Pedro Huitzil-Meléndez, Posgrado, Instituto Mexicano del Petroleo, Eje Central Lázaro Cárdenas 152, Col. San Bartolo Atepehuacan, México, D.F., 07730, Mexico, Angel Soriano, Programa de Matematicas Aplicadas y Computación, Instituto Mexicano del Petróleo, and Patricia López-Rivera, Programa de Matemáticas Aplicadas y Computación., Instituto Mexicano del Petróleo.
This paper proposes a procedure of decision making within Just in Time type of supply chains. The methodologic aspects of this approach are based on a two stage procedure. The first stage comprise an approximation of the probability distribution function of the demand in every single supplier node. From real-time recorded information consisting on the number of orders demanded and the amount of resource solicited for them. Formally this is computed by using the Panjer algorithm. The second stage of the procedure uses the information of the demand of the whole supply chain, i.e. by estimating the local demand of every supplier node then a centralized demand can be established. Based on it, then we seek to use the Maximum Principle in a profit functional by considering the demand in a fixed horizon of time. But, constrained to the decision on both initial and final inventory level within the time horizon. Such an approach allows us to obtain, in the first stage, the information upstream, and in the second stage the cost and inventory level required downstream in the supply chain. The planning obtained in such a way lead us to minimum required inventories. At this point in fact, there is a necessary service strategy to pick demands not considered within the average estimated. This strategy consist in obtaining, from other supplier nodes, the amount of demanded resource to face this kind of eventuality. The use of coalitions among clusters of suppliers, is a common scheme of organization in order to satisfy the demand of customers. This is done by seeking one or serveral alternative suppliers to fulfill the amount backlogged by the supplier node in the coalition cluster. Simultaneously, there are nodes with excess of inventory at the end of the horizon looking for other suppliers that fell out of stock. The arguments above are considered in an automated system that we have called PetroCS for control and planning operations of supply chains with the formal conditions described. The contribution in this paper includes various aspects: on one hand the use of optimal control, actuarial techniques and dynamic systems in order to construct a mathematical methodology for supply chain management, on the other hand we provide an insight of the automatization system. The structural approach of flow of demand information and supply is entirely original. Finally a variance control feature is explained as a generalization of others reported in the literature, with the purpose of reducing demand amplification.