Allocation of advertising budget between multiple channels to support sales in multiple markets

We consider the allocation of a limited marketing budget between multiple channels in order to promote sales at multiple markets. The channels differ in their type, level of targetability (or reach), and costliness. We incorporate the “threshold effect” from each market in our resource allocation which requires some positive advertising investment in each market before much sales impact can be observed from it. The increased number of channels in recent years with the advent of digital advertising, along with the added complexity created by the threshold effect, necessitates the development of new allocation approaches. In this paper, we formulate the firm’s resource allocation decision as a nonlinear and nonseparable knapsack problem. We develop a branch and cut solution method which is enhanced by a heuristic approach. A set of numerical experiments illustrate the performance of our methods and evaluate the usefulness of two rule-of-thumb strategies commonly used in practice.     

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.     

Multiattribute electronic procurement using goal programming

One of the key challenges of current day electronic procurement systems is to enable procurement decisions transcend beyond a single attribute such as cost. Consequently, multiattribute procurement have emerged as an important research direction. In this paper, we develop a multiattribute e-procurement system for procuring large volume of a single item. Our system is motivated by an industrial procurement scenario for procuring raw material. The procurement scenario demands multiattribute bids, volume discount cost functions, inclusion of business constraints, and consideration of multiple criteria in bid evaluation. We develop a generic framework for an e-procurement system that meets the above requirements. The bid evaluation problem is formulated as a mixed linear integer multiple criteria optimization problem and goal programming is used as the solution technique. We present a case study for which we illustrate the proposed approach and a heuristic is proposed to handle the computational complexity arising out of the cost functions used in the bids.     

A fuzzy attractiveness of market entry (FAME) model for market selection decisions

A Fuzzy Attractiveness of Market Entry (FAME) model is developed to address the decision-making problem of product introduction into alternative markets. FAME is a market entry selection model that is specifically designed to handle situations when information is limited and/or ambiguous, and a high level of uncertainty exists. As such, the FAME model is an easy to implement tool that supports a reasoning approach to market selection decisions. The model uses expert opinions regarding four factors: (1) fit of the firm's marketing mix in each market; (2) the fit of its key competitor's marketing mix in each market; (3) environmental conditions in each market; and (4) the strategic importance of each market to the firm. Application of the model algorithm is conducted for a small, Bulgarian winery's market selection decision. Ease of use is relevant for small to mid-size companies since a spreadsheet is sufficient to complete the algorithmic calculations.     

Dynamic asset allocation for varied financial markets under regime switching framework

Asset allocation among diverse financial markets is essential for investors especially under situations such as the financial crisis of 2008. Portfolio optimization is the most developed method to examine the optimal decision for asset allocation. We employ the hidden Markov model to identify regimes in varied financial markets; a regime switching model gives multiple distributions and this information can convert the static mean–variance model into an optimization problem under uncertainty, which is the case for unobservable market regimes. We construct a stochastic program to optimize portfolios under the regime switching framework and use scenario generation to mathematically formulate the optimization problem. In addition, we build a simple example for a pension fund and examine the behavior of the optimal solution over time by using a rolling-horizon simulation. We conclude that the regime information helps portfolios avoid risk during left-tail events.     

Optimal contracting with effort and misvaluation

We propose a new continuous-time contracting model, in which the firm value process can only be observed with noise, and there are two sources of moral hazard: the agent’s effort and misvaluation. The principal can induce the agent to alter the perceived fundamental value of the firm through misvaluation, thus changing the market estimate of that value. We consider two cases in detail: the one in which the market correctly anticipates only the effort, and the other in which it correctly anticipates both the effort and the amount of misvaluation. In the first case, we find that it is optimal for the principal to induce the agent to apply a non-zero amount of misvaluation. Using calculus of variation techniques, we find the optimal pay-per-performance sensitivity (PPS) of the contract and optimal effort and misvaluation amount, by means of solving of a second order ordinary differential equation. In the second case, which can be viewed as an extension of the seminal Holmstrom-Milgrom model to the case of noisy observations, we find that the optimal misvaluation value is zero, and we compare the resulting optimal contract to the Holmstrom-Milgrom contract.     

Market selection decisions for inventory models with price-sensitive demand

In the majority of classical inventory theory literature, demand arises from exogenous sources upon which the firm has little or no control. In many practical contexts, however, aggregate demand is comprised of individual demands from a number of distinct customers or markets. This introduces new dimensions to supply chain planning problems involving the selection of markets or customers to include in the demand portfolio. We present a nonlinear, combinatorial optimization model to address planning decisions in both deterministic and stochastic settings, where a firm constructs a demand portfolio from a set of potential markets having price-sensitive demands. We first consider a pricing strategy that dictates a single price throughout all markets and provide an efficient algorithm for maximizing total profit. We also analyze the model under a market-specific pricing policy and describe its optimal solution. An extensive computational study characterizes the effects of key system parameters on the optimal value of expected profit, and provides some interesting insights on how a given market’s characteristics can affect optimal pricing decisions in other markets.     

Real and financial interacting markets: A behavioral macro-model

In the present paper we propose a model in which the real side of the economy, described via a Keynesian good market approach, interacts with the stock market with heterogeneous speculators, i.e., optimistic and pessimistic fundamentalists, that respectively overestimate and underestimate the reference value due to a belief bias. Agents may switch between optimism and pessimism according to which behavior is more profitable. To the best of our knowledge, this is the first contribution considering both real and financial interacting markets and an evolutionary selection process for which an analytical study is performed. Indeed, employing analytical and numerical tools, we detect the mechanisms and the channels through which the stability of the isolated real and financial sectors leads to instability for the two interacting markets. In order to perform such analysis, we introduce the “interaction degree approach”, which allows us to study the complete three-dimensional system by decomposing it into two subsystems, i.e., the isolated financial and real markets, easier to analyze, that are then linked through a parameter describing the interaction degree between the two markets. We derive the stability conditions both for the isolated markets and for the whole system with interacting markets. Next, we show how to apply the interaction degree approach to our model. Among the various scenarios we are led to analyze, the most interesting one is that in which the isolated markets are stable, but their interaction is destabilizing. We choose such setting to give an economic interpretation of the model and to explain the rationale for the emergence of boom and bust cycles. Finally, we add stochastic noises to the optimists and pessimists demands and show how the model is able to reproduce the stylized facts for the real output data in the US.     

Optimal procurement strategies for online spot markets

Spot markets have emerged for a broad range of commodities, and companies have started to use them in addition to their traditional, long-term procurement contracts (forward contracts). In comparison to forward contracts, spot markets offer products at essentially negligible lead time, but typically command a higher expected price for this added flexibility while also exhibiting substantial price uncertainty. In our research, we analyze the resulting procurement challenge and quantify the benefits of using spot markets from a supply chain perspective. We develop and solve mathematical models that determine the optimal order quantity to purchase via forward contracts and the optimal quantity to purchase via spot markets. We analyze the most general situation where commodities can be both bought and sold via a spot market and derive closed-form results for this case. We compare the obtained results to the reference scenario of pure contract sourcing and we include results for situations where the use of spot markets is restricted to either buying or selling only. Our approaches can be used by decision makers to determine optimal procurement strategies based on key parameters such as, demand and spot price volatilities, correlation between demand and spot prices, and risk aversion. The results of our analysis demonstrate that significant profit improvements can be achieved if a moderate fraction of the commodity demand is procured via spot markets. The results also show that companies who use spot markets can offer a higher expected service level, but that they might experience a higher variability in profits than companies who do not use spot markets. We illustrate our analytical results with numerical examples throughout the paper.     

ZIPMAP — A Zero-One Integer Programming Model for Market Segmentation and Product Positioning

An optimization model is proposed to aid marketing managers to search for and develop new product brand ideas. The model, which is founded on individual consumer behaviour constructs, determines a position for a new brand, in the consumers' perceptual space of product attributes, that maximizes company sales. The resulting mathematical model is stated as a large-scale, mixed, zero-one, integer, non-linear mathematical programming problem whose solution is sought through a two-stage optimization approach.     

Supply capacity acquisition and allocation with uncertain customer demands

We study a class of capacity acquisition and assignment problems with stochastic customer demands often found in operations planning contexts. In this setting, a supplier utilizes a set of distinct facilities to satisfy the demands of different customers or markets. Our model simultaneously assigns customers to each facility and determines the best capacity level to operate or install at each facility. We propose a branch-and-price solution approach for this new class of stochastic assignment and capacity planning problems. For problem instances in which capacity levels must fall between some pre-specified limits, we offer a tailored solution approach that reduces solution time by nearly 80% over an alternative approach using a combination of commercial nonlinear optimization solvers. We have also developed a heuristic solution approach that consistently provides optimal or near-optimal solutions, where solutions within 0.01% of optimality are found on average without requiring a nonlinear optimization solver.     

Global optimization of multilevel electricity market models including network design and graph partitioning

We consider the combination of a network design and graph partitioning model in a multilevel framework for determining the optimal network expansion and the optimal zonal configuration of zonal pricing electricity markets, which is an extension of the model discussed in Grimm et al. (2019) that does not include a network design problem. The two classical discrete optimization problems of network design and graph partitioning together with nonlinearities due to economic modeling yield extremely challenging mixed-integer nonlinear multilevel models for which we develop two problem-tailored solution techniques. The first approach relies on an equivalent bilevel formulation and a standard KKT transformation thereof including novel primal-dual bound tightening techniques, whereas the second is a tailored generalized Benders decomposition. For the latter, we strengthen the Benders cuts of Grimm et al. (2019) by using the structure of the newly introduced network design subproblem. We prove for both methods that they yield global optimal solutions. Afterward, we compare the approaches in a numerical study and show that the tailored Benders approach clearly outperforms the standard KKT transformation. Finally, we present a case study that illustrates the economic effects that are captured in our model.     

Mature or emerging markets: Competitive duopoly investment decisions

We develop a competitive investment model wherein two competing firms consider investing into two projects targeting, separately, a mature and an emerging market. The returns firms obtain from investments into these markets are assumed to follow an S-shaped curve and depend on both firms’ actions. Considering symmetric environments (in terms of investment opportunities), we find that different forms of interactions may arise (e.g., Prisoner’s Dilemma and Game of Chicken) and outline corresponding strategies that offer higher returns by exploiting first-mover advantages, cooperation opportunities and aggressive choices. We also discuss the market conditions that can lead to these outcomes. Finally, considering non-symmetric environments, we show that a firm may be better off when its competitor’s budget increases.     

Resource allocation to defensive marketing and manufacturing strategies

In this paper, we investigate the coordinated use of marketing and manufacturing strategies to formulate a defensive business strategy for an incumbent firm upon market entry. While defensive marketing strategies have been researched extensively, little has been done on defensive manufacturing strategies and even less on coordinating these two. We propose a formulation for the joint formation of a defensive strategy by the marketing and production functions under budget constraint considerations. The incumbent firm may allocate its resourcesto advertising and distribution expenditures, as well as to manufacturing investments to reduce the unit production cost. The incumbent firm has also the option of simply allocating all of its resources purely to advertising and distribution. We show that while there exist cases where the optimal reaction to entry involves investments in manufacturing improvements, there are also cases where defense is in marketing strategies alone. We identify the market conditions that promote such reactions to entry and also provide sensitivity analysis.     

Towards an auction-driven gas supply: a simulation-based optimization framework for utilities

A platform for the study of the whole transmission problem (arrival of ships, regasification, transportation and distribution) faced by gas utilities companies is proposed. The main objective of this research is to develop a platform that includes the analysis of the new capacity auctions (and not the traditional commodity auctions) that will govern the supply chain in the near future. A simulation-optimization approach has been used to favour the more realistic abstraction of the system. The discrete-event model includes a genetic algorithm to reach the solution in a satisfactory short time, a requisite in auction markets. Design and optimization studies for the utilities are addressed using the platform, which has been validated with real data for one of the main zones in the Spanish market.     

Integrated market selection and production planning: complexity and solution approaches

Emphasis on effective demand management is becoming increasingly recognized as an important factor in operations performance. Operations models that account for supply costs and constraints as well as a supplier’s ability to influence demand characteristics can lead to an improved match between supply and demand. This paper presents a class of optimization models that allow a supplier to select, from a set of potential markets, those markets that provide maximum profit when production/procurement economies of scale exist in the supply process. The resulting optimization problem we study possesses an interesting structure and we show that although the general problem is ${\mathcal{NP}}$ -complete, a number of relevant and practical special cases can be solved in polynomial time. We also provide a computationally very efficient and intuitively attractive heuristic solution procedure that performs extremely well on a large number of test instances.     

Formulation and analysis of horizontal mergers among oligopolistic firms with insights into the merger paradox: a supply chain network perspective

In this paper, we consider oligopolistic firms with supply chain networks who are involved in the production, storage, and distribution of a homogeneous product to demand markets and explore what has become known in the literature as the “merger paradox.” We present the oligopolistic supply chain network equilibrium model associated with the competing firms before the horizontal mergers and also develop the supply chain network optimization model post the complete merger. In addition, we develop the model in which only a subset of the firms in the industry merge. The governing concept of the competing firms is that of Cournot–Nash equilibrium. We utilize finite-dimensional variational inequality theory for the formulation, analysis, and solution of both the pre and the post-merger supply chain network problems. We provide numerical examples for which we compute the total costs, the total revenues, as well as the profits obtained for the firms pre and post the mergers for a variety of distinct oligopoly problems. The generality of the network models and the flexibility of the computational approach, which yields closed form expressions for the product flows at each iteration, allows us to obtain deeper insights into the merger paradox.     

Optimal payoff under the generalized dual theory of choice

We consider portfolio optimization under a preference model in a single-period, complete market. This preference model includes Yaari’s dual theory of choice and quantile maximization as special cases. We characterize when the optimal solution exists and derive the optimal solution in closed form when it exists. The optimal portfolio yields an in-the-money payoff when the market is good and zero payoff otherwise. Finally, we extend our portfolio optimization problem by imposing a dependence structure with a given benchmark payoff.     

Competitive facility location model with concave demand

We consider a spatial interaction model for locating a set of new facilities that compete for customer demand with each other, as well as with some pre-existing facilities to capture the “market expansion” and the “market cannibalization” effects. Customer demand is assumed to be a concave non-decreasing function of the total utility derived by each customer from the service offered by the facilities. The problem is formulated as a non-linear Knapsack problem, for which we develop a novel solution approach based on constructing an efficient piecewise linear approximation scheme for the objective function. This allows us to develop exact and α-optimal solution approaches capable of dealing with relatively large-scale instances of the model. We also develop a fast Heuristic Algorithm for which a tight worst-case error bound is established.     

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.