Integrating Cardinality Constraints into Constraint Logic Programming with Sets

Formal reasoning about finite sets and cardinality is important for many applications, including software verification, where very often one needs to reason about the size of a given data structure. The Constraint Logic Programming tool $$\{ log\} $$ provides a decision procedure for deciding the satisfiability of formulas involving very general forms of finite sets, although it does not provide cardinality constraints. In this paper we adapt and integrate a decision procedure for a theory of finite sets with cardinality into $$\{ log\} $$ . The proposed solver is proved to be a decision procedure for its formulas. Besides, the new CLP instance is implemented as part of the $$\{ log\} $$ tool. In turn, the implementation uses Howe and King’s Prolog SAT solver and Prolog’s CLP(Q) library, as an integer linear programming solver. The empirical evaluation of this implementation based on +250 real verification conditions shows that it can be useful in practice. Under consideration in Theory and Practice of Logic Programming (TPLP)

CCMV Portfolio Optimization with Stocks and Options using Forecasted Data

Although the future of a financial market is ambiguous and mysterious, historical data play a key role to forecast the future of the market. Along with all the advantages of these data, they may result to some errors and consequently, some losses. In this paper, we consider the cardinality constraints mean-variance (CCMV) portfolio optimization model in the presence of short selling, risk-neutral interest rate and transaction costs. We insure the investment using options against unfavorable outcomes. The Geometric Brownian Motion model is utilized to forecast the stocks prices. Also, to improve the results, we calibrate its parameters using historical data by the maximum likelihood estimation method. We perform numerical experiments using historical and forecasted data on the S&P 500 index, to assess the efficiency of the GBM model in forecasting stocks prices. Also, to examine the effect of options in the portfolio, we compare the portfolio with stocks only versus the portfolio with stocks and options using historical and forecasted data in terms of returns and Sharpe ratios.

Joint Product Framing (Display, Ranking, Pricing) and Order Fulfillment Under the Multinomial Logit Model for E-Commerce Retailers

Problem definition: We study a joint product framing and order fulfillment problem with both inventory and cardinality constraints faced by an e-commerce retailer. There is a finite selling horizon and no replenishment opportunity. In each period, the retailer needs to decide how to “frame” (i.e., display, rank, price) each product on his or her website as well as how to fulfill a new demand. Academic/practical relevance: E-commerce retail is known to suffer from thin profit margins. Using the data from a major U.S. retailer, we show that jointly planning product framing and order fulfillment can have a significant impact on online retailers’ profitability. This is a technically challenging problem as it involves both inventory and cardinality constraints. In this paper, we make progress toward resolving this challenge. Methodology: We use techniques such as randomized algorithms and graph-based algorithms to provide a tractable solution heuristic that we analyze through asymptotic analysis. Results: Our proposed randomized heuristic policy is based on the solution of a deterministic approximation to the stochastic control problem. The key challenge is in constructing a randomization scheme that is easy to implement and that guarantees the resulting policy is asymptotically optimal. We propose a novel two-step randomization scheme based on the idea of matrix decomposition and a rescaling argument. Managerial implications: Our numerical tests show that the proposed policy is very close to optimal, can be applied to large-scale problems in practice, and highlights the value of jointly optimizing product framing and order fulfillment decisions. When inventory across the network is imbalanced, the widespread practice of planning product framing without considering its impact on fulfillment can result in high shipping costs, regardless of the fulfillment policy used. Our proposed policy significantly reduces shipping costs by using product framing to manage demand so that it occurs close to the location of the inventory.

Bin packing with lexicographic objectives for loading weight- and volume-constrained trucks in a direct-shipping system

We consider a packing problem that arises in a direct-shipping system in the food and beverage industry: Trucks are the containers, and products to be distributed are the items. The packing is constrained by two independent quantities, weight (e.g., measured in kg) and volume (number of pallets). Additionally, the products are grouped into the three categories: standard, cooled, and frozen (the latter two require refrigerated trucks). Products of different categories can be transported in one truck using separated zones, but the cost of a truck depends on the transported product categories. Moreover, splitting orders of a product should be avoided so that (un-)loading is simplified. As a result, we seek for a feasible packing optimizing the following objective functions in a strictly lexicographic sense: minimize the (1) total number of trucks; (2) number of refrigerated trucks; (3) number of refrigerated trucks which contain frozen products; (4) number of refrigerated trucks which also transport standard products; (5) and minimize splitting. This is a real-world application of a bin-packing problem with cardinality constraints a.k.a. the two-dimensional vector packing problem with additional constraints. We provide a heuristic and an exact solution approach. The heuristic meta-scheme considers the multi-compartment and item fragmentation features of the problem and applies various problem-specific heuristics. The exact solution algorithm covering all five stages is based on branch-and-price using stabilization techniques exploiting dual-optimal inequalities. Computational results on real-world and difficult self-generated instances prove the applicability of our approach.

Exploring the trade-off between liquidity, risk and return under sectoral diversification across distinct economic settings

PurposeThis paper aims to explore the trade-off between liquidity, risk and return under sectoral diversification across distinct economic settings and investment strategies.Design/methodology/approachA novel multi-objective portfolio model is proposed to assess investment decisions under sectoral diversification, where the objective functions and constraints are interval-valued. The objective functions used are risk minimization (through the semi-absolute deviation measure of risk), maximization of liquidity (using turnover as a proxy) and the maximization of logarithmic return. Besides coherence constraints (imposing that the sum of the percentages of investment assigned to each stock should be equal to 100%), constraints regarding the maximum proportion of capital that can be invested (ensuring a minimum level of diversification) and cardinality constraints (to account for transaction costs) are also imposed.FindingsBesides the trade-off between return and risk, the study findings highlight a trade-off between liquidity and return and a positive relationship between risk and liquidity. Under an economic crisis scenario, the trade-off between return and liquidity is reduced. With the economic recovery, the levels of risk increase when contrasted with the setting of the economic crisis. The highest liquidity levels are reached with the economic boom, whereas the highest returns are obtained with the economic recession.Originality/valueThis paper suggests a new modeling approach for assessing the trade-offs between liquidity, risk and return under different scenarios and investment strategies. A new interactive procedure inspired on the reference point approach is also proposed to obtain possibly efficient portfolios according to the investor's preferences. Regarding previous approaches suggested in the literature, this new procedure allows obtaining both supported and unsupported efficient solutions when cardinality constraints are included.

Selecting a Cost-Effective Seed for Maximizing the Social Influence Under Real-life Constraints

The Influence Maximization (IM) problem aims at maximizing the diffusion of information or adoption of products among users in a social network by identifying and activating a set of initial users. In real-life applications, it is not unrealistic to have a higher activation cost for a user with higher influence. However, the existing works on IM consider finding the most influential users as the seed set, ignoring either the activation costs of such individual nodes and the total budget or the size of the seed set, which may not be always an optimal solution, particularly from the financial and managerial perspectives, respectively. To address these issues, we propose a more realistic and generalized formulation termed as multi-constraint influence maximization (MCIM) aiming to achieve a cost-effective solution under both budgetary and cardinality constraints. Unlike the existing IM formulations, the proposed MCIM is no longer a monotone but a submodular function. As it is also proved to be an NP-hard problem, we propose a simple additive weighting (SAW) assisted differential evolution (DE) algorithm for solving the large-size real-world problems. Experimental results on four real-world datasets show that the proposed formulation and algorithm are effective in finding a cost-effective seed set.