Bundling retail products: Models and analysis

We consider the impact of bundling products on retail merchandising. We consider two broad classes of retail products: basic and fashion. For these product classes, we develop models to calculate the optimal bundle prices, order quantities, and profits under bundling. We use this analysis to establish conditions and insights under which bundling is profitable. Our analysis confirms that bundling profitability depends on individual product demands, bundling costs, and the nature of the relationship between the demands of the products to be bundled. We also provide detailed numerical examples.     

The discrete facility location problem with balanced allocation of customers

We consider a discrete facility location problem where the difference between the maximum and minimum number of customers allocated to every plant has to be balanced. Two different Integer Programming formulations are built, and several families of valid inequalities for these formulations are developed. Preprocessing techniques which allow to reduce the size of the largest formulation, based on the upper bound obtained by means of an ad hoc heuristic solution, are also incorporated. Since the number of available valid inequalities for this formulation is exponential, a branch-and-cut algorithm is designed where the most violated inequalities are separated at every node of the branching tree. Both formulations, with and without the improvements, are tested in a computational framework in order to discriminate the most promising solution methods. Difficult instances with up to 50 potential plants and 100 customers, and largest easy instances, can be solved in one CPU hour.     

The capacitated multiple allocation hub location problem: Formulations and algorithms

In this paper we consider and present formulations and solution approaches for the capacitated multiple allocation hub location problem. We present a new mixed integer linear programming formulation for the problem. We also construct an efficient heuristic algorithm, using shortest paths. We incorporate the upper bound obtained from this heuristic in a linear-programming-based branch-and-bound solution procedure. We present the results of extensive computational experience with both the heuristic and the exact methods.     

The deterministic product location problem under a pick-by-order policy

This paper treats the product location problem in warehouses, i.e., stock keeping units (SKUs) are to be assigned to storage positions in order to minimize the resulting picking effort when retrieving SKUs in a pick-by-order environment. We restrict our view on warehouses having a single cross aisle and show that already very simple layouts consisting of only a single rack lead to NP-hard optimization problems. In addition to a complexity analysis for different layouts, elementary solution procedures are introduced and tested. Finally, we investigate the robustness of our deterministic problem when facing erroneous input data.     

Genetic algorithm with variable neighborhood search for the optimal allocation of goods in shop shelves

Shelves on which products are being displayed are one of the most important resources in retail environment. The decision of shelf-space allocation and management is therefore a critical issue in retail operation management. In this paper a hybrid algorithm that combines a genetic algorithm with a variable neighborhood search is proposed to address the shop shelf allocation problem. Results obtained from an extensive experimental phase show the suitability of the proposed algorithm in addressing the problem at hand.     

A new index of creditworthiness for retail credit products

This paper introduces a novel family of indexes to describe borrowers’ creditworthiness in retail credit products, both for fixed term loans and for open-ended products such as credit cards. Each index is the ratio at a given time of the net present value of actually received cashflows to the contractual ones. Some interpretations of the indexes are given and it is also described how to link them to the profitability of the credit financial operation. For open-ended products, a competing risks survival analysis methodology is proposed to estimate the cashflow returns and illustrated with a simulation.     

Capacitated location allocation problem with stochastic location and fuzzy demand: A hybrid algorithm

In this article, a capacitated location allocation problem is considered in which the demands and the locations of the customers are uncertain. The demands are assumed fuzzy, the locations follow a normal probability distribution, and the distances between the locations and the customers are taken Euclidean and squared Euclidean. The fuzzy expected cost programming, the fuzzy β-cost minimization model, and the credibility maximization model are three types of fuzzy programming that are developed to model the problem. Moreover, two closed-form Euclidean and squared Euclidean expressions are used to evaluate the expected distance between customers and facilities. In order to solve the problem at hand, a hybrid intelligent algorithm is applied in which the simplex algorithm, fuzzy simulation, and a modified genetic algorithm are integrated. Finally, in order to illustrate the efficiency of the proposed hybrid algorithm, some numerical examples are presented.     

The value of competitive information in forecasting FMCG retail product sales and the variable selection problem

Sales forecasting at the UPC level is important for retailers to manage inventory. In this paper, we propose more effective methods to forecast retail UPC sales by incorporating competitive information including prices and promotions. The impact of these competitive marketing activities on the sales of the focal product has been extensively documented. However, competitive information has been surprisingly overlooked by previous studies in forecasting UPC sales, probably because of the problem of too many competitive explanatory variables. That is, each FMCG product category typically contains a large number of UPCs and is consequently associated with a large number of competitive explanatory variables. Under such a circumstance, time series models can easily become over-fitted and thus generate poor forecasting results.     

The uncapacitated facility location problem with demand-dependent setup and service costs and customer-choice allocation

We consider a generalization of the uncapacitated facility location problem, where the setup cost for a facility and the price charged for service may depend on the number of customers patronizing the facility. Customers are represented by the nodes of the transportation network, and facilities can be located only at nodes; a customer selects a facility to patronize so as to minimize his (her) expenses (price for service + the part of transportation costs paid by the customer). We assume that transportation costs are paid partially by the service company and partially by customers. The objective is to choose locations for facilities and balanced prices so as to either minimize the expenses of the service company (the sum of the total setup cost and the total part of transportation costs paid by the company), or to maximize the total profit. A polynomial-time dynamic programming algorithm for the problem on a tree network is developed.     

Product allocation to different types of distribution center in retail logistics networks

We consider the problem of assigning stockkeeping units to distribution centers (DCs) belonging to different DC types of a retail network, e.g., central, regional, and local DCs. The problem is motivated by the real situation of a retail company and solved by an MIP solution approach. The MIP model reflects the interdependencies between inbound transportation, outbound transportation and instore logistics as well as capital tied up in inventories and differences in picking costs between the warehouses. A novel solution approach is developed and applied to a real-life case of a leading European grocery retail chain. The application of the new approach results in cost savings of 6% of total operational costs compared to the present assignment. These savings amount to several million euros per year. In-depth analyses of the results and sensitivity analyses provide insights into the solution structure and the major related issues.     

Minmax regret location–allocation problem on a network under uncertainty

We consider a robust location–allocation problem with uncertainty in demand coefficients. Specifically, for each demand point, only an interval estimate of its demand is known and we consider the problem of determining where to locate a new service when a given fraction of these demand points must be served by the utility. The optimal solution of this problem is determined by the “minimax regret” location, i.e., the point that minimizes the worst-case loss in the objective function that may occur because a decision is made without knowing which state of nature will take place. For the case where the demand points are vertices of a network we show that the robust location–allocation problem can be solved in O(min{p, n − p}n³m) time, where n is the number of demand points, p (p < n) is the fixed number of demand points that must be served by the new service and m is the number of edges of the network.     

A piecewise linearization for retail shelf space allocation problem and a local search heuristic

Retail shelf space allocation problem is well known in literature. In this paper, we make three contributions to retail shelf space allocation problem considering space elasticity (SSAPSE). First, we reformulate an existing nonlinear model for SSAPSE to an integer programming (IP) model using piecewise linearization. Second, we show that the linear programming relaxation of the proposed IP model produces tight upper bound. Third, we develop a heuristic that consistently produces near optimal solutions for randomly generated instances of problems with size (products, shelves) varying from (25, 5) to (200, 50) within a minute of CPU time.     

Completeness of location families,translated moments,and uniqueness of charges

Summary A sufficient condition for statistical completeness of location families generated by a probability density in euclidean space is given. As an application, completeness of families generated by a symmetric stable law is proved. Our criterion, complementing a classical result of Wiener and recent work of Isenbeck and Rüschendorf, is in terms of regularity of the generating density and zerofreeness of its characteristic function. Its proof rests on a local version of the convolution theorem for Fourier transforms of tempered distributions. A more general version of the criterion is applicable to apparently different problems, as is illustrated by giving a simultaneous proof of a theorem on translated moments by P. Hall and a uniqueness result of M. Riesz in potential theory.     

A GRASP for simultaneously assigning and sequencing product families on flexible assembly lines

This paper introduces a new model and solution methodology for a real-world production scheduling problem arising in the electronics industry. The production environment is a high volume, just-in-time, make-to-order facility with volatile demand over many product families that are assembled on flexible lines. A distinguishing characteristic of the problem is the presence of non-traditional sequence-dependant setup costs, which complicate our ability to find high-quality solutions. The scheduling problem arose when product variety exceeded the mix that the existing lines could accommodate. A nonlinear integer programming formulation is presented for the problem of minimizing setup costs, and a greedy randomized adaptive search procedure (GRASP) is developed to find solutions. To select the GRASP parameter values, an efficient, space-filling experimental design method is used based on nearly orthogonal Latin hypercubes. The proposed methodology is tested on actual factory data and compared to a prior heuristic presented in the literature; our heuristic provides a cost savings in 7 out of the 10 cases examined, and an average improvement of 17.39 % which is shown to be highly statistically significant. This improvement is due in part to the introduction of a pre-processing step to determine preferential and non-preferential line assignment information.     

Improving product location and order picking activities in a distribution centre

This article examines the effect of different product location strategies on the distance that order pickers must cover to do their job. This distance is an important cost component in warehousing activities. Our empirical study is based on a real industrial setting, in which the products are located on both sides of a conveyor belt. We show that choosing the right product location strategy allows the current picking distance to be reduced more than 10%. We also propose a post-optimization procedure that can further reduce picking distances—up to 20% of the current distances. Through a study of the routing strategy used to dispatch pickers, we demonstrate that solving a simple travelling salesman problem can further reduce distances up to 13%, compared with the distances incurred using a predetermined route. We show that reductions of up to 27% compared to current picking distances are possible if our product location and routing methods are combined.     

Lattice properties of subspace families in an inner product space

Let be a separable inner product space over the field of real numbers. Let (resp., denote the orthomodular poset of all splitting subspaces (resp., complete-cocomplete subspaces) of . We ask whether (resp., can be a lattice without being complete (i.e. without being Hilbert). This question is relevant to the recent study of the algebraic properties of splitting subspaces and to the search for ``nonstandard' orthomodular spaces as motivated by quantum theories. We first exhibit such a space that is not a lattice and is a (modular) lattice. We then go on showing that the orthomodular poset may not be a lattice even if . Finally, we construct a noncomplete space such that with being a (modular) lattice. (Thus, the lattice properties of (resp. do not seem to have an explicit relation to the completeness of though the Ammemia-Araki theorem may suggest the opposite.) As a by-product of our construction we find that there is a noncomplete such that all states on are restrictions of the states on for being the completion of (this provides a solution to a recently formulated problem).

     

Transversals of families in complete lattices,and torsion in product modules

Suppose L is a complete lattice containing no copy of the power-set 2 and no uncountable well-ordered chains. It is shown that for any family of nonempty subsets , one can choose elements p _i X _i so that _A p _i majorizes all elements of all but finitely many of the X _i . Ring-theoretic consequences are deduced: for instance, the direct product of a family of torsion modules over a commutative Noetherian integral domain R is torsion if and only if some element of R annihilates all but finitely many of the modules.     

Maltsev families of varieties closed under join or Maltsev product

Maltsev families of varieties which are closed under join or Maltsev product are investigated. New Maltsev conditions for congruence semi-distributivity are given.