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The total demand is tons, and the demand for each order is given in Table 1. The release time and due date of each order see Table 1 fall at only 8 a. The total planning horizon is divided into 11 time periods as illustrated in Figure 2. For each order, the time window is shown in Table 1 and Figure 3. The numbers in Figure 3 indicate the demands for the orders. The deodorizer can process a maximum batch size of 7.
Aggregated time periods. Figure 3. Time window and demand for each order; amounts in tons. The processing time for each batch should be fixed to values that are multiples of 0.
For each batch, the minimum batch size is 3. The downtime is 15 min 0.
The unit processing cost is 0. All of the runs described in this section were done in GAMS The optimality gap was set to 2. The obtained objective function value is The breakdown of the optimal profit is given in Table 3. The Gantt chart of the optimal schedule obtained from model DEO-S1 is given in Figure 4, which shows that there are total of three changeovers in the planning horizon.
Different colors indicate the different product groups, and each bar contains one Figure 4.
Figure 5. Note that each batch production might satisfy multiple orders. The production levels of products and orders are given in Figures 5 and 6, respectively. As there is no inventory in the optimal solution, which means that products are processed and delivered in the same week of the processing, the sale of each order at each time period can also be seen in Figure 6. In the optimal solution, of 70 orders, 66 orders Most of the partially satisfied orders Only four orders 5.
The total sale is The service level of each order is given in Table 4. The obtained optimal objective is The breakdown of the optimal profit is given in Table 5. Although there is no inventory cost in the optimal solution of this case, inventory cost can occur for the cases with higher minimum batch sizes. As in the optimal solution of scenario 1, three changeovers occur in the scenario 2 as well.
Of the total of 70 orders, 67 orders It should be mentioned that, of the 45 fully satisfied orders, 42 orders are fully satisfied at their due dates and 3 orders are fully satisfied at later dates. The service level of each order is given in Table 6 numbers in bold indicate that the corresponding orders are fulfilled by their due dates , from which it can be seen that even the partially satisfied orders have high service levels.
The backlog of each order at the end of each period is given in Table 7. In each line, the first column with a reported backlog level is the due date of the corresponding order. A decrease of the reported backlog level means that the corresponding order Ind. From Table 7, there are three orders O21, O31, and O40 that are not satisfied by their due dates, but are satisified later by the end of the planning horizon. There are 25 orders with backlogs at the end of planning horizon, and the total backlog amount is Comparison with a Literature Model In this section, the efficiency and effectiveness of the proposed models are examined by comparison with a literature model proposed by Kelly and Zyngier.
In the third illustrative example presented in their article, a case study similar to the one in this article was considered. Their case study considered a planning horizon of 3 days and a total of 45 orders. As only sequencing constraints were presented in their article, we added our proposed objective function and constraints for production, inventory, and sales to the literature model for comparison. The details of the literature model and added constraints are presented in the Appendix. The modified literature model was also used for the case study in section 4.
Looks like you are currently in Finland but have requested a page in the United States site. Wu, D. Food and Drug Administration. Create Alert. New York: Prentice Hall. This removes most degrees of freedom, hence makes the problem computationally tractable, but provides results that are suboptimal, and very often far from optimal [1].
As the batch time and changeover time in the case study were 15 min, the length of each discrete slot used for the case study was 15 min, and a total of slots were used in the model for this case study. The modified literature model was implemented under the same computational environment and same termination criteria.
The answer to the problem are multiproduct plants designed to meet modern topic, treating the different concepts known for multiproduct plants, their technical . Multiproduct Plants. Editor(s). Dipl.‐Ing. Joachim Rauch. First published May Print ISBN |Online ISBN |DOI/.
The model sizes of the proposed model DEO-S1 and modified literature model are shown in Table 8, from which we can see that the proposed model has a much smaller model size than the literature model. The literature model was terminated by the CPU limit and required CPU s to find a solution with an objective value of On the other hand, the proposed model identifies a solution of in only 20 CPU s. The service level obtained from the literature model is only From the comparison results, it is obvious that the proposed model has a significantly better computational performance.
Concluding Remarks In this work, the short-term scheduling problem of a singlestage batch edible-oil deodorizer has been investigated, and MILP models have been developed for two scenarios. The novelty of the proposed models is that the processing sequence of the product groups is considered, instead of that of the products. In addition, the proposed formulation is based on the classic TSP formulation to model the production sequence in each time period.
The proposed models have been successfully applied to the deodorizer scheduling problem with 70 orders. Finally, the effectiveness of the models is shown through a comparison with a discrete-time literature model that addresses a similar case study. Figure 8. Parameters 38 Kelly and Zyngier presented an MILP formulation for modeling sequence-dependent changeovers for discrete-time scheduling problems. The formulation can be applied to both batch and continuous process units.
For comparison with the proposed model, operation i in the above equations is regarded as the processing operation for product i. Jeff D. Kelly from Honeywell for providing data and useful discussions for the case study used in this work.
Literature Cited 1 Pinto, J. Planning and Scheduling in the Process Industry. OR Spectrum , 24, — Finally, the proposed model is generalized to account for the case of slots having zero time duration. The novelties of the proposed formulations are demonstrated on a representative scheduling problem of a refinery. View Author Information. Cite this: Ind. Article Views Altmetric -. Citations 5. Abstract This paper addresses cyclic scheduling of continuous multiproduct plants operating in a hybrid flowshop, where the operation in the plant envelope is neither strictly sequential nor in a strictly parallel mode.
Cited By. This article is cited by 5 publications. Rohit Omar and Munawar A. DOI: Munawar A. Shaik and, Christodoulos A. Munawar and, R. Songsong Liu, Jose M. Pinto, Lazaros G. MILP-based approaches for medium-term planning of single-stage continuous multiproduct plants with parallel units. Chemical Engineering Research and Design , 83 10 ,