Ahmed Ghoniem

The Stop-And-Drop Problem in Nonprofit Food Distribution Networks

In this paper, we introduce the stop-and-drop problem (SDRP), a new variant of location-routing problems, that is mostly applicable to nonprofit food distribution networks. In these distribution problems, there is a central warehouse that contains food items to be delivered to agencies serving the people in need. The food is delivered by trucks to multiple sites in the service area and partner agencies travel to these sites to pick up their food. The tactical decision problem in this setting involves how to jointly select a set of delivery sites, assign agencies to these sites, and schedule routes for the delivery vehicles. The problem is modeled as an integrated mixed-integer program for which we delineate a two-phase sequential solution approach. We also propose two Benders decomposition-based solution procedures, namely a linear programming relaxation based Benders implementation and a logic-based Benders decomposition heuristic. We show through a set of realistic problem instances that given a fixed time limit, these decomposition based methods perform better than both the standard branch-and-bound solution and the two-phase approach. The general problem and the realistic instances used in the computational study are motivated by interactions with food banks in southeastern United States.

Complementary column generation and bounding approaches for set partitioning formulations

We present a complementary column generation feature that produces tight upper bounds, thereby enhancing heuristic and exact column generation approaches for (minimization) set partitioning formulations that possess dense column structures. We also introduce a duality-based lower bound that prompts a useful termination criterion, which can be utilized to mitigate the tailing-off effect induced by column generation approaches. Computations are presented for the one-dimensional bin packing problem and a joint vehicle assembly-routing problem.

Enhanced Models for a Mixed Arrival-Departure Aircraft Sequencing Problem

This paper addresses the static aircraft sequencing problem over a mixed-mode single runway (or closely interacting parallel runways), which commonly constitutes a critical bottleneck at airports. In contrast with disjunctive formulations, our modeling approach takes advantage of the underlying structure of an asymmetric traveling salesman problem with time-windows. This enables the development of efficient preprocessing and probing procedures, and motivates the derivation of several classes of valid inequalities along with partial convex hull representations to enhance problem solvability via tighter reformulations. The lifted model is further embedded within the framework of two proposed heuristics that are compared against the traditional first-come first-served (FCFS) heuristic with landing priority: an optimized FCFS policy (OFCFS) and a threshold-based suboptimized heuristic (TSH) with an a priori fixing of the relative order of aircraft that are sufficiently time-separated. Computational results using real data based on Doha International Airport (DOH) as well as simulated instances are reported to demonstrate the efficacy of the proposed exact and heuristic solution methods. In particular, for the DOH instances, heuristics OFCFS and TSH achieved an attractive runway utilization (4.3% and 5.0% makespan reduction, respectively, over the base FCFS policy with landing priority), while exhibiting limited aircraft position deviations (0.45 and 0.49 deviations on average, respectively, from the base FCFS positions with landing priority, with similar results being obtained for the simulated instances). The superiority of the proposed optimization models over previous disjunctive formulations is also demonstrated for challenging problem instances, resulting in over 50% CPU savings for the larger instances in our test-bed.

Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints

This article introduces the concept of defeating symmetry in combinatorial optimization via objective perturbations based on, and combined with, symmetry-defeating constraints. Under this novel reformulation, the original objective function is suitably perturbed using a weighted sum of expressions derived from hierarchical symmetry-defeating constraints in a manner that preserves optimality and judiciously guides and curtails the branch-and-bound enumeration process. Computational results are presented for a noise dosage problem, a doubles tennis scheduling problem, and a wagon load-balancing problem to demonstrate the efficacy of using this strategy in concert with traditional hierarchical symmetry-defeating constraints. The proposed methodology is shown to significantly outperform the use of hierarchical constraints or objective perturbations in isolation, as well as the automatic symmetry-defeating feature that is enabled by CPLEX, version 11.2.

An accelerated branch-and-price algorithm for multiple-runway aircraft sequencing problems

This paper presents an effective branch-and-price (B&P) algorithm for multiple-runway aircraft sequencing problems. This approach improves the tractability of the problem by several orders of magnitude when compared with solving a classical 0–1 mixed-integer formulation over a set of computationally challenging instances. Central to the computational efficacy of the B&P algorithm is solving the column generation subproblem as an elementary shortest path problem with aircraft time-windows and non-triangular separation times using an enhanced dynamic programming procedure. We underscore in our computational study the algorithmic features that contribute, in our experience, to accelerating the proposed dynamic programming procedure and, hence, the overall B&P algorithm.

Optimizing assortment and pricing of multiple retail categories with cross-selling

This paper investigates the joint optimization of assortment and pricing decisions for complementary retail categories. Each category comprises substitutable items (e.g., different coffee brands) and the categories are related by cross-selling considerations that are empirically observed in marketing studies to be asymmetric in nature. That is, a subset of customers who purchase a product from a primary category (e.g., coffee) can opt to also buy from one or several complementary categories (e.g., sugar and/or coffee creamer). We propose a mixed-integer nonlinear program that maximizes the retailer’s profit by jointly optimizing assortment and pricing decisions for multiple categories under a classical deterministic maximum-surplus consumer choice model. A linear mixed-integer reformulation is developed which effectively enables an exact solution to relatively large problem instances using commercial optimization solvers. This is encouraging, because simpler product line optimization problems in the literature have posed significant computational challenges over the last decades and have been mostly tackled via heuristics. Moreover, our computational study indicates that overlooking cross-selling between retail categories can result in substantial profit losses, suboptimal (narrower) assortments, and inadequate prices.

Promoting impulse buying by allocating retail shelf space to grouped product categories

This paper addresses a problem where a retailer seeks to optimize store-wide shelf-space allocation in order to maximize the visibility of products to consumers and consequently stimulate impulse buying. We consider a setting where the retailer, because of product affinities or the retailer’s historical practice, has pre-clustered product categories into groups each of which must be assigned to a shelf. On the basis of its location in the store layout, each shelf is partitioned into contiguous shelf segments having different anticipated customer traffic densities. The retailer seeks to assign each group of product categories to a shelf, to determine the relative location of product categories within their assigned shelf, and to specify their allocated total shelf space within given lower/upper bounds. We propose a 0–1 integer programme that takes into account expected customer traffic densities within the store, groups of product categories, their relative profitability, and the desirability to keep certain product groups in the same aisle, with the objective of maximizing the impulse buying profit. The proposed model is grounded in a preprocessing scheme that explores feasible assignments of subsets of product groups to available aisles by iteratively solving an -hard subproblem and is numerically observed to greatly outperform an alternative mixed-integer programming formulation. We demonstrate the usefulness of and the enhanced tractability achieved by the proposed approach using a case study motivated by a grocery store in New England and a variety of simulated problem instances.

Models and algorithms for the scheduling of a doubles tennis training tournament

We address a doubles tennis scheduling problem in the context of a training tournament, and develop a 0–1 mixed-integer programming model that attempts to balance the partnership and the opponentship pairings among the players. We propose effective symmetry-defeating strategies that impose certain decision hierarchies within the model, which serve to significantly enhance algorithmic performance via their pruning effect. We also discuss the concept of symmetry compatible formulations, and highlight the importance of crafting formulations in discrete optimization in a fashion that enhances the interplay between the original model structure, branch-and-bound algorithms (as implemented in commercial packages such as CPLEX), and the structure of specific symmetry-defeating hierarchical constraints. Finally, various specialized heuristics are devised and are computationally evaluated along with the exact solution schemes using a set of realistic practical test problems.

A Specialized Column Generation Approach for a Vehicle Routing Problem with Demand Allocation

Motivated by logistical operations for a food bank, this paper addresses a class of vehicle routing problems with demand allocation considerations over a network of partner agencies locations and candidate delivery sites. Any delivery tour starts at a central depot operated by the food bank and selected delivery sites are sequentially visited in order to supply goods to a set of partner agencies who travel from their respective locations to their assigned delivery sites. The problem is modelled as a mixed-integer programme with the objective of minimizing a weighted average of the distances travelled by delivery vehicles and partner agencies, and is tackled via two heuristics. First, a relax-and-fix heuristic is presented for the proposed model and is computationally enhanced using two symmetry-defeating strategies. Second, the problem is reformulated as a set partitioning model with side packing constraints that prompts a specialized column generation approach. Computational experience is provided using realistic data instances to demonstrate the usefulness of the proposed heuristics and the importance of integrated solution techniques for this class of problems.

Set partitioning and packing versus assignment formulations for subassembly matching problems

This paper addresses alternative formulations and model enhancements for two combinatorial optimization problems that arise in subassembly matching problems. The first problem seeks to minimize the total deviation in certain quality characteristics for the resulting final products from a vector of target values, whereas the second aims at maximizing the throughput under specified tolerance restrictions. We propose set partitioning and packing models in concert with a specialized column generation (CG) procedure that significantly outperform alternative assignment-based formulations presented in the literature, even when the latter are enhanced via tailored symmetry-defeating strategies. In particular, we emphasize the critical importance of incorporating a complementary CG feature to consistently produce near-optimal solutions to the proposed set partitioning and packing models. Extensive computational results are presented to demonstrate the relative effectiveness of the different proposed modelling and algorithmic strategies.