Coordination between production and sales planning in an oil company based on Lagrangean Decomposition

In our work, we study the issues between production and sales planning processes in an oil company . The planning problems involve decisions regarding procurement of crude oil, generation of components , blending of products, internal transportation of components and products , operation of depots , and sale s and distri bution of products to markets . We formulate two separated planning problems in a decoupled setting i.e. production model solved by the production department (PD) and sales model solved by the sales department (SD). Sales planning problem is formulated in s everal ways, considering different scenarios for allocation of depot operation decision and calculation of departmental premium. In addition, we consider two different formulations of re venue functions in each of the sales problems. The first way assume s q uadratic programming model with linear demand function s , whereas the second one assume s a piecewise linear approximation of the revenue function and is a mixed integer programming model. The sale s model maximizes the premium received by SD, whereas the pro duction model minimize s the cost s based on the demand from SD. We also present integrated models that assume centralized planning and maximize the company's total profit. Because in many cases integrated planning is not possible in practice, these models s erve only as a theoreti cal benchmark . We assume that coordination between the departments is achieved through internal prices. We propose two mechanisms for setting internal prices. The first mechanism includes two cost based - methods , whereas the second mechanism is based on Lagrangea n Decomposition (LD). Then we present numerical example to illustrate the methodologies. We study the performance of each of the mechanisms and compare the results achieved under different scenarios. We illustrate the potent ial advantages and possible disadvantages of LD over the cost - based methods and discuss the allocation of decision - making and sharing rule , in which the company attain s a better outcome under the decoupled planning.nhhma