Cost-Based Filtering Techniques for Stochastic Inventory Control Under Service Level Constraints

This paper(1) considers a single product and a single stocking location production/inventory control problem given a non-stationary stochastic demand. Under a widely-used control policy for this type of inventory system, the objective is to find the optimal number of replenishments, their timings and their respective order-up-to-levels that meet customer demands to a required service level. We extend a known CP approach for this problem using three cost-based filtering methods. Our approach can solve to optimality instances of realistic size much more efficiently than previous approaches, often with no search effort at all

Generalizing backdoors

Abstract. A powerful intuition in the design of search methods is that one wants to proactively select variables that simplify the problem instance as much as possible when these variables are assigned values. The notion of “Backdoor ” variables follows this intuition. In this work we generalize Backdoors in such a way to allow more general classes of sub-solvers, both complete and heuristic. In order to do so, Pseudo-Backdoors and Heuristic-Backdoors are formally introduced and then applied firstly to a simple Multiple Knapsack Problem and secondly to a complex combinatorial optimization problem in the area of stochastic inventory control. Our preliminary computational experience shows the effectiveness of these approaches that are able to produce very low run times and — in the case of Heuristic-Backdoors — high quality solutions by employing very simple heuristic rules such as greedy local search strategies.

An inventory control project in a major Danish company using compound renewal demand models

We describe the development of a framework to compute the optimal inventory policy for a large spare-parts’ distribution centre operation in the RA division of the Danfoss Group in Denmark. The RA division distributes spare parts worldwide for cooling and A/C systems. The warehouse logistics operation is highly automated. However, the procedures for estimating demands and the policies for the inventory control system that were in use at the beginning of the project did not fully match the sophisticated technological standard of the physical system. During the initial phase of the project development we focused on the fitting of suitable demand distributions for spare parts and on the estimation of demand parameters. Demand distributions were chosen from a class of compound renewal distributions. In the next phase, we designed models and algorithmic procedures for determining suitable inventory control variables based on the fitted demand distributions and a service level requirement stated in terms of an order fill rate. Finally, we validated the results of our models against the procedures that had been in use in the company. It was concluded that the new procedures were considerably more consistent with the actual demand processes and with the stated objectives for the distribution centre. We also initiated the implementation and integration of the new procedures into the company’s inventory management systemBase-stock policy; compound distribution; fill rate; inventory control; logistics; stochastic processes

Decision support for build-to-order supply chain management through multiobjective optimization

This paper aims to identify the gaps in decision-making support based on multiobjective optimization for build-to-order supply chain management (BTOSCM). To this end, it reviews the literature available on modelling build-to-order supply chains (BTO-SC) with the focus on adopting multiobjective optimization (MOO) techniques as a decision support tool. The literature has been classified based on the nature of the decisions in different part of the supply chain, and the key decision areas across a typical BTO-SC are discussed in detail. Available software packages suitable for supporting decision making in BTO supply chains are also identified and their related solutions are outlined. The gap between the modelling and optimization techniques developed in the literature and the decision support needed in practice are highlighted and future research directions to better exploit the decision support capabilities of MOO are proposed

Decision support for build-to-order supply chain management through multiobjective optimization

This is the post-print version of the final paper published in International Journal of Production Economics. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.This paper aims to identify the gaps in decision-making support based on multiobjective optimization (MOO) for build-to-order supply chain management (BTO-SCM). To this end, it reviews the literature available on modelling build-to-order supply chains (BTO-SC) with the focus on adopting MOO techniques as a decision support tool. The literature has been classified based on the nature of the decisions in different part of the supply chain, and the key decision areas across a typical BTO-SC are discussed in detail. Available software packages suitable for supporting decision making in BTO supply chains are also identified and their related solutions are outlined. The gap between the modelling and optimization techniques developed in the literature and the decision support needed in practice are highlighted. Future research directions to better exploit the decision support capabilities of MOO are proposed. These include: reformulation of the extant optimization models with a MOO perspective, development of decision supports for interfaces not involving manufacturers, development of scenarios around service-based objectives, development of efficient solution tools, considering the interests of each supply chain party as a separate objective to account for fair treatment of their requirements, and applying the existing methodologies on real-life data sets.Brunel Research Initiative and Enterprise Fund (BRIEF

Value at Risk and Inventory Control

The purposes of this paper are two-fold. On the one hand, we shall provide a decision analysis justification for the Value at Risk (VaR) approach based on ex-post, disappointment decision making arguments. We shall show that the approach is justified by a disappointment criterion. In other words, the asymmetric valuation between ex-ante expected returns above an appropriate target return and the expected returns below that same target level, provide an explanation for the VaR criterion when it is used as a tool for VaR efficiency design. Second, this paper provides applications to inventory management based on VaR risk exposure. Although the mathematical problems arising from an application of the VaR approach, tuned to current practice in financial risk management, are difficult to solve analytically, solutions can be found by application of standard computational and simulation techniques. A number of cases are solved and formulated to demonstrate the paper’s applicability.Inventory; VaR; Disappointment

A Decision Support System for Computing Optimal (R,S) Policy Parameters

Retail replenishment is a high-value activity. According to the US Commerce Department, $1.1 trillion in inventory supports$3.2 trillion in annual US retail sales [...]. Improving distribution centre efficiency of just a few percentage points through advanced automation and real-time replenishment may deliver significant savings and require less capital to be tied up in inventory. 1 An interesting class of production/inventory control problems is the one that considers the single-location, single-product case under non-stationary stochastic demand, fixed production/ordering cost and per-unit holding cost. Exact and efficient approaches for computing optimal production/replenishment decisions are a key factor for achieving profitability in retail business. One of the possible policies that can be adopted to manage stocks is the replenishment cycle policy [6]. In this policy the inventory review times are set under a here-and-now strategy at the beginning of the planning horizon. These decisions are not affected by the actual demand realized in each period. On the other hand, for each inventory review we observe the actual demand realized in former periods to comput

Confidence-based Reasoning in Stochastic Constraint Programming

In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the original problem being analysed; by solving this reduced problem, with a given confidence probability, we obtain assignments that satisfy the chance constraints in the original model within prescribed error tolerance thresholds. To achieve this, we blend concepts from stochastic constraint programming and statistics. We discuss both exact and approximate variants of our method. The framework we introduce can be immediately employed in concert with existing approaches for solving stochastic constraint programs. A thorough computational study on a number of stochastic combinatorial optimisation problems demonstrates the effectiveness of our approach.Comment: 53 pages, working draf

Controlled diffusion processes

This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and structural assumptions. Stochastic maximum principle and control under partial observations (equivalently, control of nonlinear filters) are also discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org