Quantitative analysis of multi-periodic supply chain contracts with options via stochastic programming

We propose a stochastic programming approach for quantitative analysis of supply contracts, involving flexibility, between a buyer and a supplier, in a supply chain framework. Specifically, we consider the case of multi-periodic contracts in the face of correlated demands. To design such contracts, one has to estimate the savings or costs induced for both parties, as well as the optimal orders and commitments. We show how to model the stochastic process of the demand and the decision problem for both parties using the algebraic modeling language AMPL. The resulting linear programs are solved with a commercial linear programming solver; we compute the economic performance of these contracts, giving evidence that this methodology allows to gain insight into realistic problems.stochastic programming; supply contract; linear programming; modeling software; decision tree

A Rouse-based method to integrate the chemical composition of river sediments : application to the Ganga basin

Author Posting. © American Geophysical Union, 2011. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 116 (2011): F04012, doi:10.1029/2010JF001947.The Ganga River is one of the main conveyors of sediments produced by Himalayan erosion. Determining the flux of elements transported through the system is essential to understand the dynamics of the basin. This is hampered by the chemical heterogeneity of sediments observed both in the water column and under variable hydrodynamic conditions. Using Acoustic Doppler Current Profiler (ADCP) acquisitions with sediment depth profile sampling of the Ganga in Bangladesh we build a simple model to derive the annual flux and grain size distributions of the sediments. The model shows that ca. 390 (±30) Mt of sediments are transported on average each year through the Ganga at Haring Bridge (Bangladesh). Modeled average sediment grain size parameters D50 and D84 are 27 (±4) and 123 (±9) μm, respectively. Grain size parameters are used to infer average chemical compositions of the sediments owing to a strong grain size chemical composition relation. The integrated sediment flux is characterized by low Al/Si and Fe/Si ratios that are close to those inferred for the Himalayan crust. This implies that only limited sequestration occurs in the Gangetic floodplain. The stored sediment flux is estimated to c.a. 10% of the initial Himalayan sediment flux by geochemical mass balance. The associated, globally averaged sedimentation rates in the floodplain are found to be ca. 0.08 mm/yr and yield average Himalayan erosion rate of ca. 0.9 mm/yr. This study stresses the need to carefully address the average composition of river sediments before solving large-scale geochemical budgets.This work was supported by INSU program “Relief de la Terre” and ANR Calimero. Valier Galy was supported by the U.S. National Science Foundation (grant OCE‐0851015)

Approximate solutions for large-scale piecewise deterministic control systems arising in manufacturing flow control models

We propose a numerical technique for approximately solving large-scale piecewise deterministic control systems that are typically related to manufacturing flow control problems in unreliable production systems. The method consists of reformulating the stochastic control problem under study into a Markov decision process. Then we exploit the associated dynamic programming conditions and we propose an “approximate” policy iteration algorithm. This will be based on an approximation of the Bellman functions by a combination of a set of base functions, using a specific decomposition technique. The numerical method is applicable whenever a turnpike property holds for some associated infinite horizon deterministic control problem. To illustrate the approach, we solve an example and compare this new approximation method with a more classical approximation-by-decomposition techniqu

Efficient purchaser incentive when dealing with suppliers implementing continuous improvement plans

International audienceThis paper presents incentive schemes in the framework of a collaborative purchasing cost reduction process with a supplier implementing a continuous improvement plan. Using a stochastic decision process formulation, we analyze the structure of the optimal policy and characterize its numerical robustness through numerical applications solved by dynamic programming. Then, we analyze two purchaser incentive schemes observed in practice. First, we describe some theoretical properties of the policies associated with these two schemes (schemes I and II) and show that these policies exhibit nonoptimal structures. Second, we estimate the quantitative loss for typical parameter values and, in particular, we show that for certain businesses this loss is significant. Then, we propose two easy-to-implement improvements (schemes III and IV), which result in near-optimal solutions and a significant impact on purchasing cost performances

A Note on 'Sourcing Decisions with Stochastic Supplier Reliability and Stochastic Demand'

Burke, Carillo and Vakharia [2009] consider a class of single product sourcing problems with a stochastic demand and multiple uncertain suppliers. Assuming that the demand is independent of the supplier reliabilities and uniformly distributed, they propose to write the expected profit as a quadratic function and derive a closed form expression for the optimal orders. We show that this formula is true only under special circumstances, which are not satisfied in many practical situations of interest. We give an exact formulation and solution procedure, holding under general assumptions. We illustrate our point by a complementary analysis of the numerical examples given in the quoted paper

Two-period production planning and inventory control

We study a single product two-period production/inventory model, in which the demands at each period are independent random variables. To optimally satisfy these random demands, quantities can be produced at the beginning of each period using slow or fast production mode, under capacity constraints. In addition to the usual decision variables for such models, we consider that a certain quantity can be salvaged at the beginning of each period. Such salvage processes are useful if the initial inventory of a period is considered to be too high. The unsatisfied demands for each period are backlogged to be satisfied during the next periods. After the end of the second period, a last quantity is produced in order to satisfy remaining orders and to avoid lost sales. The remaining inventory, if any, is salvaged. We formulate this model using a dynamic programming approach. We prove the concavity of the global objective function and we establish the closed-form expression of the second period optimal policy. Then, via a numerical solution approach, we solve the first period problem and exhibit the structure of the corresponding optimal policy. We provide insights, via numerical examples, that characterize the basic properties of our model and the effect of some significant parameters such as costs, demand variabilities or capacity constraints

A turnpike improvement algorithm for piecewise deterministic control

Les Cahiers du GERAD, Ecole des Hautes Etudes Commerciales, Montréal, n° G-90-2

Automatic Formulation of Stochastic Programs Via an Algebraic Modeling Language

This paper presents an open source tool that automatically generates the so-called deterministic equivalent in stochastic programming. The tool is based on the algebraic modeling language ampl. The user is only required to provide the deterministic version of the stochastic problem and the information on the stochastic process, either as scenarios or as a transitions-based event tree