Incorporating machine reliability issue and backlogging into the EMQ model - Part II: Random breakdown occurring in inventory piling time

This paper presents the second part of a research which is concerned with incorporating machine reliability issues and backlogging into the economic manufacturing quantity (EMQ) model. It may be noted that in a production system when back-ordering is permitted, a random machine failure can take place in either backorder filling stage or in on-hand inventory piling time. The first part of the research investigates the effect of a machine failure occurring in backorder filling stage on the optimal lot-size; while this paper (the second part of the research) studies the effect of random breakdown happening in inventory piling time on the optimal batch size for such an imperfect EMQ model. The objective is to determine the optimal replenishment lot-size that minimizes the overall productioninventory costs. Mathematical modelling is used and the renewal reward theorem is employed to cope with the variable cycle length. Hessian matrix equations are utilized to prove convexity of the cost function. Then, the optimal lot size for such a real-life imperfect manufacturing system is derived. Practitioners and managers in the field can adopt these replenishment policies to establish their own robust production plan accordingly

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

Purpose The 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/approach Two 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. Findings A 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/value The 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

Determining replenishment lot size and shipment policy for an extended EPQ model with delivery and quality assurance issues

AbstractThis paper derives the optimal replenishment lot size and shipment policy for an Economic Production Quantity (EPQ) model with multiple deliveries and rework of random defective items. The classic EPQ model assumes a continuous inventory issuing policy for satisfying demand and perfect quality for all items produced. However, in a real life vendor–buyer integrated system, multi-shipment policy is practically used in lieu of continuous issuing policy and generation of defective items is inevitable. It is assumed that the imperfect quality items fall into two groups: the scrap and the rework-able items. Failure in repair exists, hence additional scrap items generated. The finished items can only be delivered to customers if the whole lot is quality assured at the end of rework. Mathematical modeling is used in this study and the long-run average production–inventory-delivery cost function is derived. Convexity of the cost function is proved by using the Hessian matrix equations. The closed-form optimal replenishment lot size and optimal number of shipments that minimize the long-run average costs for such an EPQ model are derived. Special case is examined, and a numerical example is provided to show its practical usage

Enfoques para la Resolución del Problema ELSP

[ES] En este trabajo se pretende realizar una recopilación de los enfoques planteados en la literatura para la resolución del problema de Programación del Lote Económico, esto es, ELSP. Estos métodos son: Solución Independiente, Ciclo Común, Periodo Básico, Periodo Básico Extendido y Variación del Tamaño de Lote. Para cada una de las aproximaciones de solución se plantea a quien son atribuidas, el correspondiente modelo, así como una serie de referencias que lo han empleado.Este trabajo ha sido realizado gracias a la financiación de la Universidad Politécnica de Valencia, a través del proyecto PAID-05-09-4335 "Coordinación de flujos de materiales e información en sistemas distribuidos de producción".Vidal Carreras, PI. (2010). Enfoques para la Resolución del Problema ELSP. Working Papers on Operations Management. 1(2):31-43. doi:10.4995/wpom.v1i2.787SWORD314312Ballou, R. H. (2004). Logística: Administración de la cadena de suministro. Pearson Educación.Ben-Daya, M., & Hariga, M. 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C., & LEFRANÇOIS, P. (1994). Multi-item, single-machine scheduling problem with stochastic demands: a comparison of heuristics. International Journal of Production Research, 32(3), 583-596. doi:10.1080/00207549408956954Giri, B. C., Moon, I., & Yun, W. Y. (2003). Scheduling economic lot sizes in deteriorating production systems. Naval Research Logistics, 50(6), 650-661. doi:10.1002/nav.10082Goyal, S. . (1997). Observation on the economic lot scheduling problem: Theory and practice. International Journal of Production Economics, 50(1), 61. doi:10.1016/s0925-5273(97)00025-xHaessler, R. W. (1979). An Improved Extended Basic Period Procedure for Solving the Economic Lot Scheduling Problem. A I I E Transactions, 11(4), 336-340. doi:10.1080/05695557908974480Haessler, R. W., & Hogue, S. L. (1976). Note—A Note on the Single-Machine Multi-Product Lot Scheduling Problem. Management Science, 22(8), 909-912. doi:10.1287/mnsc.22.8.909Hahm, J., & Yano, C. A. (1995). The Economic Lot and Delivery Scheduling Problem: Powers of Two Policies. Transportation Science, 29(3), 222-241. doi:10.1287/trsc.29.3.222Hanssmann, F. (1962). Operations-Research in Production and Inventory Control. J. Wiley.Harris, F. W. (1913). How many parts to make an once. Factory, The Magazine of Management, Vol. 10, nº. 2, pp. 135-6-152.Hsu, W.-L. (1983). On the General Feasibility Test of Scheduling Lot Sizes for Several Products on One Machine. Management Science, 29(1), 93-105. doi:10.1287/mnsc.29.1.93HWANG, H., KIM, D. B., & KIM, Y. D. (1993). Multiproduct economic lot size models with investment costs for setup reduction and quality improvement. International Journal of Production Research, 31(3), 691-703. doi:10.1080/00207549308956751JONES, P. C., & INMAN, R. R. (1989). When Is The Economic Lot Scheduling Problem Easy? IIE Transactions, 21(1), 11-20. doi:10.1080/07408178908966202Khouja, M., Michalewicz, Z., & Wilmot, M. (1998). The use of genetic algorithms to solve the economic lot size scheduling problem. European Journal of Operational Research, 110(3), 509-524. doi:10.1016/s0377-2217(97)00270-1Khoury, B. N., Abboud, N. E., & Tannous, M. M. (2001). The common cycle approach to the ELSP problem with insufficient capacity. International Journal of Production Economics, 73(2), 189-199. doi:10.1016/s0925-5273(00)00175-4Larrañeta, J., & Onieva, L. (1988). The Economic Lot-Scheduling Problem: A Simple Approach. Journal of the Operational Research Society, 39(4), 373-379. doi:10.1057/jors.1988.65Leachman, R. C., & Gascon, A. (1988). A Heuristic Scheduling Policy for Multi-Item, Single-Machine Production Systems with Time-Varying, Stochastic Demands. Management Science, 34(3), 377-390. doi:10.1287/mnsc.34.3.377Madigan, J. G. (1968). Scheduling a Multi-Product Single Machine System for an Infinite Planning Period. Management Science, 14(11), 713-719. doi:10.1287/mnsc.14.11.713Maxwell, W. L. (1964). 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A scientific routine for stock control. Harvard Business Review, Vol. 13, nº. 1, pp. 116-128.Yao, M. J. & Chang, Y. J. (2009). Solving the economic lot scheduling problem with multiple facilities in parallel using the time-varying lot sizes approach, in Eighth International Conference on Information and Management Sciences, p. F224.Zipkin, P. H. (1991). Computing Optimal Lot Sizes in the Economic Lot Scheduling Problem. Operations Research, 39(1), 56-63. doi:10.1287/opre.39.1.5

Imperfect markets: A case study in Senegal.

Farmers in developing countries are confronted with imperfect markets. This has an impact on their production activities. When implementing developing projects these market imperfections should be taken into account. This paper is an attempt to discuss the impact of imperfect markets in the context of an irrigation project in village Pata, Senegal. The first section models the production decision of the agricultural household. The second section presents the irrigation project in Pata. The third section tests for the presence of imperfections in the credit and labour markets of Pata. I conclude by discussing the implications for the project.Case studies; Market; Markets; Studies;

Imperfect Markets: a Case Study in Senegal

Farmers in developing countries are confronted with imperfect markets. This has an impact on their production activities. When implementing developing projects these market imperfections should be taken into account. This paper is an attempt to discuss the impact of imperfect markets in the context of an irrigation project in village Pata, Senegal. The first section models the production decision of the agricultural household. The second section presents the irrigation project in Pata. The third section tests for the presence of imperfections in the credit and labour markets of Pata. I conclude by discussing the implications for the project.

Budgeting the non-profit organization: An agency theoretic approach

Agency Theory;Public Finance;Nonprofit Organizations;public economics

Social insurance and the completion of the internal market

With the completion of the internal market in the EU pressures may arise to diminish social insurance budgets. In a two-country model with an (imperfectly) integrated consumer goods market it is shown that competitive member states use the social insurance tax rate as an instrument to tax consumers abroad which buy imported goods or to improve employment and competitiveness of home-based firms. As a result, there is tax competition. If the number of firms is fixed, social insurance levels will be inefficiently high. If there is free entry and exit social insurance levels could be inefficiently low. This could be prevented by coordination of social insurance policies. In addition, it is shown that reductions of trade barriers have a downward effect on the size of social insurance budgets in the long run.Social Security;Taxation;Economic Integration;welfare economics