The cutting-wrapping problem in the textile industry: optimal overlap of fabric lengths and defects for maximizing return based on quality

This paper deals with an important problem in the last phase of manufacturing in the textile industry. This involves cutting large lengths of fabric into smaller pieces, which are then wrapped around rolls. The quality of cloth rolls transported to the customer is specified by the quality of fabric pieces that make up the roll. A piece of fabric falls within a given quality category if some of its characteristics, such as, piece length, the number of critical defects per metre, and the defective score per metre, are compatible with the corresponding quality specifications. Naturally, the selling price per metre of fabric is proportional to the quality category. Thus, it becomes necessary to determine an optimal cutting strategy of very long woven fabric (e.g. 2000 m) into smaller pieces (e.g. each 130 m long at most), which involves a difficult continuous assignment problem of identifying the optimal cutting: locations of pieces overlapping with defects of known lengths and locations. Not only must the scrap be minimized but the overall profit per metre fabric should be maximized. The two objectives may not always support each other due to relative unit selling prices of various quality categories. The solution to this problem has an immediate impact on company profit. The mathematical formulation of the problem involves numerous binary variables as well as continuous variables. A Mutative Simulated Annealing approach is proposed here to solve this problem. The solution technique is tested both on real data obtained from a textile manufacturer and hypothetical data. Results are compared against upper bounds calculated for each objective defined, as well as with a sequential heuristic designed for this problem

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This paper describes a dynamic and fuzzy logistics coordination model used for conducting disaster response activities such as evacuation of affected people, transportation of wounded people to hospitals and of commodities from warehouses to aid distribution centers. Post disaster logistics is usually carried out in uncertain environments and information obtained from affected areas might be impeded by infrastructure damage and the loss of those on official duty. Furthermore, in many situations it is not possible to access affected districts and damage assessment is carried out from airborne vehicles on a vague scale. Given the uncertainty in the number of people affected and wounded, and in the needs of people who have to stay in the region until they receive official help in finding shelter, the logistics problem is quite difficult to solve. In fact, vehicle routing and supplies coordination problems have their inherent difficulties even under certainty, because they are discrete problems classified as NP. In addition, discrete problems are known to be quite sensitive to changes in parameters. We represent uncertainty by using fuzzy parameters related to demand, supply, injured people and hospital service rates. We then de-fuzzify these parameters in an efficient routing and transportation model. During the initial response periods, the model produces logistics plans based on fuzzy parameter intervals that are calculated by usin

The capacitated lot sizing problem with overtime decisions and setup times

The Capacitated Lot Sizing Problem (CLSP) consists of planning the lot sizes of multiple items over a planning horizon with the objective of minimizing setup and inventory holding costs. In each period that an item is produced a setup cost is incurred. Capacity is limited and homogeneous. Here, the CLSP is extended to include overtime decisions and capacity consuming setups. The objective function consists of minimizing inventory holding and overtime costs. Setups incur costs implicitly via overtime costs, that is, they lead to additional overtime costs when setup times contribute to the use of overtime capacity in a certain period. The resulting problem becomes more complicated than the standard CLSP and requires methods different from the ones proposed for the latter. Consequently, new heuristic approaches are developed to deal with this problem. Among the heuristic approaches are the classical HPP approach and its modifications, an iterative approach omitting binary variables in the model, a Genetic Algorithm approach based on the transportation-like formulation of the single item production planning model with dynamic demand and a Simulated Annealing approach based on shifting family lot sizes among consecutive periods. Computational results demonstrate that the Simulated Annealing approach produces high quality schedules and is computationally most efficient