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

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

Robust production planning and control for multi-stage systems with flexible final assembly lines

Production planning of final assembly systems is a challenging task, as the often fluctuating order volumes require flexible solutions. Besides, the calculated plans need to be robust against the process-level disturbances and stochastic nature of some parameters like manual processing times or machine availability. In the paper, a simulation-based optimisation method is proposed that utilises lower level shop floor data to calculate robust production plans for final assembly lines of a flexible, multi-stage production system. In order to minimise the idle times when executing the plans, the capacity control that specifies the proper operatorâtask assignments is also determined. The analysed multi-stage system is operated with a pull strategy, which means that the production at the final assembly lines generates demands for the preceding stages providing the assembled components

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

A practical assessment of risk-averse approaches in production lot-sizing problems

This paper presents an empirical assessment of four state-of-the-art risk-averse approaches to deal with the capacitated lot-sizing problem under stochastic demand. We analyse two mean-risk models based on the semideviation and on the conditional value-at-risk risk measures, and alternate first and second-order stochastic dominance approaches. The extensive computational experiments based on different instances characteristics and on a case-study suggest that CVaR exhibits a good trade-off between risk and performance, followed by the semideviation and first-order stochastic dominance approach. For all approaches, enforcing risk-aversion helps to reduce the cost-standard deviation substantially, which is usually accomplished via increasing production rates. Overall, we can say that very risk-averse decision-makers would be willing to pay an increased price to have a much less risky solution given by CVaR. In less risk-averse settings, though, semideviation and first-order stochastic dominance can be appealingalternatives to provide significantly more stable production planning costs with a marginal increase of the expected costs.Peer reviewe

Mathematics in the Supply Chain

[no abstract available

Stochastic make-to-stock inventory deployment problem: an endosymbiotic psychoclonal algorithm based approach

Integrated steel manufacturers (ISMs) have no specific product, they just produce finished product from the ore. This enhances the uncertainty prevailing in the ISM regarding the nature of the finished product and significant demand by customers. At present low cost mini-mills are giving firm competition to ISMs in terms of cost, and this has compelled the ISM industry to target customers who want exotic products and faster reliable deliveries. To meet this objective, ISMs are exploring the option of satisfying part of their demand by converting strategically placed products, this helps in increasing the variability of product produced by the ISM in a short lead time. In this paper the authors have proposed a new hybrid evolutionary algorithm named endosymbiotic-psychoclonal (ESPC) to decide what and how much to stock as a semi-product in inventory. In the proposed theory, the ability of previously proposed psychoclonal algorithms to exploit the search space has been increased by making antibodies and antigen more co-operative interacting species. The efficacy of the proposed algorithm has been tested on randomly generated datasets and the results compared with other evolutionary algorithms such as genetic algorithms (GA) and simulated annealing (SA). The comparison of ESPC with GA and SA proves the superiority of the proposed algorithm both in terms of quality of the solution obtained and convergence time required to reach the optimal/near optimal value of the solution