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### Browsing by Author "Kian, R."

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Item Open Access The dynamic lot-sizing problem with convex economic production costs and setups(Elsevier, 2014-09) Kian, R.; Gurler, U.; Berk, E.Show more 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.Show more Item Open Access The effect of economies-of-scale on the performance of lot-sizing heuristics in rolling horizon basis(Taylor & Francis, 2020-02-26) Kian, R.; Berk, Emre; Gürler, Ülkü; Rezazadeh, H.; Yazdani, B.Show more In this article, we consider the production planning problem in the presence of (dis)economies-of-scale in production costs on a rolling horizon basis with a fixed forecast horizon. We propose variants of three well-known and commonly used heuristics (Wagner–Whitin, Silver–Meal and Least Unit Cost) adapted for this particular setting. In an extensive numerical study with demands exhibiting stationary, increasing and decreasing trends and seasonality, we demonstrate that having longer forecast horizon is less effective in obtaining more cost effective production plans when the production cost function is convex and also when fixed setup cost is lower, which both are proxy to lack of economies-of-scale.Show more Item Open Access An integrated replenishment and transportation model: Computational performance assessment(CRC Press, 2014) Kian, R.; Berk, Emre; Gürler, Ülkü; Kara, B. Y.; Sabuncuoğlu, İ.; Bidanda, B.Show more Item Open Access Minimal conic quadratic reformulations and an optimization model(Elsevier, 2019) Kian, R.; Berk, Emre; Gürler, ÜlküShow more In this paper, we consider a particular form of inequalities which involves product of multiple variables with rational exponents. These inequalities can equivalently be represented by a number of conic quadratic forms called cone constraints. We propose an integer programming model and a heuristic algorithm to obtain the minimum number of cone constraints which equivalently represent the original inequality. The performance of the proposed algorithm and the computational effect of reformulations are numerically illustrated.Show more Item Open Access On guarding real terrains: the terrain guarding and the blocking path problems(Elsevier, 2020) Eliş, Haluk; Tansel, Barbaros; Oğuz, Osman; Güney, M.; Kian, R.Show more Locating a minimum number of guards on a terrain such that every point on the terrain is guarded by at least one of the guards is known as the Terrain Guarding Problem (TGP). In this paper, a realistic example of the terrain guarding problem is studied, involving the surveillance of a rugged geographical terrain by means of thermal cameras. A number of issues related to TGP are addressed with integer-programming models proposed to solve the problem. Also, a sensitivity analysis is carried out in which five fictitious terrains are created to see the effect of the resolution of the terrain, and of terrain characteristics, on coverage optimization and the required number of guards. Finally, a new problem, which is called the Blocking Path Problem (BPP), is introduced. BPP is about guarding a path on the terrain with a minimum number of guards such that the path blocks all possible infiltration routes. A discussion is provided about the relation of BPP to the Network Interdiction Problem (NIP), which has been studied extensively by the operations research community, and to the k-Barrier Coverage Problem, which has been studied under the Sensor Deployment Problem. BPP is solved via an integer-programming formulation based on a network paradigm.Show more