A Model for Integrated Inventory and Assortment Planning

Integrating inventory and assortment planning decisions is a challenging task that requires comparing the value of demand expansion through broader choice for consumers with the value of higher in-stock availability. We develop a stockout-based substitution model for trading off these values in a setting with inventory replenishment, a feature missing in the literature. Using the closed form solution for the single-product case, we develop an accurate approximation for the multiproduct case. This approximated formulation allows us to optimize inventory decisions by solving a fractional integer program with a fixed point equation constraint. When products have equal margins, we solve the integer program exactly by bisection over a one-dimensional parameter. In contrast, when products have different margins, we propose a fractional relaxation that we can also solve by bisection and that results in near-optimal solutions. Overall, our approach provides solutions within 0.1% of the optimal policy and finds the optimal solution in 80% of the random instances we generate. This paper was accepted by David Simchi-Levi, optimization.

Algorithms for Smooth, Safe and Quick Routing on Sensor-Equipped Grid Networks

Automation plays an important role in modern transportation and handling systems, e.g., to control the routes of aircraft and ground service equipment in airport aprons, automated guided vehicles in port terminals or in public transportation, handling robots in automated factories, drones in warehouse picking operations, etc. Information technology provides hardware and software (e.g., collision detection sensors, routing and collision avoidance logic) that contribute to safe and efficient operations, with relevant social benefits in terms of improved system performance and reduced accident rates. In this context, we address the design of efficient collision-free routes in a minimum-size routing network. We consider a grid and a set of vehicles, each moving from the bottom of the origin column to the top of the destination column. Smooth nonstop paths are required, without collisions nor deviations from shortest paths, and we investigate the minimum number of horizontal lanes allowing for such routing. The problem is known as fleet quickest routing problem on grids. We propose a mathematical formulation solved, for small instances, through standard solvers. For larger instances, we devise heuristics that, based on known combinatorial properties, define priorities, and design collision-free routes. Experiments on random instances show that our algorithms are able to quickly provide good quality solutions.

A Novel Heuristic to Minimize the Bottlenecks Presence in Batch Generation. Case of Study.

This paper presents a new heuristic method capable of minimizing the presence of bottlenecks generated when production batches have a distinct makespan. The proposed heuristic groups the jobs into items, where the one with the longest processing time in the batch determines the makespan. To test the heuristic, information was collected from a real paint process with two stations: one with a single cabin and the other with two parallel cabins. The capacity of processing jobs is limited by the cabin dimensions where jobs have different sizes and processing times. A makespan comparison between the heuristic proposed versus the First in First out (FIFO) dispatching rule that the case of study uses. Additionally, ten random instances based on data taken from the real process were created with the purpose to compare the new heuristic method versus Genetic Algorithm (GA) and Simulated Annealing (SA). The result of the comparison to FIFO, GA and SA showed that the proposed heuristic minimizes the bottleneck in a and creating batches almost with the same makespan. Results indicated a bottleneck time reduction of 96% when new heuristic method were compared to FIFO rule, while compared to Generic Algorithm and Simulated Annealing the bottleneck reduction were around 89% in both cases.

Chapter 6. Incomplete Algorithms

Research on incomplete algorithms for satisfiability testing lead to some of the first scalable SAT solvers in the early 1990’s. Unlike systematic solvers often based on an exhaustive branching and backtracking search, incomplete methods are generally based on stochastic local search. On problems from a variety of domains, such incomplete methods for SAT can significantly outperform DPLL-based methods. While the early greedy algorithms already showed promise, especially on random instances, the introduction of randomization and so-called uphill moves during the search significantly extended the reach of incomplete algorithms for SAT. This chapter discusses such algorithms, along with a few key techniques that helped boost their performance such as focusing on variables appearing in currently unsatisfied clauses, devising methods to efficiently pull the search out of local minima through clause re-weighting, and adaptive noise mechanisms. The chapter also briefly discusses a formal foundation for some of the techniques based on the discrete Lagrangian method.

Solving the one-warehouse N-retailers problem with stochastic demand: An inter-ratio policies approach

In this paper, we consider a two-echelon supply chain in which one warehouse provides a single product to N retailers, using integer-ratio policies. Deterministic version of the problem has been widely studied. However, this assumption can lead to inaccurate and ineffective decisions. In this research, we tackle the stochastic version of two-echelon inventory system by designing an extension of a well-known heuristic. This research considers customer demands as following a normal density function. A set of 240 random instances was generated and used in evaluating both the deterministic and stochastic solution approaches. Due to the nature of the objective function, evaluation was carried out via Monte Carlo simulation. For variable demand settings, computational experiments shows that: i) the use of average demand to define the inventory policy implies an underestimation of the total cost and ii) the newly proposed method offers cost savings.

Two-Layer Path Planning for Multi-Area Coverage by a Cooperated Ground Vehicle and Drone System

A novel two-layer path planning method for a cooperated ground vehicle (GV) and drone system is investigated, where the GV acts as the mobile platform of the drone and is used to conduct multiple area covering tasks collaboratively. The GV takes the drone to visit a set of discrete areas, while the drone takes off from the GV at potential nodes around each area and scans each area for collecting information. The drone can be recharged in the GV during the time when it travels between different areas. The objective is to optimize the drone’s scanning path for all areas’ coverage and the GV’s travel path for visiting all areas. A 0-1 integer programming model is developed to formulate the problem. A two-stage heuristic based on cost saving strategy is designed to quickly construct a feasible solution, then the Adaptive Large Neighborhood Search (ALNS) algorithm is employed to improve the quality of the solution. A simulation experiment based on the parks in Changsha, China, is presented to illustrate the application of the method. Random instances are designed to further test the performance of the proposed algorithm.

Two-Layer Path Planning for Multi-Area Coverage by a Cooperated Ground Vehicle and Drone System

A novel two-layer path planning method for a cooperated ground vehicle (GV) and drone system is investigated, where the GV acts as the mobile platform of the drone and is used to conduct multiple area covering tasks collaboratively. The GV takes the drone to visit a set of discrete areas, while the drone takes off from the GV at potential nodes around each area and scans each area for collecting information. The drone can be recharged in the GV during the time when it travels between different areas. The objective is to optimize the drone’s scanning path for all areas’ coverage and the GV’s travel path for visiting all areas. A 0-1 integer programming model is developed to formulate the problem. A two-stage heuristic based on cost saving strategy is designed to quickly construct a feasible solution, then the Adaptive Large Neighborhood Search (ALNS) algorithm is employed to improve the quality of the solution. A simulation experiment based on the parks in Changsha, China, is presented to illustrate the application of the method. Random instances are designed to further test the performance of the proposed algorithm.

Improving WalkSAT for Random 3-SAT Problems

Stochastic local search (SLS) algorithms are well known for their ability to efficiently find models of random instances of the Boolean satisfiability (SAT) problems. One of the most famous SLS algorithms for SAT is called WalkSAT, which has wide influence and performs well on most of random 3-SAT instances. However, the performance of WalkSAT lags far behind on random 3-SAT instances equal to or greater than the phase transition ratio. Motivated by this limitation, in the present work, firstly an allocation strategy is introduced and utilized in WalkSAT to determine the initial assignment, leading to a new algorithm called WalkSATvav. The experimental results show that WalkSATvav significantly outperforms the state-of-the-art SLS solvers on random 3-SAT instances at the phase transition for SAT Competition 2017. However, WalkSATvav cannot rival its competitors on random 3-SAT instances greater than the phase transition ratio. Accordingly, WalkSATvav is further improved for such instances by utilizing a combination of an improved genetic algorithm and an improved ant colony algorithm, which complement each other in guiding the search direction. The resulting algorithm, called WalkSATga, is far better than WalkSAT and significantly outperforms some previous known SLS solvers on random 3-SAT instances greater than the phase transition ratio from SAT Competition 2017. Finally, a new SAT solver called WalkSATlg, which combines WalkSATvav and WalkSATga, is proposed, which is competitive with the winner of random satisfiable category of SAT competition 2017 on random 3-SAT problem.

A Sustainable Multimodal Transport System: The Two-Echelon Location-Routing Problem with Consolidation in the Euro–China Expressway

Sustainable development of transport systems is a common topic of concern and effort in multiple countries, in which reducing carbon emissions is one of the core goals. Multimodal transport is an effective way to achieve carbon emission reduction and to efficiently utilize transport resources. The intercontinental transport system, represented by the Euro–China Expressway, is a prominent exploration that has recently received attention, which promotes the sustainable development of transport between countries and carbon emission reduction. In the intercontinental multimodal transport system, the reasonable connection of roads and railways, especially the optimization of consolidation, is an important link which affects the system's carbon emissions. This paper focuses on the consolidation of sustainable multimodal transport and summarizes the multimodal transport two-echelon location-routing problem with consolidation (MT-2E-LRP-C). We aim to solve multimodal consolidation optimization problem, especially locations of multimodal station, by routing of highway and railway. We propose a two-layer mixed integer linear problem (MILP) model, which highlights the consolidation of roads and railways, focuses on road and rail transport connections, and optimizes road routes and railway schemes. To validate the MT-2E-LRP-C model, we design a series of random instances for different quantities of nodes. In order to solve large-scale instances and realistic transport problems, we propose a hybrid differential evolution algorithm, which decomposes the problem into a railway layer and a highway layer for heuristic algorithm solving. Furthermore, the MILP model and algorithm are tested by small-scale random instances, and the hybrid differential evolution algorithm is solved for the large-scale random instances. Finally, we solve the realist instance from the Euro–China Expressway to develop instructive conclusions.