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The replenishment size/production lot size problem both for perfect and imperfect quality products studied in this paper is motivated by the optimal strategy in a three layer supply chain consisting of multiple suppliers, manufacturers and retailers. In this model, each manufacturer produces each product with a combination of several raw materials which are supplied by each supplier. The defective products at suppliers and manufacturers are sent back to the respective upstream members at lower price than the respective purchasing price. Finally, the expected average profits of suppliers, manufacturers and retailers are formulated by trading off set up costs, purchasing costs, screening costs, production costs, inventory costs and selling prices. The objective of this chain is to compare between the collaborating system and Stakelberg game structure so that the expected average profit of the chain is maximized. In a numerical illustration, the optimal solution of the collaborating system shows a better optimal solution than the approach by Stakelberg.

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RESUMENEste trabajo presenta una Metodología de Gestión de Inventarios que determina los niveles de integración y colaboración en una cadena de suministro, de tal forma que se generen políticas y estrategias conjuntas para mejorar el desempeño de los actores en la cadena. En ella se definen los cinco pasos para implementar procesos de planificación colaborativa entre los actores de la cadena de suministro y la integración de procesos al interior de los mismos, así como también los indicadores que permitan medir su desempeño como resultado de una estrategia de seguimiento. La metodología es validada en empresas del sector madera y muebles de la ciudad de Barranquilla, en las que se evidencian deficiencias en el manejo del inventario, debido a que no se han adoptado buenas prácticas para gestionar los inventarios de manera colaborativa entre actores de distintos niveles de la cadena de suministro. Los resultados muestran bajos niveles de integración de procesos de gestión de inventarios al interior de las empresas, lo que es el resultado de una baja colaboración e integración de procesos entre actores de diferentes niveles de la cadena de suministro de madera y muebles, lo que permitió definir unas estrategias para mejorar la gestión de inventarios entre las empresas que la conforman.Palabras clave: Cadena de suministro, gestión de inventarios, integración, colaboración. ABSTRACT This paper presents a Methodology of Inventory Management that determines the levels of integration and cooperation in a supply chain, so that policies and joint actions to improve the performance of the actors in the chain strategies are generated. It defined the five steps to implement collaborative planning between actors in the supply chain and integration of processes within the same processes as well as indicators to measure their performance as a result of a monitoring strategy. The methodology is validated in

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.