Competitive facility location on decentralized supply chains

This paper addresses a novel competitive facility location problem about a firm that intends to enter an existing decentralized supply chain comprised of three tiers of players with competition: manufacturers, retailers and consumers. It first proposes a variational inequality for the supply chain network equilibrium model with production capacity constraints, and then employs the logarithmic-quadratic proximal prediction–correction method as a solution algorithm. Based on this model, this paper develops a generic mathematical program with equilibrium constraints for the competitive facility location problem, which can simultaneously determine facility locations of the entering firm and the production levels of these facilities so as to optimize an objective. Subsequently, a hybrid genetic algorithm that incorporates with the logarithmic-quadratic proximal prediction–correction method is developed for solving the proposed mathematical program with an equilibrium constraint. Finally, this paper carries out some numerical examples to evaluate proposed models and solution algorithms.     

Optimal trading and shipping of agricultural commodities

We develop and implement a model for a profit maximizing firm that provides an intermediation service between commodity producers and commodity end-users. We are motivated by the grain intermediation business at Los Grobo—one of the largest commodity-trading firms in South America. Producers and end-users are distributed over a realistic spatial network, and trade with the firm through contracts for delivery of grain during the marketing season. The firm owns spatially distributed storage facilities, and begins the marketing season with a portfolio of prearranged purchase and sale contracts with upstream and downstream counterparts. The firm aims to maximize profits while satisfying all previous commitments, possibly through the execution of new transactions. Under realistic constraints for capacities, network structure and shipping costs, we identify the optimal trading, storing and shipping policy for the firm as the solution of a profit-maximizing optimization problem, encoded as a minimum cost flow problem in a time-expanded network that captures both geography and time. We perform extensive numerical examples and show significant efficiency gains derived from the joint planning of logistics and trading.     

A branch and price solution approach for order acceptance and capacity planning in make-to-order operations

Make-to-order (MTO) operations have to effectively manage their capacity to make long-term sustainable profits. This objective can be met by selectively accepting available customer orders and simultaneously planning for capacity. We model a MTO operation of a job-shop with multiple resources having regular and non-regular capacity. The MTO firm has a set of customer orders at time zero with fixed due-dates. The process route, processing times, and sales price for each order are given. Since orders compete for limited resources, the firm can only accept some orders. In this paper a Mixed-Integer Linear Program (MILP) is proposed to aid an operational manager to decide which orders to accept and how to allocate resources such that the overall profit is maximized. A branch-and-price (B&P) algorithm is devised to solve the MILP effectively. The MILP is first decomposed into a master problem and several sub-problems using Dantzig-Wolfe decomposition. Each sub-problem is represented as a network flow problem and an exact procedure is proposed to solve the sub-problems efficiently. We also propose an approximate B&P scheme, Lagrangian bounds, and approximations to fathom nodes in the branch-and-bound tree. Computational analysis shows that the proposed B&P algorithm can solve large problem instances with relatively short time.     

Optimization-based Distribution Planning for Consumer Electronic Items

This paper describes the application of network modeling and optimization for short-term distribution planning in an Indian electronica firm. The company has three production centres, each comprising several factories. Each day, it ships finished product from the three production centres to 23 distribution centres (namely, its branches and sub-branches) spread all over the country. The present problem may be stated as: given the planned production quantity at each production centre and the estimated demand at each distribution centre for each week of a given month, specify the quantities to be dispatched from each production centre to the various distribution centres in each week of the month. The problem is modelled as a multi-period, minimum-cost, network flow model for each product item. The paper also discusses the implementation and actual use of the model for monthly distribution planning at the company.     

The construction of a comprehensive model for production strategy evaluation

To acquire reasonable profits and to be competitive in the globalize market, more and more firms today have exploited various kinds of production strategies, such as outsourcing, joint venture, or some kind of strategic alliance. Since every production strategy has its benefits and costs and may bring a firm different opportunities and risks, which kind of production strategy is the most suitable for a firm to carry out is a difficult and complicated decision with a high degree of uncertainty. Therefore, this research proposes a comprehensive production strategy evaluation model that can facilitate such a decision making for a firm. The factors that should be considered for devising a production strategy are listed for the benefits, opportunities, costs and risks (BOCR) merits first, and fuzzy Delphi method is applied next to select the most important factors under each merit. A network with BOCR merits is constructed to incorporate the selected factors, and fuzzy analytic network process is then applied to consider the interdependence and feedback inside the network. The proposed model can effectively aid decision making on which kind of production strategy should be adopted by a firm. A case of a printed circuit board manufacturer is presented for the illustration of the proposed model.     

A supply chain network economic model with time-based competition

This paper presents an integrated model for time-cost competition between supply chains with heterogeneous customers. The firms in our model can offer various time options for their production/service to time-sensitive customers. This gives rise of a new concept of time-based supply chain, which we call T-chain, to be the basic element in the competition and extends the inter supply chain competition to a new dimension of time. Assuming the customers are heterogeneous in time-cost bi-criteria decision making, we integrate the discrete choice theory into supply chain network competition and formulate the equilibrium conditions as a multinomial logit based variational inequality problem. Numerical examples are presented for model illustration and managerial insights such as profit maximization for a firm who participates in this supply chain network.     

Global facility network design in the presence of competition

We study the facility network design problem for a global firm that is a monopolist seller in its domestic market but faces local competition in its foreign market. The global firm produces in the face of demand and exchange rate uncertainty but can postpone localization and distribution of the output until after uncertainties are resolved. The competitor in the foreign market, however, enjoys the flexibility of postponing all production activities until after uncertainties are resolved. The two firms engage in an ex-post Cournot competition in the foreign market. We consider three potential network configurations for the global firm. Under a linear demand function, we provide the necessary and sufficient condition that one of the three networks is the global firm’s optimal choice, and explore how the presence of foreign competition affects the sensitivity of the global firm’s design to various cost parameters and market uncertainties.     

Formation of a strategic manufacturing and distribution network with transfer prices

We propose a profit maximization model for the decision support system of a firm that wishes to establish or rationalize a multinational manufacturing and distribution network to produce and deliver finished goods from sources to consumers. The model simultaneously evaluates all traditional location factors in a manufacturing and distribution network design problem and sets intra-firm transfer prices that take account of tax and exchange rate differentials between countries. Utilizing the generalized Benders decomposition approach, we exploit the partition between the product flow and the cash allocation (i.e., the pricing and revenue assignment) decisions in the supply chain to find near optimal model solutions. Our proposed profit maximizing strategic planning model produces intuitive results. We offer computational experiments to illustrate the potential valuable guidance the model can provide to a firm's supply chain design strategic planning process.     

The optimal resource portfolio under consumer choice and demand risk for vertically differentiated products

We study the optimal resource portfolio of a firm that sells two vertically differentiated products and utilizes resource flexibility and responsive pricing. We model this decision problem as a two-stage stochastic programming problem with recourse: In the first stage, the firm determines its resource mix and capacities so as to maximize the expected profit under demand uncertainty; in the second stage, uncertainty is resolved and the firm determines its production and pricing decision, constrained by its investment decision. We show that the objective function of this decision problem is not well-behaved (ie, it may have multiple local maxima). Using the concept of Pareto dominance, we reduce the feasible investment region, without loss of optimality, to one in which the objective function is well-behaved everywhere. This reduction allows us to derive the necessary and sufficient conditions for the optimal capacity decision and to gain insights.     

Learning horizon and optimal alliance formation

We develop a theoretical Bayesian learning model to examine how a firm’s learning horizon, defined as the maximum distance in a network of alliances across which the firm learns from other firms, conditions its optimal number of direct alliance partners under technological uncertainty. We compare theoretical optima for a ‘close’ learning horizon, where a firm learns only from direct alliance partners, and a ‘distant’ learning horizon, where a firm learns both from direct and indirect alliance partners. Our theory implies that in high tech industries, a distant learning horizon allows a firm to substitute indirect for direct partners, while in low tech industries indirect partners complement direct partners. Moreover, in high tech industries, optimal alliance formation is less sensitive to changes in structural model parameters when a firm’s learning horizon is distant rather than close. Our contribution lies in offering a formal theory of the role of indirect partners in optimal alliance portfolio design that generates normative propositions amenable to future empirical refutation.     

Supply chain performance assessment and supplier and component importance identification in a general competitive multitiered supply chain network model

In this paper, we develop a multitiered competitive supply chain network game theory model, which includes the supplier tier. The firms are differentiated by brands and can produce their own components, as reflected by their capacities, and/or obtain components from one or more suppliers, who also are capacitated. The firms compete in a Cournot–Nash fashion, whereas the suppliers compete a la Bertrand since firms are sensitive to prices. All decision-makers seek to maximize their profits with consumers reflecting their preferences through the demand price functions associated with the demand markets for the firms’ products. We construct supply chain network performance measures for the full supply chain and the individual firm levels that assess the efficiency of the supply chain or firm, respectively, and also allow for the identification and ranking of the importance of suppliers as well as the components of suppliers with respect to the full supply chain or individual firm. The framework is illustrated through a series of numerical supply chain network examples.     

Application of the fuzzy–stochastic methodology to appraising the firm value as a European call option

The valuing of a firm equity as a call option is a crucial problem in financial decision-making. There are two basic aspects that are studied; contingent claim features (payoff functions) and risk (stochastic process of underlying assets). However, non-preciseness (vagueness, uncertainty) of input data is often neglected. Thus, a combination of risk (stochastic) and uncertainty (fuzzy instruments) could be a useful approach in calculating a firm value as a call option. The Black–Scholes methodology of appraising equity as a European call option is applied. Fuzzy–stochastic methodology under fuzzy numbers (T-numbers) is proposed and described. Fuzzy–stochastic model of appraising a firm equity is proposed. Input data are in a form of fuzzy numbers and result, firm possibility-expected equity value is also determined vaguely as a fuzzy set. Illustrative example is introduced.     

基于时间和渠道敏感顾客选择偏好的双渠道定价策略

随着网络技术的发展,带动了网络销售模式的发展。网络渠道为顾客带来了便利性,也为制造商提供了扩大市场占有率和提高利润的机会,如何合理定价关系到企业的长久发展。在考虑顾客对网络渠道交付时间和网络渠道接受敏感的基础上,研究了制造商的单渠道和双渠道定价策略问题。研究结果表明,两种销售模式下零售渠道的定价相同,而网络渠道的定价低于零售渠道的定价。制造商可以通过引入网络渠道提高市场占有率、降低顾客时间敏感性和提高网络渠道接受程度,从而提高利润。最后,通过数值实验分析了交付时间敏感性和网络渠道接受程度对企业决策的影响,并对比分析了单渠道和双渠道的最优决策。     

Production and location on a network under demand uncertainty

The Hakimi theorem is fundamental in location theory. It says that the set of nodes and market-places necessarily contains a profit-maximizing location when the transportation costs are concave in distance. The purpose of this letter is to discuss the validity of this theorem in the context of a two-stage stochastic model of the location of a firm on a network. In the first stage, the firm chooses its location and production level before knowing the exact demands. In the second stage, it observes the realization of the random variables representing the demands and decides upon the distribution of its production. It is shown that the Hakimi theorem still holds in this model when the firm is risk-neutral. On the other hand, in the case of a risk-averse firm, it ceases to be true in that all the points of the network must be considered to obtain an optimal location.     

Capital Accumulation and Embodied Technological Progress

This paper combines technology adoption with capital accumulation taking into account technological progress. We model this as a multi-stage optimal control problem and solve it using the corresponding maximum principle. The model with linear revenue can be solved analytically, while the model with market power is solved numerically. We obtain that investment jumps upwards right at the moment that a new technology is adopted. We find that, if the firm has market power, the firm cuts down on investment before a new technology is adopted. Furthermore, we find that larger firms adopt a new technology later.     

Reinsurance control in a model with liabilities of the fractional Brownian motion type

We propose a model for reinsurance control for an insurance firm in the case where the liabilities are driven by fractional Brownian motion, a stochastic process exhibiting long-range dependence. The problem is transformed to a nonlinear programming problem, the solution of which provides the optimal reinsurance policy. The effect of various parameters of the model, such as the safety loading of the reinsurer and the insurer, the Hurst parameter, etc. on the optimal reinsurance program is studied in some detail. Copyright © 2007 John Wiley & Sons, Ltd.     

An advertising game with multiplicative interference

Two competing manufacturers provide a homogeneous market with substitutable products and want to maximize their profits. Each firm may advertise its brand, with a positive effect on its own brand and negative on the competitor's one. Moreover, each firm may choose an advertising medium to use among several available media. We assume that the advertising effect on demand is mediated by the goodwill variable and that a competitor's interference may be represented as a proportional reduction of the virtual goodwill. We model the manufacturers' problem as a noncooperative game under complete information and discuss the existence and features of its Nash equilibria.     

Pricing and equity in cross-regional green supply chains

This paper addresses the problem of the firms operating on cross-border or inter-regional platforms that are subject to the enforcement of each local government's carbon emissions regulatory policy, thus causing an imbalance in the sharing of the burden of the greening of the total supply chain. We introduce the concept of equity as the incentive mechanism to coordinate this green supply chain which is a function of the carbon emission permits and the revenue generated by the firms. Due to the complexity and imbalance in the original incentive mechanism to this problem, we provide a new equivalent supply chain network equilibrium model under elastic demand based on user equilibrium theory. We state the user equilibrium conditions and provide the equivalent formulation. We show the trade-offs under various carbon emissions regulatory policies. A product with higher price elasticity and carbon emission intensity not only hampers the firm from gaining a higher revenue, but it also reduces the equity of the system under an invariant emission regulatory policy.     

Optimal sequencing of skip collections and deliveries

The purpose of this paper is to model and solve a complex routing problem associated with the collection and delivery of skips. This study is motivated by a real-life problem encountered by a skip rental firm in Belgium. Two simple heuristics as well as an exact enumerative algorithm are developed for the problem. Computational experiments carried out on both randomly generated and real-life data confirm the efficiency of the proposed approach.     

Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution

We are concerned with a problem in which a firm or franchise enters a market by locating new facilities where there are existing facilities belonging to a competitor. The firm aims at finding the location and attractiveness of each facility to be opened so as to maximize its profit. The competitor, on the other hand, can react by adjusting the attractiveness of its existing facilities with the objective of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the facilities of the firm can be located at predetermined candidate sites. We employ Huff’s gravity-based rule in modeling the behavior of the customers where the fraction of customers at a demand point that visit a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. In order to find the optimal solution of this model, we convert it into an equivalent one-level mixed-integer nonlinear program so that it can be solved by global optimization methods. Apart from reporting computational results obtained on a set of randomly generated instances, we also compute the benefit the leader firm derives from anticipating the competitor’s reaction of adjusting the attractiveness levels of its facilities. The results on the test instances indicate that the benefit is 58.33% on the average.