Production Decisions with Convex Costs and Carbon Emission Constraints
Ph.D. Thesis Presentation by
Department of Industrial Engineering
In this study, different variants of the production planning problem are considered.
We first study an uncapacitated deterministic lot sizing model with a special production function which determines the relation between resource and output quantities. In particular, we have considered the Cobb-Douglas production function which is applied in sectors such as energy, agriculture and cement industry. We demonstrate that this problem can be reformulated as a lot sizing problem with nonlinear production cost which is convex under certain assumptions. We develop a polynomial time dynamic programming based algorithm and several fast heuristics to solve the model. We compare the performances of the heuristics with extensive numerical tests.
Next, motivated from the reformulation of the first problem, we consider a lot sizing problem with convex nonlinear production and holding costs for decaying items. The problem is investigated from mathematical programming perspective. We propose a structural procedure to reformulate the problem in the form of second order cone programming and employ some optimality and valid cuts to strengthen the model. We conduct an extensive computational test to see the effect of cuts in different formulations. We also study the performance of the heuristics in a rolling horizon basis. We conduct an extensive numerical study to compare the heuristics and to see the effect of forecast horizon length on heuristic dominance order and to see where they outperform exact solution approaches. Finally, we study the lot sizing problem with carbon emission constraints. We propose two Lagrangian heuristics when emission constraint is cumulative over periods. We extend the model with possibility of lost sales and examine several carbon cap policies for a cost minimizer manufacturer. We conduct a cost-emission Pareto analysis for different emission cap configurations.