A supply chain network equilibrium model with random demands

This paper first develops a multitiered supply chain network equilibrium model with fixed demands and proves that the governing equilibrium conditions satisfy a finitedimensional variational inequality. The paper then establishes that the static supply chain network model with its governing equilibrium conditions can be reformulated as a transportation network equilibrium model over an appropriately constructed abstract network or supernetwork. This identification provides a new interpretation of equilibrium in supply chain networks with fixed demands in terms of path flows. The equivalence is then further exploited to construct a dynamic supply chain network model with time-varying demands (and flows) using an evolutionary (time-dependent) variational inequality formulation. Recent theoretical results in the unification of projected dynamical systems and evolutionary variational inequalities are presented and then applied to formulate dynamic numerical supply chain network examples and to compute the curves of equilibria. An example with step-wise time-dependent demand is also given for illustration purposes.

Supply chain optimization schemes have more often than not underplayed the role of inherent stochastic fluctuations in the associated variables. The present article focuses on the associated reengagement and correlated renormalization of supply chain predictions now with the inclusion of stochasticity induced fluctuations in the structure. With a processing production plant in mind that involves stochastically varying production and transportation costs both from the site to the plant as well as from the plant to the customer base, this article proves that the producer may benefit through better outlay in the form of higher sale prices with lowered optimized production costs only through a suitable selective choice of producers whose production cost probability density function abides a Pareto distribution. Lower the Pareto exponent, better is the supply chain prediction for cost optimization. On the other hand, other symmetric (normal) and asymmetric (lognormal) distributions lead ...

Annals of Operations Research, 2005

In this paper, we present a supply chain network model with multiple tiers of decision-makers, consisting, respectively, of manufacturers, distributors, and retailers, who can compete within a tier but may cooperate between tiers. We consider multicriteria decision-making for both the manufacturers and the distributors whereas the retailers are subject to decision-making under uncertainty since the demands associated with the product are random. We derive the optimality conditions for the decision-makers, establish the equilibrium conditions, and derive the variational inequality formulation. We then utilize the variational inequality formulation to provide both qualitative properties of the equilibrium product shipment, service level, and price pattern and to propose a computational procedure, along with convergence results. This is the first supply chain network model to capture both multicriteria decision-making and decision-making under uncertainty in an integrated equilibrium framework.

International Journal of Science and Research (IJSR), 2015

The life cycle of new product is becoming shorter and shorter in all markets. Given these short product life cycles, product demand is increasingly difficult to forecast. Furthermore, demand is never really stationary because the demand rates evolves over the life of the product. In this paper, we consider the problem of where in supply chain to place strategic safety stocks to provide a high level service to the final customer with minimum cost, and extend the model for stationary demand to the case of stationary demand, as might occur for products with short life cycles. We assume that we can model the supply chain as a network that each stage in the supply chain operates with a periodic reviuw base-stock policy, that demand is bounded and that there is guaranteed service time between every stage and its customers. This study uses the analytic solver program in excel that does the randomization process on the variable demand.

Netnomics, 2002

In this paper, we develop a framework for the formulation, analysis, and computation of solutions to supply chain network problems in the presence of electronic commerce. Specifically, we consider manufacturers who are involved in the production of a homogeneous product and can now sell and have delivered the product not only to retailers but also directly to consumers. In addition, the manufacturers can transact with the retailers electronically. We assume that both the manufacturers and the retailers seek to maximize their profits, whereas the consumers take both the prices charged by the retailers and the manufacturers, along with the associated transaction costs, in making their consumption decisions. We identify the network structure of the problem, derive the equilibrium conditions, and establish the finite-dimensional variational inequality formulation. We then utilize variational inequality theory to obtain qualitative properties of the equilibrium pattern. In addition, we propose a continuous time adjustment process for the study of the disequilibrium dynamics and establish that the set of stationary points of the resulting projected dynamical system coincides with the set of solutions of the variational inequality problem. Finally, we apply an algorithm for the determination of equilibrium prices and product shipments in several supply chain examples. This paper synthesizes Business-to-Consumer (B2C) and Business-to-Business (B2B) decision-making in a supply chain context within the same framework.

This paper presents the problem of redesigning a supply network of large scale by considering variability of the demand. The central problematic takes root in determining strategic decisions of closing and adjusting of capacity of some network echelons and the tactical decisions concerning to the distribution channels used for transporting products. We have formulated a deterministic Mixed Integer Linear Programming Model (MILP) and a stochastic MILP model (SMILP) whose objective functions are the maximization of the EBITDA (Earnings before Interest, Taxes, Depreciation and Amortization). The decisions of Network Design on stochastic model as capacities, number of warehouses in operation, material and product flows between echelons, are determined in a single stage by defining an objective function that penalizes unsatisfied demand and surplus of demand due to demand changes. The solution strategy adopted for the stochastic model is a scheme denominated as Sample Average Approximation (SAA). The model is based on the case of a Colombian company dedicated to production and marketing of foodstuffs and supplies for the bakery industry. The results show that the proposed methodology was a solid reference for decision support regarding to the supply networks redesign by considering the expected economic contribution of products and variability of the demand.

Multiagent based Supply Chain Management

In this paper, we develop a global supply chain network model in which both physical and electronic transactions are allowed and in which supply-side risk as well as demand-side risk are included in the formulation. The model consists of three tiers of decision-makers/agents: the manufacturers, the distributors, and the retailers who may be located in the same or in different countries and may conduct their transactions in distinct 1 currencies. We model the optimizing behavior of the various decision-makers, with the manufacturers and the distributors being multicriteria decision-makers, and concerned with both profit maximization and risk minimization. The retailers, in turn, are faced with random demands for the product. We derive the governing equilibrium conditions and establish the finite-dimensional variational inequality formulation. We provide qualitative properties of the equilibrium product flow and price pattern in terms of existence and uniqueness results and also establish conditions under which the proposed computational procedure is guaranteed to converge. Finally, we illustrate the global supply chain network model and the computational procedure through several numerical examples. This research illustrates the modeling, analysis, and computation of solutions to decentralized supply chain networks with multiple agents in the presence of electronic commerce and risk management in the global arena. Moreover, it highlights and applies some of the theoretical tools that are now available for such multi-agent problems.