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Linear weighing is a common approach to handle multiple criteria and the "knapsack" is a well-known combinatorial optimization problem. A knapsack problem with two linearly weighted, objective criteria is considered in this paper. For better support, it is important to provide the decision maker with information that covers the whole range of alternatives. Toward this goal, an algorithm for the construction of a parametric solution to the problem, i.e., for any combination of weights, is developed, which is based on finding a longest path in a network which compactly represents all feasible solutions to the knapsack problem. Exploiting the special structure of the knapsack model, the algorithm efficiently constructs the parametric solution in time that is linear in the product of the number of variables, the resource limit (right-hand side of the constraint), and the (finite) number of vectors which constitute the solution. The amount of memory required is linear in the product of the number of variables and the resource limit. Results of computational study are reported. The results are used to assess the efficiency of the algorithm and characterize its behavior with respect to the parameter values.programming-multiple criteria, solution for linear-bicriteria knapsack problems, network/graphs-applications, of the shortest path model

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Purpose -Labor is the largest single cost contributor in agriculture. Accurate estimation of labor requirements is, thus, a key to cost reduction. Work measurement is the professional discipline for this type of estimations, in the industrial engineering domain. Horticulture, however, lays a substantial barrier to work and, thus, to work measurement. Till harvesting, its products -fruits/flowers, are in fixed positions, and for all tasks the workers have to arrive at the plant. The purpose of this paper is to develop, test and analyze a system to perform horticultural work study in agricultural environments in order to accurately estimate the required amount of labor for each activity and to improve productivity. Design/methodology/approach -In this paper, the development of an advanced system for work study on a hand-held computer (HHC) platform for horticultural work measurement is presented and an experimental study was conducted. The methodology consists of characteristics of the system platform including hardware, interface and software, development of a dedicated measuring software, a controlled experiment in agricultural environment and a statistical analysis. Findings -The study shows that a single surveyor who uses traditional tools is subject to measurement errors, which can be reduced only with the assistance of a second surveyor. The study further shows that the HHC platform enables to avoid this second surveyor -a single surveyor who uses the HHC platform performs as accurate as two surveyors who use traditional tools. Of course, being computers, the HHC platform maintains the advantage of error free data transfer, in practically negligible time. Originality/value -This paper presents a unique approach to perform work study in agricultural environment and contributes to minimize the errors accumulated in the process and the manpower required to perform the measurements.