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Breakability rate of fragile item depends on the accumulated stress of heapedstock level. So breakablility rate can be considered as dependent parameter ofstock variable. The unit production cost is a function of production rate andalso dependent on raw material cost, development cost and wear-tear cost. Theholding cost is assumed to be non-linear, dependent on time. Here optimalcontrol problem for a fragile item under finite time horizon is considered. Theprofit function which consists of revenue, production and holding costs isformulated as a Fixed-Final Time and Fixed State System(cf. Naidu (2000))optimal control problem with finite time horizon. Here production rate isunknown and considered as a control variable and stock level is taken as astate variable. It is formulated to optimize the production rate so that totalprofit is maximum. As particular cases, models are evaluated with and withoutbreakability. The models are solved by using conventional Variational Principlealong with the non-linear optimization technique-Generalised Reduced GradientMethod (LINGO 12.0). The optimum results are illustrated both numerically andgraphically. Some sensitivity analysis on breakability coefficient arepresented.

Optimum Production for a heaped stock dependent breakable item through variational principle