8 research outputs found
Comparison of different approaches to multistage lot sizing with uncertain demand
We study a new variant of the classical lot sizing problem with uncertain demand where neither the planning horizon nor demands are known exactly. This situation arises in practice when customer demands arriving over time are confirmed rather lately during the transportation process. In terms of planning, this setting necessitates a rolling horizon procedure where the overall multistage problem is dissolved into a series of coupled snapshot problems under uncertainty. Depending on the available data and risk disposition, different approaches from online optimization, stochastic programming, and robust optimization are viable to model and solve the snapshot problems. We evaluate the impact of the selected methodology on the overall solution quality using a methodology-agnostic framework for multistage decision-making under uncertainty. We provide computational results on lot sizing within a rolling horizon regarding different types of uncertainty, solution approaches, and the value of available information about upcoming demands
Adaptive Two-stage Stochastic Programming with an Application to Capacity Expansion Planning
Multi-stage stochastic programming is a well-established framework for
sequential decision making under uncertainty by seeking policies that are fully
adapted to the uncertainty. Often such flexible policies are not desirable, and
the decision maker may need to commit to a set of actions for a number of
planning periods. Two-stage stochastic programming might be better suited to
such settings, where the decisions for all periods are made here-and-now and do
not adapt to the uncertainty realized. In this paper, we propose a novel
alternative approach, where the stages are not predetermined but part of the
optimization problem. Each component of the decision policy has an associated
revision point, a period prior to which the decision is predetermined and after
which it is revised to adjust to the uncertainty realized thus far. We motivate
this setting using the multi-period newsvendor problem by deriving an optimal
adaptive policy. We label the proposed approach as adaptive two-stage
stochastic programming and provide a generic mixed-integer programming
formulation for finite stochastic processes. We show that adaptive two-stage
stochastic programming is NP-hard in general. Next, we derive bounds on the
value of adaptive two-stage programming in comparison to the two-stage and
multi-stage approaches for a specific problem structure inspired by the
capacity expansion planning problem. Since directly solving the mixed-integer
linear program associated with the adaptive two-stage approach might be very
costly for large instances, we propose several heuristic solution algorithms
based on the bound analysis. We provide approximation guarantees for these
heuristics. Finally, we present an extensive computational study on an
electricity generation capacity expansion planning problem and demonstrate the
computational and practical impacts of the proposed approach from various
perspectives
Stochastic lot sizing problem with nervousness considerations
© 2018 Elsevier Ltd In this paper, we consider the multistage stochastic lot sizing problem with controllable processing times under nervousness considerations. We assume that the processing times can be reduced in return for extra cost (compression cost). We generalize the static and static-dynamic uncertainty strategies to eliminate setup oriented nervousness and control quantity oriented nervousness. We restrict the quantity oriented nervousness by introducing a new concept called promised production amounts, and considering new range constraints and a nervousness cost function. We formulate the problem as a second-order cone mixed integer program (SOCMIP), and apply the conic strengthening. We observe the continuous mixing set substructure in our formulation that arises due the controllable processing times. We reformulate the problem by using an extended formulation for the continuous mixing set and solve the problem by a branch-and-cut approach. The computational experiments indicate that the reformulation reduces the root gaps and this helps to solve the problem in less computation times. Moreover, in our computational experiments we investigate the impact of new restrictions, specifically the additional cost of eliminating the setup oriented nervousness, on the total costs and the system nervousness. Our computational results clearly indicate that we could significantly reduce the nervousness costs and generate more stable production schedules with a relatively small increase in the total cost.status: publishe
Stochastic lot sizing problem with nervousness considerations
In this paper, we consider the multistage stochastic lot sizing problem with controllable processing times under nervousness considerations. We assume that the processing times can be reduced in return for extra cost (compression cost). We generalize the static and static-dynamic uncertainty strategies to eliminate setup oriented nervousness and control quantity oriented nervousness. We restrict the quantity oriented nervousness by introducing a new concept called promised production amounts, and considering new range constraints and a nervousness cost function. We formulate the problem as a second-order
cone mixed integer program (SOCMIP), and apply the conic strengthening. We observe the continuous mixing set substructure in our formulation that arises due the controllable processing times. We reformulate the problem by using an extended formulation for the continuous mixing set and solve the problem by a branch-and-cut approach. The computational experiments indicate that our solution method can solve larger instances in less computation times than the off-the-shelf solver. Moreover, in our computational experiments we investigate the impact of new restrictions, specifically the additional cost of eliminating the setup oriented nervousness, on the total costs and the system nervousness. Our computational results clearly indicate that we could significantly reduce
the nervousness costs and generate more stable production schedules with a relatively small increase in the total cost
Doğrusal olmayan üretim maliyeti fonksiyonları olan kafile büyüklüğü problemi
Cataloged from PDF version of thesis.Includes bibliographical references (leaves 100-110).Thesis (Ph. D.): Bilkent University, Department of Industrial Engineering, İhsan Doğramacı Bilkent University, 2015.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.by Esra Koca.Ph.D