(610f) An Efficient Routine to Increase Robustness of Production Plans Embedded in an Integrated Multi-Scale Planning and Scheduling Approach

Make to order production within the process industries is generally operated in a very unpredictable and competitive environment where the key factors to succeed are to provide high service levels and flexibility at the same time as offering inexpensive products. To receive customers production companies must often promise shorter lead-times and the option of adjusting order quantities and changing delivery dates. It is a challenging task to cope with uncertainty and variation in the demand and when combined with the challenge of cutting down the production costs to be able to provide inexpensive products, the proper planning and scheduling of the production becomes very difficult and crucial for success. The pharmaceutical industry is a good example of an industry where planning and scheduling of make to order production is a big challenge. Flexible multi-product production processes have become commonly used as they help companies to respond to changing customer demand and increase plant utilization, but the greater complexity of these processes together with the altered market conditions have rendered the relatively simple planning and scheduling techniques previously used insufficient [1] which emphases the current need for flexible and efficient methods. In this paper we propose an efficient and useful modeling approach based on integrated multi-scale optimization models and solution methods for planning and scheduling of a make to order production process under uncertain and varying demand conditions. As an inspiration we have a large real world problem originating from a complex pharmaceutical enterprise. The approach is based on a hierarchically structured moving horizon algorithm. On each level in the algorithm we propose optimization models to provide support for the relevant decisions and the models are solved with efficient decomposition heuristics. The levels are diverse regarding the time scope, aggregation, update rate and availability of data at the time applied. The maximum effective time horizon of the multi-scale approach is one year and we use sale forecasts as input demand instead of actual orders which are usually only available 3 months ahead in time although raw materials need to be procured up to one year in advance. The sale forecasts have historically proven to be rather uncertain and to increase the robustness of our long-term plans we use an iterative procedure where the first step is to use a MILP model to obtain a solution based on the sale forecasts. In the next step we generate a number of alternative demand samples and run LP models to test the robustness of the MILP solution with each of the demand samples. If the long-term production plan is feasible for enough many of the demand samples, depending on our robustness criteria, then we use the current plan, but if not then we change the demand forecast and run the MILP model again iteratively until the robustness criteria has been met. The demand samples are generated with tailor made methods based on statistical error analysis that include both temporal and quantitative error factors. Approaches based on the framework of scenarios can be widely found in the chemical engineering literature [2]. Those approaches attempt to forecast and account for all possible future outcomes through the use of a number of scenarios but the size of the problem increases exponentially with the number of uncertain parameters which make a scenario based approach unsuitable for large real-world problems such as under consideration in this study. Our approach is a computationally efficient alternative to these approaches and it increases the robustness of the plan but it does however not guaranty a feasible plan or schedule for all possible outcomes. The approach has been tested and implemented with industrial data from a pharmaceutical enterprise and has proved to be capable of obtaining realistic and profitable solutions within acceptable computational times.

[1] Shah, N., Pharmaceutical supply chains: key issues and strategies for optimisation. Computers & Chemical Engineering, 2004. 28(6-7): p. 929-941. [2] Floudas, C.A. and X.X. Lin, Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review. Computers & Chemical Engineering, 2004. 28(11): p. 2109-2129.