On the determination of the control parameters of the optimal can-order policy

Inventory Control

Computing policy parameters for stochastic inventory control using stochastic dynamic programming approaches

The objective of this work is to introduce techniques for the computation of optimal and near-optimal inventory control policy parameters for the stochastic inventory control problem under Scarf’s setting. A common aspect of the solutions presented herein is the usage of stochastic dynamic programming approaches, a mathematical programming technique introduced by Bellman. Stochastic dynamic programming is hybridised with branch-and-bound, binary search, constraint programming and other computational techniques to develop innovative and competitive solutions. In this work, the classic single-item, single location-inventory control with penalty cost under the independent stochastic demand is extended to model a fixed review cost. This cost is charged when the inventory level is assessed at the beginning of a period. This operation is costly in practice and including it can lead to significant savings. This makes it possible to model an order cancellation penalty charge. The first contribution hereby presented is the first stochastic dynamic program- ming that captures Bookbinder and Tan’s static-dynamic uncertainty control policy with penalty cost. Numerous techniques are available in the literature to compute such parameters; however, they all make assumptions on the de- mand probability distribution. This technique has many similarities to Scarf’s stochastic dynamic programming formulation, and it does not require any ex- ternal solver to be deployed. Memoisation and binary search techniques are deployed to improve computational performances. Extensive computational studies show that this new model has a tighter optimality gap compared to the state of the art. The second contribution is to introduce the first procedure to compute cost- optimal parameters for the well-known (R, s, S) policy. Practitioners widely use such a policy; however, the determination of its parameters is considered com- putationally prohibitive. A technique that hybridises stochastic dynamic pro- gramming and branch-and-bound is presented, alongside with computational enhancements. Computing the optimal policy allows the determination of op- timality gaps for future heuristics. This approach can solve instances of consid- erable size, making it usable by practitioners. The computational study shows the reduction of the cost that such a system can provide. Thirdly, this work presents the first heuristics for determining the near-optimal parameters for the (R,s,S) policy. The first is an algorithm that formally models the (R,s,S) policy computation in the form of a functional equation. The second is a heuristic formed by a hybridisation of (R,S) and (s,S) policy parameters solvers. These heuristics can compute near-optimal parameters in a fraction of time compared to the exact methods. They can be used to speed up the optimal branch-and-bound technique. The last contribution is the introduction of a technique to encode dynamic programming in constraint programming. Constraint programming provides the user with an expressive modelling language and delegates the search for the solution to a specific solver. The possibility to seamlessly encode dynamic programming provides new modelling options, e.g. the computation of optimal (R,s,S) policy parameters. The performances in this specific application are not competitive with the other techniques proposed herein; however, this encoding opens up new connections between constraint programming and dynamic programming. The encoding allows deploying DP based constraints in modelling languages such as MiniZinc. The computational study shows how this technique can outperform a similar encoding for mixed-integer programming

An Inverse Method for Policy-Iteration Based Algorithms

We present an extension of two policy-iteration based algorithms on weighted graphs (viz., Markov Decision Problems and Max-Plus Algebras). This extension allows us to solve the following inverse problem: considering the weights of the graph to be unknown constants or parameters, we suppose that a reference instantiation of those weights is given, and we aim at computing a constraint on the parameters under which an optimal policy for the reference instantiation is still optimal. The original algorithm is thus guaranteed to behave well around the reference instantiation, which provides us with some criteria of robustness. We present an application of both methods to simple examples. A prototype implementation has been done

An Advanced Heuristic for Multiple-Option Spare Parts Procurement after End-of-Production

After-sales service is a major profit generator for more and more OEMs in industries with durable products. Successful engagement in after-sales service improves customer loyalty and allows for competitive differentiation through superior service like an extended service period after end of production during which customers are guaranteed to be provided with service parts. In order to fulfill the service guarantee in these cases, an effective and efficient spare parts management has to be implemented, which is challenging due to the high uncertainty concerning spare parts demand over such a long time horizon. The traditional way of spare parts acquisition for the service phase is to set up a huge final lot at the end of regular production of the parent product which is sufficient to fulfill demand up to the end of the service time. This strategy results in extremely high inventory levels over a long period and generates major holding costs and a high level of obsolescence risk. With increasing service time more flexible options for spare parts procurement after end of production gain more and more importance. In our paper we focus on the two most relevant ones, namely extra production and remanufacturing. Managing all three options leads to a complicated stochastic dynamic decision problem. For that problem type, however, a quite simple combined decision rule with order-up-to levels for extra production and remanufacturing turns out to be very effective. We propose a heuristic procedure for parameter determination which accounts for the main stochastic and dynamic interactions between the different order-up-to levels, but still consists of quite simple calculations so that it can be applied to problem instances of arbitrary size. In a numerical study we show that this heuristic performs extremely well under a wide range of conditions so that it can be strongly recommended as a decision support tool for the multi-option spare parts procurement problem.Spare Parts, Inventory Management, Reverse Logistics, Final Order

Optimal policy and Taylor rule cross-checking under parameter uncertainty : [Version 26 September 2013]

We examine whether the robustifying nature of Taylor rule cross-checking under model uncertainty carries over to the case of parameter uncertainty. Adjusting monetary policy based on this kind of cross-checking can improve the outcome for the monetary authority. This, however, crucially depends on the relative welfare weight that is attached to the output gap and also the degree of monetary policy commitment. We find that Taylor rule cross-checking is on average able to improve losses when the monetary authority only moderately cares about output stabilization and when policy is set in a discretionary way