Browsing by Subject "Lot sizing"

Now showing 1 - 9 of 9

Open Access
Dynamic lot sizing and tool management in automated manufacturing systems
(Elsevier, 2002) Aktürk, M. S.; Önen, S.
The overall aim of this study is to show that there is a critical interface between the lot sizing and tool management decisions, and these two problems cannot be viewed in isolation. We propose "ve alternative algorithms to solve lot sizing, tool allocation and machining conditions optimization problems simultaneously. The "rst algorithm is an exact algorithm which "nds the global optimum solution, and the others are heuristics equipped with a look-ahead mechanism to guarantee at least local optimality. The computational results indicate that the amount of improvement is statistically signi"cant for a set of randomly generated problems. The magnitude of cost savings is dependent on the system parameters.
Open Access
Dynamic lot sizing for a warm/cold process: heuristics and insights
(Elsevier, 2013-09) Toy, A. Ö.; Berk, E.
We consider the dynamic lot sizing problem for a warm/cold process where the process can be kept warm at a unit variable cost for the next period if more than a prespecified quantity has been produced. Exploiting the optimal production plan structures, we develop nine rule-based forward solution heuristics. Proposed heuristics are modified counterparts of the heuristics developed previously for the classical dynamic lot sizing problem. In a numerical study, we investigate the performance of the proposed heuristics and identify operating environment characteristics where each particular heuristic is the best or among the best. Moreover, for a warm/cold process setting, our numerical studies indicate that, when used on a rolling horizon basis, a heuristic may also perform better costwise than a solution obtained using a dynamic programming approach.
Open Access
Integrated lot sizing and tool management in automated manufacturing systems
(IIE, 1997) Aktürk, Mehmet Selim; Önen, Siraceddin
We propose a new algorithm to solve lot sizing, tool allocation and machining conditions optimization problems simultaneously to minimize total production cost in a CNC environment. Most of the existing lot sizing and tool management methods solve these problems independently using a two-level optimization approach. Thus, we not only improve the overall solution by exploiting the interactions, but also prevent any infeasibility that might occur for the tool management problem due to decisions made at the lot sizing level. We showed that in a set of randomly generated problems 22.5% of solutions found by the two-level approach were infeasible and we improved the solution on the average by 6.79% for the remaining cases with an average computation time of 63.4 seconds.
Open Access
Joint lot sizing and tool management in a CNC environment
(Elsevier, 1999) Aktuük, M. S.; Önen, S.
We propose a new algorithm to solve lot sizing, tool allocation and machining conditions optimization problems simultaneously to minimize total production cost in a CNC environment. Most of the existing lot sizing and tool management methods solve these problems independently using a two-level optimization approach. Thus, we not only improve the overall solution by exploiting the interactions among these decision making problems, but also prevent any infeasibility that might occur for the tool management problem due to decisions made at the lot sizing level. The computational experiments showed that in a set of randomly generated problems 22.5% of solutions found by the two-level approach were infeasible and the proposed joint approach improved the solution on the average by 6.79% for the remaining cases.
Open Access
Lot sizing with nonlinear production cost functions
(2015-07) Koca, Esra
In this study, we consider di erent variations of the lot sizing problem encountered in many real life production, procurement and transportation systems. First, we consider the deterministic lot sizing problem with piecewise concave production cost functions. A piecewise concave function can represent quantity discounts, subcontracting, overloading, minimum order quantities, and capacities. Computational complexity of this problem was an open question in the literature. We develop a dynamic programming (DP) algorithm to solve the problem and show that the problem is polynomially solvable when number of breakpoints of the production cost function is xed and the breakpoints are time-invariant. We observe that the time complexity of our algorithm is as good as the complexity of existing algorithms in the literature for the special cases with capacities, minimum order quantities, and subcontracting. Our algorithm performs quite well for small and medium sized instances. For larger instances, we propose a DP based heuristic to nd a good quality solution in reasonable time. Next, we consider the stochastic lot sizing problem with controllable processing times where processing times can be reduced in return for extra compression cost. We assume that the compression cost function is a convex function in order to re ect the increasing marginal cost of larger reductions in processing times. We formulate the problem as a second-order cone mixed integer program, strengthen the formulation and solve it by a commercial solver. Moreover, we obtain some convex hull and computational complexity results. We conduct an extensive computational study to see the e ect of controllable processing times in solution quality and observe that even with small reductions in processing times, it is possible to obtain a less costly production plan. As a nal problem, we study the multistage stochastic lot sizing problem with nervousness considerations and controllable processing times. System nervousness is one of the main problems of dynamic solution strategies developed for stochastic lot sizing problems. We formulate the problem so that the nervousness of the system is restricted by some additional constraints and parameters. Mixing and continuous mixing set structures are observed as relaxations of our formulation. We develop valid inequalities for the problem based on these structures and computationally test these inequalities.
Open Access
Lot sizing with perishable items
(2019-07) Arslan, Nazlıcan
We address the uncapacitated lot sizing problem for a perishable item that has a deterministic and fixed lifetime. In the first part of the study, we assume that the demand is also deterministic. We conduct a polyhedral analysis and derive valid inequalities to strengthen the LP relaxation. We develop a separation algorithm for the valid inequalities and propose a branch and cut algorithm to solve the problem. We conduct a computational study to test the effiectiveness of the valid inequalities. In the second part, we study the multistage stochastic version of the problem where the demand is uncertain. We use the valid inequalities we found for the deterministic problem to strengthen the LP relaxation of the stochastic problem and test their effiectiveness. As the size of the stochastic model grows exponentially in the number of periods, we also implement a decomposition method based on scenario grouping to obtain lower and upper bounds.
Open Access
Lot sizing with piecewise concave production costs
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2014) Koca, E.; Yaman, H.; Aktürk, M. S.
We study the lot-sizing problem with piecewise concave production costs and concave holding costs. This problem is a generalization of the lot-sizing problem with quantity discounts, minimum order quantities, capacities, overloading, subcontracting or a combination of these. We develop a dynamic programming algorithm to solve this problem and answer an open question in the literature: we show that the problem is polynomially solvable when the breakpoints of the production cost function are time invariant and the number of breakpoints is fixed. For the special cases with capacities and subcontracting, the time complexity of our algorithm is as good as the complexity of algorithms available in the literature. We report the results of a computational experiment where the dynamic programming is able to solve instances that are hard for a mixed-integer programming solver. We enhance the mixed-integer programming formulation with valid inequalities based on mixing sets and use a cut-and-branch algorithm to compute better bounds. We propose a state space reduction-based heuristic algorithm for large instances and show that the solutions are of good quality by comparing them with the bounds obtained from the cut-and-branch.
Open Access
A polyhedral study of multiechelon lot sizing with intermediate demands
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2012) Zhang, M.; Küçükyavuz, S.; Yaman, H.
In this paper, we study a multiechelon uncapacitated lot-sizing problem in series (m-ULS), where the output of the intermediate echelons has its own external demand and is also an input to the next echelon. We propose a polynomial-time dynamic programming algorithm, which gives a tight, compact extended formulation for the two-echelon case (2-ULS). Next, we present a family of valid inequalities for m-ULS, show its strength, and give a polynomial-time separation algorithm. We establish a hierarchy between the alternative formulations for 2-ULS. In particular, we show that our valid inequalities can be obtained from the projection of the multicommodity formulation. Our computational results show that this extended formulation is very effective in solving our uncapacitated multi-item two-echelon test problems. In addition, for capacitated multi-item, multiechelon problems, we demonstrate the effectiveness of a branch-and-cut algorithm using the proposed inequalities.
Open Access
Production decisions with convex costs and carbon emission constraints
(2016-03) Kian, Ramez
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.