A single product, finite horizon production planning model with known requirements is considered. Production and holding-backorder cost functions are assumed to be piecewise concave, thereby allowing an arbitrarily close approximation to a wide range of cost functions which one might encounter in practice. In each period production, inventories and backlogged orders may not exceed prescribed levels. Production (inventory) breakpoints are the endpoints of the intervals over which the production (holding-backorder) cost functions are concave. It is shown that there is an optimal production schedule which has the property that between successive periods in which ending inventories are at inventory breakpoint levels there is at most one period in which production is not at a production breakpoint level. This property, which is an extension of recent results obtained by Florian and Klein [Florian, Michael, Morton Klein. 1971. Deterministic production planning with concave costs and capacity constraints. Management Sci. 18 (1, September) 12-20.] and Love [Love, Steven F. 1973. Bounded production and inventory models with piecewise concave costs. Management Sci. 20 (3, November) 313-318.], suggests a straight-forward dynamic programming algorithm for obtaining an optimal solution.
In this paper a probabilistic branch and bound procedure is developed for the ambulance location problem. Information on system characteristics under various ambulance assignments and dispatch rules was provided by a digital simulation. The output of the simulation was also used to construct the objective function for the optimal location problem. The procedure was used to determine ambulance locations in Vancouver, Canada. Solutions obtained from the branch and bound procedure were verified by simulation runs.
This paper employs multiattribute value assessment and risk analysis to evaluate the benefits of four alternatives to improve electrical system reliability in British Columbia. A multiattribute value model is constructed as a cost-equivalent function, based on value judgments provided by a group of senior system planners and two senior vice presidents from BC Hydro. Using data drawn from the utility's service records and probabilities elicited from the utility's technical specialists, a risk analysis is developed to estimate the magnitude and duration of outages associated with the various alternatives. The value model and probabilities are combined to estimate the expected equivalent costs of outages over time, for the four alternatives. The influence of this analysis on BC Hydro's transmission system planning is also discussed.
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