Browsing by Subject "Lot-sizing"
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Item Open Access An application of capacitated lot-sizing model in petroleum sector(Bilkent University, 2006) Nurlu, Nuri BarışIn this thesis, we study capacitated lot-sizing problem with special feature, applicable to the petroleum refinery sector. In our model, the end-products should be stored in item-specific and capacitated storage tanks during pre-determined lead-time. Our aim is to find the optimum production schedule resulting minimum total cost whilst satisfying customer demand. To solve this problem in a reasonable amount of time, we propose a branch-and-cut algorithm. We perform experiments based on the data gathered from Turkish Petroleum Refineries Corporation. In order to evaluate our algorithm, we compare the results of our algorithm and the solution results of the optimization software.Item Open Access A branch and cut algorithm for the inventory routing problem(Bilkent University, 2019-07) Mahmutoğulları, ÖzlemThe inventory routing problem arises in vendor managed systems where products are distributed from a supplier to a set of retailers by a homogeneous eet of capacitated vehicles. The routes of the vehicles and the quantities of products sent to each retailer in each time period are determined in such a way that no stockouts occur and total costs arising from inventory holding and transportation are minimized. Different inventory replenishment policies can be used while managing the inventories at retailers. We consider the problem with the maximum level inventory replenishment policy. We present a mixed integer linear programming model and derive valid inequalities using several structured relaxations. We relate our valid inequalities to those in the previous studies. We also propose new valid inequalities, implement a branch and cut algorithm and present computational results on benchmark instances from the literature as well as new randomly generated instances.Item Open Access Dynamic lot sizing and scheduling in cellular manufacturing systems using hybrid simulation analytic model(International Journal of Industrial Engineering, 1995) Aktürk, M. S.; Dağlıoğlugil, O.In most of the production systems, lot-sizing and scheduling decisions are made at different levels of hierarchy; although there is a strong interaction between these decisions. Furthermore, most of the existing models do not utilize the shop floor conditions in lot-sizing and scheduling decisions, even though such a decision might improve the system performance. In this study, a dynamic lot-sizing and scheduling algorithm is suggested for cellular manufacturing systems, which utilizes a hybrid simulation/analytic modeling approach. The performance of the proposed algorithm is tested against the push and pull systems under different shop floor conditions, and shown that we can improve tardiness, flow time and makespan criteria when comparedto other systems.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.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.Item Open Access Polyhedral analysis for the two-item uncapacitated lot-sizing problem with one-way substitution(Elsevier, 2009-07-28) Yaman, H.We consider a production planning problem for two items where the high quality item can substitute the demand for the low quality item. Given the number of periods, the demands, the production, inventory holding, setup and substitution costs, the problem is to find a minimum cost production and substitution plan. This problem generalizes the well-known uncapacitated lot-sizing problem.Westudy the projection of the feasible set onto the space of production and setup variables and derive a family of facet defining inequalities for the associated convex hull. We prove that these inequalities together with the trivial facet defining inequalities describe the convex hull of the projection if the number of periods is two. We present the results of a computational study and discuss the quality of the bounds given by the linear programming relaxation of the model strengthened with these facet defining inequalities for larger number of periods.Item Open Access Relaxations for two-level multi-item lot-sizing problems(Springer, 2014-08) Vyve, M. V.; Wolsey, L. A.; Yaman, H.We consider several variants of the two-level lot-sizing problem with one item at the upper level facing dependent demand, and multiple items or clients at the lower level, facing independent demands. We first show that under a natural cost assumption, it is sufficient to optimize over a stock-dominant relaxation. We further study the polyhedral structure of a strong relaxation of this problem involving only initial inventory variables and setup variables. We consider several variants: uncapacitated at both levels with or without start-up costs, uncapacitated at the upper level and constant capacity at the lower level, constant capacity at both levels. We finally demonstrate how the strong formulations described improve our ability to solve instances with up to several dozens of periods and a few hundred products.