. (Planning Production, Inventories, and Work Forces, Prentice-Hall, Englewood Cliffs, NJ, 1960) model with two warehouses. After solving the problem, we give some numerical examples to represent the optimal path in dependence of the demand rates.

Analysis of the EOQ repair and waste disposal problem with integer setup numbers

In this paper EOQ repair and waste disposal model with variable setup number n and m for production and repair, respectively, within some collection time interval is considered as an integer nonlinear program. The cost analysis is extended to the extreme waste disposal rates and it is shown that the pure strategy for either total repair or total waste disposal is dominant. Furthermore, the minimal cost function and the optimal solution for that integer program is characterised and optimal and approximate solutions are presented for several subclasses of the problem.

Production strategies under environmental constraints in an Arrow-Karlin model

Abstract 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.

Production-inventory control under environmental constraints

The aim of the paper is to investigate how environmental policies, in the form of emission charges or emission limits, affect the production-inventory decisions of a firm. Our framework applies control theory to analyze optimal production policies. The paper modifies the Holt-Modigliani-Muth-Simon model.

A dynamic input-output model with renewable resources

The paper studies a generalisation of the dynamic Leontief input-output model. The standard dynamic Leontief model will be extended with the balance equation of renewable resources. The renewable stocks will increase regenerating and decrease exploiting primary natural resources. In this study the controllability of this extended model is examined by taking the consumption as the control parameter. Assuming balanced growth for both consumption and production, we investigate the exhaustion of renewable resources in dependence on the balanced growth rate and on the rate of natural regeneration. In doing so, classic results from control theory and on eigenvalue problems in linear algebra are applied.

The efficiency of remanufacturing in a dynamic input–output model

For industrialised economy of ourdays, remanufacturing represents perhaps the largest unexploited resource and opportunity for realising a greater growth of the economy in an environmental-conscious manner. The aim of this paper is to investigate of the impact of remanufacturing in the economy from an economic-efficiency point of view. In static context this phenomenon was analysed in the literature. We use the multi-sector input–output framework in a dynamic context to study intra-period relationships of the sectors of economy. We extend the classical dynamic input–output model taking into consideration the activity of remanufacturing .We try to answer the question, whether the remanufacturing/reuse increases the growth possibility of an economy. We expose a sufficient condition concerning the effectivity of an economy with remanufacturing. By this evaluation we analyse a possible sustainable development of the economy on the basis of the product recovery management of industries.

Production-Inventory Control in an EOQ-Type Reverse Logistics System

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.

Design of contract parameters in a closed-loop supply chain

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.

Motivations Behind Sustainable Purchasing

Sustainability issues in purchasing are receiving greater attention. Literature is rapidly growing, with several research programmes being initiated to investigate the topic. This study presents the results of a research project which aims to reveal and structure the motivating forces leading companies to make efforts in sustainability purchasing and the means used to attain achievements in some fields of sustainability. Results presented in the literature are scattered in terms of the fields of sustainability: most of the studies focus only on green or corporate social responsibility issues and there is a lack of exploratory models. Sustainability in purchasing is addressed in a comprehensive way including green, social responsibility and corporate growth issues. After presenting the results of a literature review, theoretical development was undertaken to create a framework in which it is possible to describe the means of sustainability applied and the motivating forces behind them. This framework serves as the basis for an empirical investigation among Hungarian companies. Empirical results confirm the usefulness of the theoretical framework: the number and the characteristics of sustainability activities were determined by the particular types of motivation – to avoid negative effects, to achieve compliance with expectations and to attain positive effects.

A Dynamic Leontief Model with Non-renewable Resources

Abstract In this paper we study a generalization of the dynamic Leontief input–output model. We extend the standard dynamic Leontief model with the balance equation of non-renewable resources. Obviously, the non-renewable stocks will decrease, exploiting primary resources. In this study we examine the controllability of this extended model by taking the consumption as the control parameter. Assuming balanced growth for both consumption and production, we investigate how long these scarce resources will cover the input needs of production and how the lifetime of the system depends on the balanced growth rate and on the consumption. In doing so, we apply classic results from control theory and on eigenvalue problems in linear algebra.