Production decisions with convex costs and carbon emission constraints

Abstract

In this thesis, di erent variants of the production planning problem are considered. We rst 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 nes 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 rst 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 di erent 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 e ect of cuts in di erent 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 e ect 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 carbon emission cap policies for a cost minimizing manufacturer and conduct a cost-emission Pareto analysis for each policy.