Browsing by Author "Vergara, Francisco P."
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Item A comparison of optimization models for lumber production planning(2015) Palma, Cristian D.; Sepúlveda, Héctor; Vergara, Francisco P.The performance of sawmills is strongly dependent on how logs are sawn into lumber in order to satisfy the customer demands. To do this, sawmill managers have to decide which cutting patterns have to be applied to logs of different dimensions. Optimization models have been proposed to assist decision makers in this process, but only the profit maximization and the cost minimization of the decisions have been considered as the models objective. In this paper, a linear optimization model was formulated to address lumber production planning and applied to a real problem. The current decisions at sawmills were compared with five different objective functions: the two previously mentioned plus waste minimization, log number minimization and production time minimization. Only profit maximization and waste minimization models reported positive economic returns. Although the current decision at sawmills also reported a positive economic return, the same economic result was obtained with significantly fewer resources using the waste minimization model. The effects of the different objectives on the production indicators were discussedItem A Multiobjective Model for the Cutting Pattern Problem with Unclear Preferences(2016) Palma, Cristian D.; Vergara, Francisco P.The cutting pattern problem has been traditionally approached using single objective optimization models, although the sawmill performance is usually measured using more than a single indicator. One of the shortcoming of using multiobjective approaches is that they need a preference relationship among the objectives, which is difficult to determine in practice, and solutions are very sensitive to these preferences. In this article, we consider different criteria in a sawmill decisionmaking context using a multiobjective linear optimization model and handle the unclear definition of the objective preferences by formulating a robust version of the model. Although the deterministic formulation assumes perfect information of the objective preferences, in the robust formulation we consider that preferences may be different from their estimate. We show that deterministic decisions are more balanced in terms of the different criteria than the traditional single objective models, although their quality is very sensitive to the objective preferences. We also show that robust decisions are also balanced but less sensitive to the preferences. We explore how the level of the different indicators and the cutting decisions are affected when the preferences are unclear.Publication Assessing the effectiveness of static heuristics for scheduling lumber orders in the sawmilling production process(2024) Vergara, Francisco P.; Palma, Cristian D.; Nelson, John D.Although optimization models can be used to plan the production process, in most cases static heuristics, such as earliest due date (E), longest processing time (L), and shortest processing time (S), are used because of their simplicity. This study aims to analyze the production cost of the static heuristics and to determine how this cost relates to the size of the production orders in the sawmilling industry. We set a planning problem with different orders and due dates and solved it using two cost-minimization models to compare their solutions. The first was a planning model (PL) where orders were split up into products demand by period, and the second, a planning scheduling (PS) where the sequence of processing orders based on static heuristics was assumed as known. In the latter, the minimum production cost for each static heuristic was found. In both models, the same resource constraints were assumed. The costs showed no significant changes based on order sizes. However, 0,5 % of orders were delayed using PS-E, and 17 % of orders were delayed using PL. PL was an efficient solution method when changing the orders´ size and when looking for the best static heuristic to process the orders. However, PS-E showed the ability to reduce the backlog close to zero while the PL backlog ratio was 17 %. No penalties were applied to backlogs due to their subjective nature; however, when shortages occurred, the demand was unmet or backlogged with substantial costs. Thus, in case the proposed method is adopted using a conservative backlog cost, a sawmill producing under the cut-to-order environment that produces 300000 m3 /year would reduce backlogged orders by 51000 m3. If the holding lumber cost is 2 $/m3, annual savings would be $408000.Item Desarrollo de un algoritmo para la generación y elección de soluciones de corte en la operación de canteo y despuntado en aserraderos(2011) Vergara, Francisco P.; Baesler, Felipe; Ramos, MarioIn this research work an algorithm that gathers the best procedures applied in sawmills was developed, along with a methodology based on cutting geometrical line analysis. This application was programmed under the C(++) language, sizes objective board and its prices, and the 2-D slab geometry are the input data, obtaining length and width solutions for every slab. Its outcomes have been compared with a pattern that matches the solutions provided by an "optimized" cutting machine in a southern sawmill in Chile. Four types of solutions were obtained when inputting slabs geometry, which was captured with four different reading steps. Outcomes show that solutions achieved with a reading width of 100 mm were 4% better in average than the pattern, and far better to other solutions achieved with the remaining 3 steps. Leaving aside the particular operating conditions of either method; a theoretical comparison of time by solution method, indicates that the 77 milliseconds SISCORMAD employed are significantly lower than those obtained with dynamic programming 320 milliseconds, 890 milliseconds with total enumeration, and 140 milliseconds obtained with geometric heuristic as solution times reported by [6]. This feature makes the developed algorithm very attractive for future applications. However, given the heuristic nature SISCORMAD, it is just a high quality solution, but not optimal.Publication Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model(2024) Palma, Cristian D.; Vergara, Francisco P.; Muñoz-Herrera, SebastiánIn many industries, companies receive customer orders that include multiple products. To simplify the use of optimization models for planning purposes, these orders are broken down, and the quantities of each product are grouped with the same products from other orders to be completed in the same period. Consequently, traditional production planning models enforce minimum demand constraints by product and period rather than by individual orders. An important drawback of this aggregation procedure is that it requires a fixed order fulfillment period, potentially missing opportunities for more efficient resource use through early completion. This paper introduces a novel mathematical formulation that preserves the integrity of customer orders, allowing for early fulfillment when possible. We compare a traditional linear programming model with a new mixed-integer programming approach using a sawmill case study. Although more complex than the traditional model, the proposed formulation reduces costs by approximately 6% by enabling early order completion and offers greater flexibility and control over the production process. This approach leads to better resource utilization and more precise order management, presenting a valuable alternative to conventional production planning models.