The Capacitated Supplier Selection problem with Total Quantity Discount policy and Activation Costs under uncertainty (original) (raw)
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2017
We study the Capacitated Supplier Selection problem with Total Quantity Discount policy and Activation Costs, a procurement problem where a company needs a certain quantity of different products from a set of potential suppliers, and introduce its variant under uncertainty. In its deterministic form, the problem aims at selecting a subset of the suppliers and the relative purchasing plan satisfying the demands at minimum cost, taking into account that the suppliers offer discounts based on the total quantity of products purchased and that the activation of a business activity with a supplier has a fixed cost. However, due to the long-term nature of the problem, several parameters may be affected by uncertainty. Thus, we propose a two-stage stochastic programming formulation with recourse, highlighting the strategic and the operational decisions involved, as well as the effect of the different sources of uncertainty. In particular, we focus on the cases in which only the products pri...
Incorporating uncertainty into a supplier selection problem
Supplier selection is an important strategic supply chain design decision. Incorporating uncertainty of demand and supplier capacity into the optimization model results in a robust selection of suppliers. A two-stage stochastic programming (SP) model and a chance-constrained programming (CCP) model are developed to determine a minimal set of suppliers and optimal order quantities with consideration of business volume discounts. Both models include several objectives and strive to balance a small number of suppliers with the risk of not being able to meet demand. The SP model is scenario-based and uses penalty coefficients whereas the CCP model assumes a probability distribution and constrains the probability of not meeting demand. Both formulations improve on a deterministic mixed integer linear program and give the decision maker a more complete picture of tradeoffs between cost, system reliability and other factors. We present Pareto-optimal solutions for a sample problem to demonstrate the benefits of the SP and CCP models. In order to describe the tradeoffs between costs and risks in an analytical form, we use multi-parametric programming techniques to more completely analyze the alternative Pareto-optimal supplier selection solutions in the CCP model. This analysis gives insights into the robustness of the solutions with respect to number of suppliers, costs and probability of not meeting demand.
International Journal of Risk Assessment and Management, 2022
In this paper, we develop two stochastic mixed integers linear programming (SMILP) models for supplier selection under disruption risk considering different capacity, failure probability, uncertain demand and quantity discounts. The suppliers are assumed domestic suppliers and global suppliers. The obtained combinatorial stochastic optimisation problem is formulated as a mixed integer program with conditional value-at-risk technique (CVaR). Numerical examples and computational results are presented. The proposed models can optimise the present problem through an estimated value at risk (VaR) and minimised CVaR simultaneously. The computational results reveal that the proposed models allow the decision maker to make an efficient selection of suppliers under disruption risk. Results also show that the decisions are not univocal because they depend on the risk proneness of the decision maker.
A three-stage procurement optimization problem under uncertainty
Naval Research Logistics (NRL), 2013
This article examines a problem faced by a firm procuring a material input or good from a set of suppliers. The cost to procure the material from any given supplier is concave in the amount ordered from the supplier, up to a supplier-specific capacity limit. This NP-hard problem is further complicated by the observation that capacities are often uncertain in practice, due for instance to production shortages at the suppliers, or competition from other firms. We accommodate this uncertainty in a worst-case (robust) fashion by modeling an adversarial entity (which we call the "follower") with a limited procurement budget. The follower reduces supplier capacity to maximize the minimum cost required for our firm to procure its required goods. To guard against uncertainty, the firm can "protect" any supplier at a cost (e.g., by signing a contract with the supplier that guarantees supply availability, or investing in machine upgrades that guarantee the supplier's ability to produce goods at a desired level), ensuring that the anticipated capacity of that supplier will indeed be available. The problem we consider is thus a three-stage game in which the firm first chooses which suppliers' capacities to protect, the follower acts next to reduce capacity from unprotected suppliers, and the firm then satisfies its demand using the remaining capacity. We formulate a three-stage mixed-integer program that is well-suited to decomposition techniques and develop an effective cutting-plane algorithm for its solution. The corresponding algorithmic approach solves a sequence of scaled and relaxed problem instances, which enables solving problems having much larger data values when compared to standard techniques.
This paper investigates a model for pricing the demand for a set of goods when suppliers operate discount schedules based on total business value. We formulate the buyers's decision problem as a mixed binary integer program, which is a generalization of the capacitated facility location problem (CFLP). A branch and bound (BnB) procedure using Lagrangean relaxation and subgradient optimization is developed for solving large-scale problems that can arise when suppliers' discount schedules contain multiple price breaks. Results of computer trials on specially adapted large benchmark instances of the CFLP confirm that a sub-gradient optimization procedure based on Shor and Zhurbenko's r-algorithm, which employs a space dilation in the direction of the difference between two successive subgradients, can be used efficiently for solving the dual problem at any node of the BnB tree.
Optimal supplier choice with discounting
This paper investigates a model for pricing the demand for a set of goods when suppliers operate discount schedules based on total business value. We formulate the buyers's decision problem as a mixed binary integer program (MIP) which is a generalization of the capacitated facility location problem (CFLP). A branch and bound procedure using Lagrangean relaxation and subgradient optimization is developed for solving large-scale problems that can arise when suppliers' discount schedules contain multiple price breaks. Results of computer trials on specially adapted large benchmark instances of the CFLP, con…rm that a subgradient optimization procedure based on Shor and Zhurbenko's r-algorithm, which employs a space dilation strategy in the direction of the di¤erence between two successive subgradients, can solve such instances e¢ ciently.
2003
We present a two-stage stochastic 0-1 modeling and a related algorithmic approach for Supply Chain Management under uncertainty, whose goal consists of determining the production topology, plant sizing, product selection, product allocation among plants and vendor selection for raw materials. The objective is the maximization of the expected benefit given by the product net profit over the time horizon minus the investment depreciation and operations costs. The main uncertain parameters are the product net price and demand, the raw material supply cost and the production cost. The first stage is included by the strategic decisions. The second stage is included by the tactical decisions. A tight 0-1 model for the deterministic version is presented. A splitting variable mathematical representation via scenario is presented for the stochastic version of the model. A two-stage version of a Branch and Fix Coordination (BFC) algorithmic approach is proposed for stochastic 0-1 program solving, and some computational experience is reported for cases with dozens of thousands of constraints and continuous variables and hundreds of 0-1 variables.
Robust solutions and risk measures for a supply chain planning problem under uncertainty
Journal of the Operational Research Society, 2007
We consider a strategic supply chain planning problem formulated as a two-stage Stochastic Integer Programming (SIP) model. The strategic decisions include site locations, choices of production, packing and distribution lines, and the capacity increment or decrement policies. The SIP model provides a practical representation of real world discrete resource allocation problems in the presence of future uncertainties which arise due to changes in the business and economic environment. Such models that consider the future scenarios (along with their respective probabilities) not only identify optimal plans for each scenario, but also determine a hedged strategy for all the scenarios. We, (1) exploit the natural decomposable structure of the SIP problem through Benders' decomposition, (2) approximate the probability distribution of the random variables using the Generalised Lambda distribution, and (3) through simulations, calculate the performance statistics and the risk measures for the two models, namely the expected-value and the here-and-now.
International Journal of Production Economics, 2010
We consider the joint acquisition and pricing problem where the retailer sells multiple products with uncertain demands and the suppliers provide all unit quantity discounts. The problem is to determine the optimal acquisition quantities and selling prices so as to maximize the retailer's expected profit, subject to a budget constraint. This is the first extension to consider supplier discounts in the constrained multi-product newsvendor pricing problem. We establish a mixed integer nonlinear programming (MINLP) model to formulate the problem, and develop a Lagrangian-based solution approach. Computational results for the test problems involving up to thousand products are reported, which show that the proposed approach can obtain high quality solutions in a very short time.
A multi-objective stochastic programming approach for supply chain design considering risk
International Journal of Production Economics, 2008
In this paper, we develop a unified mixed integer linear modelling approach to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under static-dynamic uncertainty strategy. The proposed approach applies to settings in which unmet demand is backordered or lost; and it can accommodate variants of the problem for which the quality of service is captured by means of backorder penalty costs, non-stockout probabilities, or fill rate constraints. This approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the stochastic lot sizing problem, some of which have been previously tackled via ad hoc solution methods and some others that have not yet been addressed in the literature; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds based on piecewise linearisation of the first order loss function. We illustrate the effectiveness and flexibility of the proposed approach by means of a computational study.