دانلود رایگان مقاله زمانبندی برنامه ریزی خطی عدد صحیح مختلط در تاسیسات پروسه تولید بستنی

Abstract

This paper presents a multi-week mixed integer linear programming (MILP) scheduling model for an ice cream processing facility. The ice cream processing is a typical complex food manufacturing process and a simplified version of this processing has been adapted to investigate scheduling problems in the literature. Most of these models only considered the production scheduling for a week. In this paper, multi-week production scheduling is considered. The problem has been implemented as an MILP model. The model has been tested on a set of cases from the literature, and its results were compared to the results of problems solved using hybrid MILP-heuristics methods in the literature. The inclusion of clean-up session, weekend break and semi-processed product from previous week were also assessed with two additional sets of experiments. The experiments result show that the proposed MILP is able to handle multi-week scheduling efficiently and effectively within a reasonable time limit.

5. Conclusion and future work

This paper proposed an MILP model (without heuristics) for an ice cream multi-week production scheduling problem. The model adopted the makespan objective and a number of constraints including start/stop interval formulation, and processed product arranging constraints. Multi-week constraints were formulated to address the unique arrangements required to transfer products from week to week. This included constraints for integrating products from preceding production week, proper break-up points of products processing for the weekend break, and end of the week clean-up session. The model is implemented in CPLEX and three sets of optimization experiments were conducted. The first set of experiments showed that proposed MILP model was capable of solving problem instances that necessitated the use of heuristics to an MILP model in the past. The second and third sets of experiments compared the run results for cases with transferred products from prior week as well as added weekly clean-up and process break-up points for weekends. Proper break-up of process affected the final makespan value and hence would have to be integrated into the model. In particular, these runs showed that adding the clean-up sessions at the end may not give the same result as scheduling the sessions with proper break-up points