Browsing by Subject "Production functions"

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Open Access
The dynamic lot-sizing problem with convex economic production costs and setups
(Elsevier, 2014-09) Kian, R.; Gurler, U.; Berk, E.
In this work the uncapacitated dynamic lot-sizing problem is considered. Demands are deterministic and production costs consist of convex costs that arise from economic production functions plus set-up costs. We formulate the problem as a mixed integer, non-linear programming problem and obtain structural results which are used to construct a forward dynamic-programming algorithm that obtains the optimal solution in polynomial time. For positive setup costs, the generic approaches are found to be prohibitively time-consuming; therefore we focus on approximate solution methods. The forward DP algorithm is modified via the conjunctive use of three rules for solution generation. Additionally, we propose six heuristics. Two of these are single-stepSilver-Meal and EOQ heuristics for the classical lot-sizing problem. The third is a variant of the Wagner-Whitin algorithm. The remaining three heuristics are two-step hybrids that improve on the initial solutions of the first three by exploiting the structural properties of optimal production subplans. The proposed algorithms are evaluated by an extensive numerical study. The two-step Wagner-Whitin algorithm turns out to be the best heuristic.
Open Access
Technology improvements under carbon emissions taxes
(2023-08) Ayas, Onurcan
In this thesis, we consider two technology improvement problems under carbon taxation policies. In the first one, a manufacturer subjected to a carbon tax producing a single product using multiple inputs and employing an initial technology level, which is modeled using the Cobb Douglas production function. We find out that 1) when the output and the technology level are binding, amount of a production input is increasing in carbon tax if the share of the tax due to its carbon footprint in its total variable cost is less than the weighted average of that of all production inputs; 2) when the output is binding, but the technology level is non-binding, while the technology level is always increasing in carbon tax; amount of an input is increasing in carbon tax only if the share of the tax times its carbon footprint in its total variable cost is less than the weighted average of that of all production factors (including technology level); 3) when the output is non-binding, but the technology level is binding, the output, as well as the inputs, is decreasing in carbon tax, at optimality; 4) when the output and the technology level are non-binding, all of the decision variables are decreasing in carbon tax, at optimality. In the second problem, we consider setup reduction activities for a stochastic inventory system, where improvement efforts are modeled via production functions. We derive the optimality quantities of required labor and capital input for improvement, as well as the ordering quantity and reorder point.