7,038 research outputs found
Mathematical programming for single- and multi-location non-stationary inventory control
Stochastic inventory control investigates strategies for managing and regulating
inventories under various constraints and conditions to deal with uncertainty in
demand. This is a significant field with rich academic literature which has broad
practical applications in controlling and enhancing the performance of inventory
systems. This thesis focuses on non-stationary stochastic inventory control and
the computation of near-optimal inventory policies for single- and two-echelon
inventory systems. We investigate the structure of optimal policies and develop
effective mathematical programming heuristics for computing near-optimal policy
parameters. This thesis makes three contributions to stochastic inventory control.
The first contribution concerns lot-sizing problems controlled under a staticdynamic
uncertainty strategy. From a theoretical standpoint, I demonstrate the
optimality of the non-stationary (s,Q) form for the single-item single-stocking
location non-stationary stochastic lot-sizing problem in a static-dynamic setting;
from a practical standpoint, I present a stochastic dynamic programming approach
to determine optimal (s,Q)-type policy parameters, and I introduce mixed integer
non-linear programming heuristics that leverage piecewise linear approximation of
the cost function. The numerical study demonstrates that the proposed solution
method efficiently computes near-optimal parameters for a broad class of problem
instances.
The second contribution is to develop computationally efficient approaches for
computing near-optimal policy parameters for the single-item single-stocking location
non-stationary stochastic lot-sizing problem under the static-dynamic uncertainty
strategy. I develop an efficient dynamic programming approach that,
starting from a relaxed shortest-path formulation, leverages a state space augmentation
procedure to resolve infeasibility with respect to the original problem.
Unlike other existing approaches, which address a service-level-oriented formulation,
this method is developed under a penalty cost scheme. The approach can
find a near-optimal solution to any instance of relevant size in negligible time by
implementing simple numerical integrations.
This third contribution addresses the optimisation of the lateral transshipment
amongst various locations in the same echelon from an inventory system. Under
a proactive transshipment setting, I introduce a hybrid inventory policy for twolocation
settings to re-distribute the stock throughout the system. The policy
parameters can be determined using a rolling-horizon technique based on a twostage
dynamic programming formulation and a mixed integer linear programme.
The numerical analysis shows that the two-stage formulation can well approximate
the optimal policy obtained via stochastic dynamic programming and that the
rolling-horizon heuristic leads to tight optimality gaps
Computing (R, S) policies with correlated demand
This paper considers the single-item single-stocking non-stationary
stochastic lot-sizing problem under correlated demand. By operating under a
nonstationary (R, S) policy, in which R denote the reorder period and S the
associated order-up-to-level, we introduce a mixed integer linear programming
(MILP) model which can be easily implemented by using off-theshelf optimisation
software. Our modelling strategy can tackle a wide range of time-seriesbased
demand processes, such as autoregressive (AR), moving average(MA),
autoregressive moving average(ARMA), and autoregressive with autoregressive
conditional heteroskedasticity process(AR-ARCH). In an extensive computational
study, we compare the performance of our model against the optimal policy
obtained via stochastic dynamic programming. Our results demonstrate that the
optimality gap of our approach averages 2.28% and that computational
performance is good
Demand uncertainty and lot sizing in manufacturing systems: the effects of forecasting errors and mis-specification
This paper proposes a methodology for examining the effect of demand uncertainty and forecast error on lot sizing methods, unit costs and customer service levels in MRP type manufacturing systems. A number of cost structures were considered which depend on the expected time between orders. A simple two-level MRP system where the product is manufactured for stock was then simulated. Stochastic demand for the final product was generated by two commonly occurring processes and with different variances. Various lot sizing rules were then used to determine the amount of product made and the amount of materials bought in. The results confirm earlier research that the behaviour of lot sizing rules is quite different when there is uncertainty in demand compared to the situation of perfect foresight of demand. The best lot sizing rules for the deterministic situation are the worst whenever there is uncertainty in demand. In addition the choice of lot sizing rule between ‘good’ rules such as the EOQ turns out to be relatively less important in reducing unit cost compared to improving forecasting accuracy whatever the cost structure. The effect of demand uncertainty on unit cost for a given service level increases exponentially as the uncertainty in the demand data increases. The paper also shows how the value of improved forecasting can be analysed by examining the effects of different sizes of forecast error in addition to demand uncertainty. In those manufacturing problems with high forecast error variance, improved forecast accuracy should lead to substantial percentage improvements in unit costs
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