73 research outputs found
Piecewise linear approximations for the static-dynamic uncertainty strategy in stochastic lot-sizing
In this paper, we develop mixed integer linear programming models to compute
near-optimal policy parameters for the non-stationary stochastic lot sizing
problem under Bookbinder and Tan's static-dynamic uncertainty strategy. Our
models build on piecewise linear upper and lower bounds of the first order loss
function. We discuss different formulations of the stochastic lot sizing
problem, in which the quality of service is captured by means of backorder
penalty costs, non-stockout probability, or fill rate constraints. These models
can be easily adapted to operate in settings in which unmet demand is
backordered or lost. The proposed approach has a number of advantages with
respect to existing methods in the literature: it enables seamless modelling of
different variants of the above problem, which have been previously tackled via
ad-hoc solution methods; and it produces an accurate estimation of the expected
total cost, expressed in terms of upper and lower bounds. Our computational
study demonstrates the effectiveness and flexibility of our models.Comment: 38 pages, working draf
Inventory control for a non-stationary demand perishable product: comparing policies and solution methods
This paper summarizes our findings with respect to order policies for an inventory control problem for a perishable product with a maximum fixed shelf life in a periodic review system, where chance constraints play a role. A Stochastic Programming (SP) problem is presented which models a practical production planning problem over a finite horizon. Perishability, non-stationary demand, fixed ordering cost and a service level (chance) constraint make this problem complex. Inventory control handles this type of models with so-called order policies.
We compare three different policies: a) production timing is fixed in advance combined with an order up-to level, b) production timing is fixed in advance and the production quantity takes the age distribution into account and c) the decision of the order quantity depends on the age-distribution of the items in stock. Several theoretical properties for the optimal solutions of the policies are presented. In this paper, four different solution approaches from earlier studies are used to derive parameter values
for the order policies. For policy a), we use MILP approximations and alternatively the so-called Smoothed Monte Carlo method with sampled demand to optimize values. For policy b), we outline a sample based approach to determine the order quantities. The flexible policy c) is derived by SDP. All policies are compared on feasibility regarding the α-service level, computation time and ease of implementation to support management in the choice for an order policy.National project TIN2015-66680-C2-2-R, in part financed by the European Regional Development Fund (ERDF)
An extended mixed-integer programming formulation and dynamic cut generation approach for the stochastic lot sizing problem
We present an extended mixed-integer programming formulation of the stochastic lot-sizing problem for the static-dynamic uncertainty strategy. The proposed formulation is significantly more time efficient as compared to existing formulations in the literature and it can handle variants of the stochastic lot-sizing problem characterized by penalty costs and service level constraints, as well as backorders and lost sales. Also, besides being capable of working with a predefined piecewise linear approximation of the cost function-as is the case in earlier formulations-it has the functionality of finding an optimal cost solution with an arbitrary level of precision by means of a novel dynamic cut generation approach
Single item stochastic lot sizing problem considering capital flow and business overdraft
This paper introduces capital flow to the single item stochastic lot sizing
problem. A retailer can leverage business overdraft to deal with unexpected
capital shortage, but needs to pay interest if its available balance goes below
zero. A stochastic dynamic programming model maximizing expected final capital
increment is formulated to solve the problem to optimality. We then investigate
the performance of four controlling policies: (), (), () and
(, , ); for these policies, we adopt simulation-genetic
algorithm to obtain approximate values of the controlling parameters. Finally,
a simulation-optimization heuristic is also employed to solve this problem.
Computational comparisons among these approaches show that policy and
policy provide performance close to that of optimal
solutions obtained by stochastic dynamic programming, while
simulation-optimization heuristic offers advantages in terms of computational
efficiency. Our numerical tests also show that capital availability as well as
business overdraft interest rate can substantially affect the retailer's
optimal lot sizing decisions.Comment: 18 pages, 3 figure
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
Computing replenishment cycle policy parameters for a perishable item
In many industrial environments there is a significant class of problems for which the perishable nature of the inventory cannot be ignored in developing replenishment order plans. Food is the most salient example of a perishable inventory item. In this work, we consider the periodic-review, single-location, single-product production/inventory control problem under non-stationary stochastic demand and service level constraints. The product we consider can be held in stock for a limited amount of time after which it expires and it must be disposed of at a cost. In addition to wastage costs, our cost structure comprises fixed and unit variable ordering costs, and inventory holding costs. We propose an easy-to-implement replenishment cycle inventory control policy that yields at most 2N control parameters, where N is the number of periods in our planning horizon. We also show, on a simple numerical example, the improvement brought by this policy over two other simpler inventory control rules of common use
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