6,057 research outputs found
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
The linear dynamic lot size problem with minimum order quantities
This paper continues the analysis of a special uncapacitated single item lot sizing problem where a minimum order quantity restriction, instead of the setup cost, guarantees a certain level of production lots. A detailed analysis of the model and an investigation of the particularities of the cumulative demand structure allowed us to develop a solution algorithm based on the concept of minimal sub-problems. We present an optimal solution to a minimal sub-problem in an explicit form and prove that it serves as a construction block for the optimal solution of the initial problem. The computational tests and the comparison with the published algorithm confirm the efficiency of the solution algorithm developed here. --lot sizing problem,minimum order quantity,dynamic programming
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
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
Non-stationary stochastic inventory lot-sizing with emission and service level constraints in a carbon cap-and-trade system
Firms worldwide are taking major initiatives to reduce the carbon footprint of their supply chains in response to the growing governmental and consumer pressures. In real life, these supply chains face stochastic and non-stationary demand but most of the studies on inventory lot-sizing problem with emission concerns consider deterministic demand. In this paper, we study the inventory lot-sizing problem under non-stationary stochastic demand condition with emission and cycle service level constraints considering carbon cap-and-trade regulatory mechanism. Using a mixed integer linear programming model, this paper aims to investigate the effects of emission parameters, product- and system-related features on the supply chain performance through extensive computational experiments to cover general type business settings and not a specific scenario. Results show that cycle service level and demand coefficient of variation have significant impacts on total cost and emission irrespective of level of demand variability while the impact of product's demand pattern is significant only at lower level of demand variability. Finally, results also show that increasing value of carbon price reduces total cost, total emission and total inventory and the scope of emission reduction by increasing carbon price is greater at higher levels of cycle service level and demand coefficient of variation. The analysis of results helps supply chain managers to take right decision in different demand and service level situations
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