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Yayın Tractable supply chain production planning, modeling nonlinear lead time and quality of service constraints(Elsevier Ltd, 2007) Anlı, Osman Murat; Caramanis, Michael C.; Paschalidis, Ioannis Ch.This paper addresses the task of coordinated planning of a supply chain (SC). Work in process (WIP) in each facility participating in the SC, finished goods inventory, and backlogged demand costs are minimized over the planning horizon. In addition to the usual modeling of linear material flow balance equations, variable lead time (LT) requirements, resulting from the increasing incremental WIP as a facility's utilization increases, are also modeled. In recognition of the emerging significance of quality of service (QoS), that is control of stockout probability to meet demand on time, maximum stockout probability constraints are also modeled explicitly. Lead time and QoS modeling require incorporation of nonlinear constraints in the production planning optimization process. The quantification of these nonlinear constraints must capture statistics of the stochastic behaviour of production facilities revealed during a time scale for shorter than the customary weekly time scale of the planning process. The apparent computational complexity of planning production against variable LT and QoS constraints has long resulted in MRP-based scheduling practices that ignore the LT and QoS constraints has long resulted in MRP-based scheduling practices that ignore the LT and QoS impact to the plan's detriment. The computational complexity challenge was overcome by proposing and adopting a time-scale decomposition approach to production planning where short-time-scale stochastic dynamics are modeled in multiple facility-specific subproblems that receive tentative targets from a deterministic master problem and return statistics to it. A converging and scalable iterative methodology is implemented, providing evidence that significantly lower cost production plans are achievable in a computationally tractable manner.Yayın Optimal project duration for resource leveling(Elsevier Science BV, 2018-04-16) Atan, Sabri Tankut; Eren, ElifResource leveling is important in project management as resource fluctuations are costly and undesired. Typically, schedules with better resource profiles are obtained by shifting the activities within their float times using the schedule of fixed duration found by Critical Path Method. However, if the project duration can be extended, it is plausible to find a schedule with enhanced resource leveling since a longer duration allows for more float time for all activities. In this work, we relax the assumption of fixed durations in resource leveling formulations and investigate what the minimal project duration for the best leveled schedule should be. We provide mixed-integer linear models for several leveling objectives including the Release and Rehire metric. We show that not all metrics used for leveling under fixed durations may be appropriate when the project duration becomes a decision variable. Optimal solutions from smaller problems are used to find the magnitude of the extension needed and benefits obtained thereby. Since the problem is a NP-hard problem for which exact solutions cannot be obtained for large networks in reasonable time, we provide a greedy heuristic to be used with the Release and Rehire metric. Using an iterative framework, we also test the performance of a state-of-the-art heuristic algorithm from the literature on our problem. Computational experiments indicate that the more the number of resources is increased, the less leveling benefits are gained from extending the project. The optimal project durations and extension benefits can also be significantly different for different metrics.
