Konveks üretiım maliıyetleri ve karbon emisyon kısıtları altında üretim planlaması

In this thesis, different variants of the production planning problem are considered. We first study an uncapacitated deterministic lot sizing model with a nonlinear convex production cost function. The nonlinearity and convexity of the cost function may arise due to the extra fines paid by a manufacturer for environmental regulations or it may originate from some production functions. 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. To solve the problem we have developed a polynomial time dynamic programming based algorithm and nine fast heuristics which rest on some well known lot sizing rules such as Silver-Meal, Least Unit Cost and Economic Order Quantity. We compare the performances of the heuristics with extensive numerical tests. Next, motivated from 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 and different formulations are provided. 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 our heuristics on a rolling horizon setting. We conduct an extensive numerical study to compare the performance of heuristics and to see the effect of forecast horizon length on their dominance order and to see when they outperform exact solution approaches. Finally, we study the lot sizing problem with carbon emission constraints. We propose two Lagrangian heuristics when the emission constraint is cumulative over periods. We extend the model with possibility of lost sales and examine several carb on emission cap policies for a cost minimizing manufacturer and conduct a cost-emission Pareto analysis for each policy.