Multi-Level Production and Distribution Planning with Transportation Fleet Optimization

We present an application of mathematical programming for solving a complex multi-level production and distribution network optimization problem faced by a petrochemical company. Two liquified petroleum gas (LPG) products, propane and butane, are produced at refineries, from where they are shipped in bulk to plants for bottling. Then the company distributes the gas bottles to the customers either directly or via depots and transportation breakpoints. Transportation is carried out by the company's own truck fleet or by contract carriers. The own trucks can operate on different shift systems allowing for overtime. The problem is to find the location of the bottling plants and the depots, the production levels at the refineries and the plants, the stock levels at the plants and the depots, the transportation volumes on each link of the distribution network, the number of trucks and drivers, the transportation shift systems and schedules, and the customer assignments so as to meet LPG demand at minimal cost. The actual problem has 2 commodities, 2 refineries, 10 potential bottling plant locations, 40 potential depot locations, 40 breakpoints (transporters), and 200 customer regions. The problem was solved using a matrix generator designed for network-like problems and MPSARX, a state-of-the-art general-purpose mathematical programming software system augmented with advanced automatic reformulation and cut generation features.