Trim Loss Research Articles

Efficient waste reduction algorithms based on alternative underestimates for the modified Wang method

This paper is concerned with wastage reduction in constrained two-dimensional guillotine-cut cutting stock problems, often called trim loss problems. A number of researchers report in the literature on algorithmic approaches to find exact solutions for the trim loss problem. Alternative heuristic functions are investigated and applied to the modified Wang method. This involves the sharpening of underestimates used in the methods heuristic function. Two aspects of these solution approaches are considered and some empirical results are given. The first part considers the feasibility to construct more informed heuristic functions. The second part investigates the role of more informedness on the computational cost of these search processes.

Heuristic for the two-dimensional arbitrary stock-size cutting stock problem

A heuristic is presented for the two-dimensional arbitrary stock-size cutting stock problem, where a set of rectangular items with specified demand are cut from plates of arbitrary sizes that confirm to the supplier’s provisions, such that the plate cost is minimized. The supplier’s provisions include: the lengths and widths of the plates must be in the specified ranges; the total area of the plates with the same size must reach the area threshold. The proposed algorithm uses a pattern-generation procedure with all-capacity property to obtain the patterns, and combines it with a sequential heuristic procedure to obtain the cutting plan, from which the purchasing decision can be made. Practical and random instances are used to compare the algorithm with a published approach. The results indicate that the trim loss can be reduced by more than half if the algorithm is used in the purchasing decision of the plates.

Three-step solutions for cutting stock problem of construction steel bars

The cutting stock problem of construction steel bars has a strongly heterogeneous assortment of demand items. This research develops new solution procedures which result in the efficient cutting plans with minimum trim loss and number of stocks used. The procedures consist of three steps namely the generation of a set of efficient cutting patterns, the optimization of one dimensional cutting stock problem, and the cut of undersupplied items with the best fit decreasing algorithm. The first step, the Intensive Search algorithm generates a set of efficient cutting patterns which are made up of various demand lengths according to their demands quantities. The second step, the optimization of One Dimensional Cutting Stock Problem (1D-CSP) using Genetic Algorithm is proceeded to determine the numbers of cutting times of the patterns. All these cut items are constrained to not exceed the demanded pieces. The third step, few remaining undersupplied items are cut using the best fit decreasing algorithm. Test results showed that the solutions from different runtimes gave comparable percentages of waste. Important parameters such as the number of efficient cutting patterns and the allowable trim loss of the patterns could affect the solutions. Test results indicated that the new solution procedures could give low-waste cutting plans.

Two‐stage two‐dimensional guillotine cutting stock problems with usable leftover

AbstractIn this study, we solve the nonexact two‐stage two‐dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (nonused material or trim loss) can be used in the future, if they are large enough to fulfill future demands for items (ordered smaller plates). This cutting problem can be characterized as a residual bin‐packing problem because of the possibility of putting back into stock residual pieces, as the trim loss of each cutting/packing pattern does not necessarily represent waste of material depending on its size. Two bilevel mathematical programming models to represent this nonexact two‐stage two‐dimensional residual bin‐packing problem are presented. The models basically consist of cutting/packing the ordered items using a set of plates of minimum cost and, among all possible solutions of minimum cost, choosing one that maximizes the value of the generated usable leftovers. Because of special characteristics of these bilevel models, they can be reformulated as one‐level mixed integer programming models. Results of some numerical experiments are presented to show that the models represent appropriately the problem and illustrate their performance.

A New Decision Model for Reducing Trim Loss and Inventory in the Paper Industry

In the paper industry, numerous studies have explored means of optimizing order allocation and cutting trim loss. However, enterprises may not adopt the resulting solutions because some widths of the inventory exceed or are less than those required for acceptable scheduling. To ensure that the results better suit the actual requirements, we present a new decision model based on the adjustment of scheduling and limitation of inventory quantity to differentiate trim loss and inventory distribution data. Differential analysis is used to reduce data filtering and the information is valuable for decision making. A numerical example is presented to illustrate the applicability of the proposed method. The results show that our proposed method outperforms the manual method regarding scheduling quantity and trim loss.

Flexible Stock Allocation and Trim Loss Control for Cutting Problem in the Industrial-Use Paper Production

We consider a one-dimensional cutting stock problem (CSP) in which the stock widths are not used to fulfill the order but kept for use in the future for the industrial-use paper production. We present a new model based on the flexible stock allocation and trim loss control to determine the production quantity. We evaluate our approach using a real data and show that we are able to solve industrial-size problems, while also addressing common cutting considerations such as aggregation of orders, multiple stock widths, and cutting different patterns on the same machine. In addition, we compare our model with others, including trim loss minimization problem (TLMP) and cutting stock problem (CSP). The results show that the proposed model outperforms the other two models regarding total flexibility and trim loss ratio.

Effects of blade tenderization, aging method and aging time on meat quality characteristics of Longissimus lumborum steaks from cull Holstein cows

The effects of blade tenderization (BT), two aging methods (dry (D) and wet (W)), and aging time (2 and 23 d) on tenderness, color, and sensory properties of Longissimus lumborum muscles from 12 cull Holstein cows were evaluated. Dry-aged loins had higher combined trim and aging losses than control (C) for both D- and W-aging, mostly because of excess trim losses. BT steaks had WBSF of 33.13N while C steaks had WBSF of 41.46N (P=0.09). Aging decreased WBSF. Blade tenderized steaks had higher cook loss than C steaks. Aging, W-aging, and BT×W-aging improved myofibrillar (sensory) tenderness scores. Aging and/or BT improves sensory panel tenderness cull cow Longissimus lumborum steaks. Aging and blade tenderization combined can increase tenderness and value of Longissimus steaks from cull Holstein cows.

Approaches to real world two-dimensional cutting problems

We consider a real world generalization of the 2-Dimensional Guillotine Cutting Stock Problem arising in the wooden board cutting industry. A set of rectangular items has to be cut from rectangular stock boards, available in multiple formats. In addition to the classical objective of trim loss minimization, the problem also asks for the maximization of the cutting equipment productivity, which can be obtained by cutting identical boards in parallel. We present several heuristic algorithms for the problem, explicitly considering the optimization of both objectives. The proposed methods, including fast heuristic algorithms, Integer Linear Programming models and a truncated Branch and Price algorithm, have increasing complexity and require increasing computational effort. Extensive computational experiments on a set of realistic instances from the industry show that high productivity of the cutting equipment can be obtained with a minimal increase in the total area of used boards. The experiments also show that the proposed algorithms perform extremely well when compared with four commercial software tools available for the solution of the problem.

Meat quality, microbiological status and consumer preference of beef gluteus medius aged in a dry ageing bag or vacuum

This study investigated meat quality and consumer preference after ageing beef gluteus medius in a water vapour-permeable dry-ageing bag or in vacuum for 14days. Higher ageing and trim losses but lower thawing loss, cooking loss and water content were found in samples aged in dry ageing bags compared to those aged in vacuum. Samples aged in dry ageing bags had higher total bacteria and yeast counts but lower lactic acid bacteria counts than those aged in vacuum, both before and after trimming. Meat aged in dry ageing bag was more tender and juicier and overall preferred by consumers compared with samples aged in vacuum. Female participants outperformed the males in detecting differences in palatability. No differences were found in pH, smell, shear force, colour, Enterobacteriaceae, and mould counts. Thus, by using a dry ageing bag, it is possible to produce dry-aged meat in a more controlled condition without negative effects on sensory or other quality attributes.

Trim Loss Minimization for Construction Reinforcement Steel with Oversupply Constraints

Construction work consumes a large amount of construction reinforcement steel and it demands this steel in various particular sizes according to structural designs. The steel have to be cut to the right sizes before uses. The cutting process creates a lot of trim loss and costly wastes. This research develops a new procedure for arranging cutting plans with minimum trim loss. The procedure is based on the optimization of one dimensional cutting stock problem. A set of efficient cutting patterns is generated first and then the cutting replications are determined from the optimization. The problem model has oversupply constraints which do not allow cutting any item more than the demanded pieces. Few remaining undersupplied items are lastly cut using the best fit decreasing algorithm. Therefore, the cutting plans created from this procedure will not make any oversupply which becomes waste and they will cut all pieces exactly as demanded. Test results indicated that this developed procedure could produce low trim-loss cutting plans. Also, the suitable number of efficient cutting patterns and the suitable allowable trim loss of the patterns could help result good cutting plans. 

Trim Loss Optimization by an Improved Differential Evolution

The “trim loss problem” (TLP) is one of the most challenging problems in context of optimization research. It aims at determining the optimal cutting pattern of a number of items of various lengths from a stock of standard size material to meet the customers’ demands that the wastage due to trim loss is minimized. The resulting mathematical model is highly nonconvex in nature accompanied with several constraints with added restrictions of binary variables. This prevents the application of conventional optimization methods. In this paper we use synergetic differential evolution (SDE) for the solution of this type of problems. Four hypothetical but relevant cases of trim loss problem arising in paper industry are taken for the experiment. The experimental results compared with those of the other techniques show the competence of the SDE to solve the problem.

Solving 2-Dimensional Multiple Length Cutting Stock Problem with MILP

This paper considers a 2-dimensional cutting stock problem. Unlike previous works, we study multiple lengths in each cutting pattern and 3 types of production loss including trim loss, setup loss, and over-production loss. The problem is first formulated as a MINLP model to minimize total production loss, which has a non-convex feasible region. All the model constraints are developed based upon real settings. To solve the model, the MINLP model is transformed to a MILP model by prespecifying all cutting patterns. Compared to the manual planning method currently used by the company, the proposed method can provide 20.3% improvement. Other benefits include the saving of man hours in the planning process, and the planning process can be performed by any workers instead of an expert.

New Hybrid Discrete PSO for Solving Non Convex Trim Loss Problem

Trim loss minimization is the most common problem that arises during the cutting process, when products with variable width or length are to be produced in bulk to satisfy customer demands from limited available/stocked materials. The aim is to minimize inevitable waste material. Under various environmental and physical constraints, the trim loss problem is highly constrained, non convex, nonlinear, and with integer restriction on all variables. Due to the highly complex nature of trim loss problem, it is not easy for manufacturers to select an appropriate method that provides a global optimal solution, satisfying all restrictions. This paper proposes a discrete variant of PSO, which embeds a mutation operator, namely power mutation during the position update stage. The proposed variant is named as Hybrid Discrete PSO (HDPSO). Binary variables in HDPSO are generated using sigmoid function with its domain derived from position update equation. Four examples with different levels of complexity are solved and results are compared with two recently developed GA and PSO variants. The computational studies indicate the competitiveness of proposed variant over other considered methods.

Aging method, USDA quality grade, and endpoint temperature affect eating quality of beef longissimus lumborum steaks

Tenderness is one of the most important factors affecting consumers' perceptions and acceptance of palatability. Tenderness is affected by both myofibrillar proteins and connective tissue content and quality. Both marbling and carcass maturity can have a significant effect on beef palatability, with higher consumer sensory scores generally given to USDA Choice loin steaks than to Select steaks for tenderness, juiciness, and overall palatability. Endpoint temperature can also have a significant effect, with higher endpoint temperatures generally decreasing palatability. Aging beef is a common practice in the meat industry because it increases tenderness and flavor development. The meat industry generally utilizes two types of aging, vacuum and dry aging. Vacuum aging, in which meat is aged in a sealed barrier package at refrigerated temperatures, is the most widely used practice. Dry aging refers to aging meat without packaging, and requires greater environmental control to achieve consistent product quality. Vacuum-aged beef has a sourer and stronger bloody/serumy flavor, whereas dry-aged beef has a more beefy, brown-roasted flavor. Dry aging generally results in greater aged flavor of steaks with no advantage for tenderness, and it is a costly procedure because of decreased yields due to greater weight and trim losses than vacuum aging. Flavor benefits of dry aging and distinct yield advantages of vacuum aging stimulated researchers to develop a "special bag" with a very high water vapor transmission rate and very low oxygen transmission rate to decrease shrink and trim loss but create a dry-aged flavor.

Hybrid heuristic algorithm for two-dimensional steel coil cutting problem

This paper is concerned with the problem of two-dimensional cutting of small rectangular items, each of which has its own deadline and size, from a large rectangular plate, whose length are more than one thousand times its width, so as to minimize the trim loss and the reduction of the times of clamping and changing speed are also concerned. This problem is different with the classical two-dimensional cutting problem. In view of the distinguishing features of the problem proposed, we put forward the definition of non-classical cutting, that is to say, put a series of items on the rectangular plates in their best layout, so as to enhance utility and efficiency at the same time. These objectives may be conflicting and a balance should be necessary, so we present a Hybrid Heuristic Algorithm (HHA), consisting of clustering, ordering, striping and integer programming etc. We demonstrate the efficiency of the proposed algorithm through the comparison with the algorithm we studied before.

Building Information Modeling–Based Analysis to Minimize Waste Rate of Structural Reinforcement

AbstractBuilding information modeling (BIM) is an emerging tool in architecture/engineering/construction (A/E/C) industry that is used to design, document, and enhance communication among all the project stakeholders. Trim loss of rebar can be minimized with the use of discrete bars. To achieve this goal, a model to analyze reinforced concrete structure with one-dimensional (1D) cutting waste-optimization technique, integrated with BIM, is proposed. Building information modeling is selected as the hub in communicating project information among diverse design teams. This process permits project teams to utilize BIM models to simulate architectural and structural design requirements, and compare results speedily to make necessary changes in the designs to minimize rebar waste. The BIM rebar optimization analysis approach also supports cost-effective decision making during the design process. The proposed approach was validated with a two-story reinforced concrete structure, and the results indicated a high ...

A GENERALIZED APPROACH TO THE SOLUTION OF ONE-DIMENSIONAL STOCK-CUTTING PROBLEM FOR SMALL SHIPYARDS

A generalized approach is introduced for the optimization of one-dimensional cutting stock problem (1D-CSP), which occurs in wide variety of engineering manufacturing processes especially in ship building industry, Instead of making preliminary specifications and accordingly ignoring many alternative arrangements, the suggested optimization technique selectively considers feasible arrangements by eliminating majority of the possible but inefficient arrangements thus rendering the problem solvable for practical applications. The introduced approach, which minimizes the piece arrangement plans and trim losses in the material, achieves the ideal solution implied by the analytical methods. Another important advantage of the present method is its ability to produce integer results, which usually cannot be obtained by means of analytical methods used in linear programming. Overall, the solution of the problem has been drastically simplified even to allow hand calculations instead of long computer runs. Thus the introduced approach can be very functional for small shipyards and single boat builders. The introduced approach is evaluated by two numerical examples.

On the Lambert W function: Economic Order Quantity applications and pedagogical considerations

We illustrate the use of the Lambert W function by analysing two Economic Order Quantity (EOQ) scenarios: an EOQ model with perishable inventory; and a Net Present Value analysis of an EOQ problem with trim loss. Both scenarios are motivated by real-world situations. Via these two examples, we reflect upon the pedagogical aspects of using the Lambert W function. We present a Lambert W function ‘look-up’ table for classroom use and a Microsoft Excel ‘Add-In’ for self-study and practical use. We also illustrate the use of the Laplace transform to conduct NPV analyses of the EOQ model.

Large Scale Production Planning in the Stainless Steel Industry

We introduce a new formulation for a cutting stock problem in the stainless steel industry. The formulation extends some previous models developed for the paper industry. In this formulation, mother coils are assumed to have finite lengths, and the widths and lengths of the mother coils are considered variables as well as the lengths of the product coils along with the cutting patterns to be used. To enable reuse of scrap material, the trim loss at the end of a mother coil is preferred and collected into a single coil. Finally, the scattering of an order to multiple mother coils is minimized to facilitate the shipping of the order in a single batch. For numerical solution, the inherently nonlinear problem is transformed to a linear one by a decomposition technique. The procedure is illustrated with numerical examples. The presented model has been successfully utilized in large scale industrial environment as a part of the production planning system developed for Outokumpu Stainless by Accenture.

Assessment of stock size to minimize cutting stock production costs

Abstract A method for assessing the optimal stock size for the expected order size for a single-period one-dimensional cutting stock problem is proposed. The stock size is optimal when the expected total costs of trim loss, warehousing, and non-fulfilment are minimum. The stock size is the sum of all bar lengths in the stock, and the order size is the sum of shorter bar lengths in various numbers of pieces. Using simulated test cases, a statistical estimation of optimal stock size is conducted, which in our case is approximately 50% above the expected order. The proposed method can help company choose the appropriate level of stock to minimize their total costs.