Some novel applications and pragmatic variations of knapsack problem (KP) are presented and constructed, which are formulated and developed from a model initiated in this paper on profit allocation from partition of jobs in terms of two-person discrete cooperation game. §1 Introduction Now the production of high value-added products, which needs advanced techniques and enormous throughput, has been globally highlighted and pursued on account of the putatively potential or existent scarcity of metal mineral resources, woods, petroleum, natural gas, and water, the severe atmospheric and aquatic pollution, and the unavailing rapid increase in population. Consequently it is probable that a single producer does not possess enough facilities and trained manpower simultaneously when he faces a large-scale manufacturing project. In order to acquire the benefit, some producers have to cooperate by obtaining or completing those tasks together. Then how to share manufacturing profit becomes the core concern in an alliance of those manufacturers. Hence the research on new cooperation game involving profit allocation from job partition and schedule seems to be more and more necessary and striking in the domain of manufacturing management recently.In this type of models there are some common and elementary problem characteristics as follows. Two parties (producers) are interested in the processing task of n jobs offered by a customer and neither of them can or will undertake the project independently. But after an alliance composed of these two parties or one of them obtains the orders on those n jobs via a bid, they can collaborate to finish the relevant operations.Perhaps the initial work on this topic appears in [1]. Between our model and the one in [1] there are two differences. First, we are concerned with the scenario where the bargaining power of one party is much greater than that of the other party and therefore the former can
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