Comparison of stochastic approaches to the transportation problem: a case study

The objective of this case study is to provide insight to practitioners about the methodology of using the space-time autoregressive integrated moving average (STARIMA) class of models to formulate stochastic demand of the transportation problem. While providing insight, two other methods-expected value (EV) and stochastic approximation (SA)-are also employed to formulate demand. A comparative evaluation of the methods using brewery data for the distribution of four products from five production plants to 64 distribution centers is presented. It is shown that the demand characterized by the STARIMA approach results in a lower total cost of transportation. This occurs because the STARIMA approach results in better forecasts. Based upon the case study, the cost analysis indicated that the STARIMA method when used without (with) updating resulted in a 9.49% (10.5%) increase in the Company´s net profit as compared with the SA method. Similarly, the STARIMA approach when used without (with) updating resulted in an 11.36% (12.37%) increase in the net profit as compared with the EV method. For the STARIMA approach, computations for a large size problem are shown to be identical to those of the deterministic transportation problem given the demand forecasts. Extra computation effort for producing STARIMA forecasts are easily justified in terms of the increased profit margin