A column generation-based heuristic algorithm for an inventory routing problem with perishable goods

An inventory routing problem is a variation of the vehicle routing problem in which inventory and routing decisions are determined simultaneously over a given time horizon. The objective is to minimize the sum of transportation and inventory costs. In this paper, we study a specific inventory routing problem in which goods are perishable (PIRP). We develop a mathematical model for PIRP and exploit its structure to develop a column generation-based solution approach. Cutting planes are added to improve the formulation. We present computational experiments to demonstrate that our methodology is effective, and that the integration of routing and inventory can yield significant cost savings.     

An integrated model for warehouse and inventory planning

The purpose of this article is to evaluate the value of integrating tactical warehouse and inventory decisions. Therefore, a global warehouse and inventory model is presented and solved. In order to solve this mathematical model, two solution methodologies are developed which offer different level of integration of warehouse and inventory decisions. Computational tests are performed on a real world database using multiple scenarios differing by the warehouse capacity limits and the warehouse and inventory costs. Our observation is that the total cost of the inventory and warehouse systems can be reduced drastically by taking into account the warehouse capacity restrictions in the inventory planning decisions, in an aggregate way. Moreover additional inventory and warehouse savings can be achieved by using more sophisticated integration methods for inventory and warehouse decisions.     

Predictive control of periodic-review production inventory systems with deteriorating items

In this paper a predictive control strategy is applied to a periodic-review dynamic inventory system with deteriorating items. Given the current inventory level, we determine the optimal production rates to be implemented at the beginning of each of the following periods over the control horizon. The effectiveness of this approach is the use of future information of the inventory target level and the desired production rate, which are available, along the fixed horizon. The deterioration coefficient may be known or unknown and both cases are considered. In the case where it is unknown, the self-tuning predictive control is applied. The proposed control algorithms are illustrated by simulations.     

A stochastic multi-period industrial hazardous waste location-routing problem: Integrating NSGA-II and Monte Carlo simulation

The present study extends a multi-objective mathematical model in the context of industrial hazardous waste management, which covers the integrated decisions of three levels with locating, vehicle routing, and inventory control. Analyzing these decisions simultaneously not only may lead to the most effective structure in the waste management network, but also may reduce the potential risk of managing the hazardous waste. Furthermore, because of the inherent complexity of the waste management system, uncertainty is inevitable and should be acknowledged to guarantee reliability in the decision-making process. From this perspective, the proposed model is novel in the following three aspects: (1) shifting from a deterministic to stochastic environment; (2) considering a multi-period planning horizon; and (3) incorporating the inventory decisions into the problem. The problem is formulated as a multi-objective stochastic Mixed-Integer Nonlinear Programming (MINLP) model, which can be easily converted into a MILP one. In terms of methodological contribution, a new simheuristic approach that is an integration of Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) and Monte Carlo simulation is developed to overcome the stochastic combinatorial optimization problem of this study. Our findings verify the efficiency of the proposed approach as it is able to find a high-quality solution within a relatively reasonable computational time.     

Integrating operations and marketing decisions using delayed differentiation of products and guaranteed delivery time under stochastic demand

In this research, we integrate the issues related to operations and marketing strategy of firms characterized by large product variety, short lead times, and demand variability in an assemble-to-order environment. The operations decisions are the inventory level of components and semi-finished goods, and configuration of semi-finished goods. The marketing decisions are the products price and a lead time guarantee which is uniform for all products. We develop an integrated mathematical model that captures trade-offs related to inventory of semi-finished goods, inventory of components, outsourcing costs, and customer demand based on guaranteed lead time and price.The mathematical model is a two-stage, stochastic, integer, and non-linear programming problem. In the first stage, prior to demand realization, the operation and marketing decisions are determined. In the second stage, inventory is allocated to meet the demand. The objective is to maximize the expected profit per-unit time. The computational results on the test problems provide managerial insights for firms faced with the conflicting needs of offering: (i) low prices, (ii) guaranteed and short lead time, and (iii) a large product variety by leveraging operations decisions.     

Conflict and cooperation in designing international telecommunication networks

In this paper, we study the problem of designing an international telecommunication network when multiple countries are involved. Each Country has the option of cooperating in the design of the overall international network, or simply forming bilateral arrangements with individual countries. Most countries will gain by having a truly international network which allows routing via transit countries; this takes advantage of distributed peak traffic hours, and improves the network resource utilization. However there are many situations when countries may obtain greater gains by either behaving pre-emptively or by waiting for the major countries to make their decisions, and then being followers in a Stackelberg game. Using mathematical programming models, we examine conditions under which each of these behaviours are optimal.     

Synchronized routing of seasonal products through a production/distribution network

This paper presents a multi-period vehicle routing problem for a large-scale production and distribution network. The vehicles must be routed in such a way as to minimize travel and inventory costs over a multi-period horizon, while also taking retailer demands and the availability of products at a central production facility into account. The network is composed of one distribution center and hundreds of retailers. Each retailer has its demand schedule representing the total number of units of a given product that should have been received on a given day. Many high value products are distributed. Product availability is determined by the production facility, whose production schedule determines how many units of each product must be available on a given day. To distribute these products, the routes of a heterogeneous fleet must be determined for a multiple period horizon. The objective of our research is to minimize the cost of distributing products to the retailers and the cost of maintaining inventory at the facility. In addition to considering product availability, the routing schedule must respect many constraints, such as capacity restrictions on the routes and the possibility of multiple vehicle trips over the time horizon. In the situation studied, no more than 20 product units could be carried by a single vehicle, which generally limited the number of retailers that could be supplied to one or two per route. This article proposes a mathematical formulation, as well as some heuristics, for solving this single-retailer-route vehicle routing problem. Extensions are then proposed to deal with the multiple-retailer-route situation.     

Selective and periodic inventory routing problem for waste vegetable oil collection

We consider a biodiesel production company that collects waste vegetable oil from source points that generate waste in large amounts. The company uses the collected waste as raw material for biodiesel production. The manager of this company needs to decide which of the present source points to include in the collection program, which of them to visit on each day, which periodic routing schedule to repeat over an infinite horizon and how many vehicles to operate such that the total collection, inventory and purchasing costs are minimized while the production requirements and operational constraints are met. For this selective and periodic inventory routing problem, we propose two different formulations, compare them and apply the better performing one on a real-world problem with 36 scenarios. We generate lower bounds using a partial linear relaxation model, and observe that the solutions obtained through our model are within 3.28% of optimality on the average. Several insights regarding the customer selection, routing and purchasing decisions are acquired with sensitivity analysis.     

District design for arc-routing applications

In this paper we address the problem of district design for the organisation of arc-routing activities. In particular, the focus is on operations like winter gritting and road maintenance. The problem involves how to allocate the road network edges to a set of depots with given locations. The collection of edges assigned to a facility forms a district in which routes have to be designed that start and end at the facility. Apart from the ability to support good arc routing, well-designed districts for road-maintenance operations should have the road network to be serviced connected and should define clear geographical boundaries. We present three districting heuristics and evaluate the quality of the partitions by solving capacitated arc routing problems in the districts, and by comparing the solution values with a multi-depot CARP cutting plane lower bound. Our experiments reveal that based on global information about the distribution system (ie the number of facilities or districts, the average edge demand and the vehicle capacity) and by using simple guidelines, an adequate districting policy may be selected.     

Routing,ship size,and sailing frequency decision-making for a maritime hub-and-spoke container network

This study formulates a two-objective model to determine the optimal liner routing, ship size, and sailing frequency for container carriers by minimizing shipping costs and inventory costs. First, shipping and inventory cost functions are formulated using an analytical method. Then, based on a trade-off between shipping costs and inventory costs, Pareto optimal solutions of the two-objective model are determined. Not only can the optimal ship size and sailing frequency be determined for any route, but also the routing decision on whether to route containers through a hub or directly to their destination can be made in objective value space. Finally, the theoretical findings are applied to a case study, with highly reasonable results. The results show that the optimal routing, ship size, and sailing frequency with respect to each level of inventory costs and shipping costs can be determined using the proposed model. The optimal routing decision tends to be shipping the cargo through a hub as the hub charge is decreased or its efficiency improved. In addition, the proposed model not only provides a tool to analyze the trade-off between shipping costs and inventory costs, but it also provides flexibility on the decision-making for container carriers.     

基于时间的随机需求二级分销网络物流系统集成优化研究

分销网络设计包括设施选址、库存控制、运输等方面的设计与优化,但以往只是从战略层、战术层、运作层来分别进行各自的研究。实际上,这三个层次的决策要素之间存在着复杂的互动关系,并存在着广泛的效益悖反关系,这些在变化的环境下显得尤为突出。本文充分考虑时间因素的重要性,从物流系统的集成优化高度出发,研究建立需求随机的多分销中心多顾客的设施选址———运输路线安排———库存控制问题(ILRIP)的模型,对此设计了一个两层粒子群优化(PSO)算法,并给出了计算实例。研究结果有助于供应链分销网络的集成优化,缩短商品流转周期,提高顾客服务水平,提升竞争力。     

A possibilistic decision model for new product supply chain design

This paper models supply chain (SC) uncertainties by fuzzy sets and develops a possibilistic SC configuration model for new products with unreliable or unavailable SC statistical data. The supply chain is modeled as a network of stages. Each stage may have one or more options characterized by the cost and lead-time required to fulfill required functions and may hold safety stock to prevent an inventory shortage. The objective is to determine the option and inventory policy for each stage to minimize the total SC cost and maximize the possibility of fulfilling the target service level. A fuzzy SC model is developed to evaluate the performance of the entire SC and a genetic algorithm approach is applied to determine near-optimal solutions. The results obtained show that the proposed approach allows decision makers to perform trade-off analysis among customer service levels, product cost, and inventory investment depending on their risk attitude. It also provides an alternative tool to evaluate and improve SC configuration decisions in an uncertain SC environment.     

Mathematical expressions for the transit time of merchandise through a liner shipping network

Recent publications on the design of liner shipping networks are limited in their treatment of the level of service (LoS) experienced by shippers. We propose the use of inventory holding costs—a function of merchandise transit time—as a proxy for LoS. We assume the existence of a two-tier optimization model, where fleet deployment, vessel routing, and vessel speed are determined in the higher tier. Merchandise flows and transshipment quantities are determined in the lower tier. We partition the total merchandise transit time into time spent in open waters, time spent during port calls, and time spent dwelling in the terminal yard. Using the notions of service frequency and service phase, we develop mathematical expressions for the three aforementioned quantities within the lower tier of the optimization model. We arrive at a bilinear expression for overall inventory holding costs that is suitable for liner shipping network design.     

Inventory constrained maritime routing and scheduling for multi-commodity liquid bulk,Part I: Applications and model

This paper formulates a model for finding a minimum cost routing in a network for a heterogeneous fleet of ships engaged in pickup and delivery of several liquid bulk products. The problem is frequently encountered by maritime chemical transport companies, including oil companies serving an archipelago of islands. The products are assumed to require dedicated compartments in the ship. The problem is to decide how much of each product should be carried by each ship from supply ports to demand ports, subject to the inventory level of each product in each port being maintained between certain levels that are set by the production rates, the consumption rates, and the storage capacities of the various products in each port. This important and challenging inventory constrained multi-ship pickup–delivery problem is formulated as a mixed-integer nonlinear program. We show that the model can be reformulated as an equivalent mixed-integer linear program with special structure. Over 100 test problems are randomly generated and solved using CPLEX 7.5. The results of our numerical experiments illuminate where problem structure can be exploited in order to solve larger instances of the model. Part II of the sequel will deal with new algorithms that take advantage of model properties.     

Petrol delivery tanker assignment and routing: a case study in Hong Kong

In this paper, we present a case study on a tanker assignment and routing problem for petrol products in Hong Kong. A fleet of heterogeneous dangerous goods vehicles has been assigned to deliver several types of petroleum products to petrol stations with different tank capacities. Under the vendor-managed inventory system, the delivery company is responsible for controlling the station's inventory and replenishment. The operational characteristics and challenges such as geographic zoning, size of petrol stations, routing restrictions and so on are unique and have been described in this paper. A decision support system (DSS) combining heuristic clustering and optimal routing is employed to find the optimal fleet assignment and routing. Multiple objectives are considered simultaneously such that the number of tankers used could be minimized, the number of drops in trips is minimized, profit in terms of total products delivered is maximized and utilization of resources is maximized. The case illustrates the benefit and advantages of using the proposed DSS.     

An interactive approach for hierarchical analysis of helicopter logistics in disaster relief operations

This study develops a mathematical model for helicopter mission planning during a disaster relief operation. The decisions inherent in the problem decompose hierarchically into two sub-problems where tactical decisions are made at the top level, and the operational routing and loading decisions are made at the base level. Consistency between the decomposed problems is achieved with an iterative coordination procedure which transfers anticipated information from the base level to improve the top level decisions. The existence of conflicting multiple objectives in this hierarchical structure requires the development of a multi-criteria analysis, and an interactive procedure is designed with the top level decision-maker to assess the preference of alternative non-dominated solutions.     

A mathematical model of a flexible manufacturing system with limited in-process inventory

This paper describes a computationally simple, asymptotic model of a flexible job shop, especially designed for estimating the influence of limited in-process inventory level on the production rate. Its main features make it very similar to the one by Solberg. While Solberg's model consists of a closed queuing network, we propose an open queuing network with a limited amount of inprocess customers; a single customer class is assumed, the various actual processing routes being accounted for by routing probabilities. For such a queuing network, the product form of state probabilities is valid, and the normalization constant can be very simply obtained by a convolution algorithm, close to the one used by Solberg. Various performance indices are calculated, regarding the job shop behaviour over a long period of time. Comparison of analytical results of the model and simulation results are provided in order to estimate the amount of error introduced by assuming exponentially distributed processing times and Poisson inputs in the mathematical representation. Simulations were carried out in FORTRAN-based SLAM language.     

A new VRPPD model and a hybrid heuristic solution approach for e-tailing

We analyze a business model for e-supermarkets to enable multi-product sourcing capacity through co-opetition (collaborative competition). The logistics aspect of our approach is to design and execute a network system where “premium” goods are acquired from vendors at multiple locations in the supply network and delivered to customers. Our specific goals are to: (i) investigate the role of premium product offerings in creating critical mass and profit; (ii) develop a model for the multiple-pickup single-delivery vehicle routing problem in the presence of multiple vendors; and (iii) propose a hybrid solution approach. To solve the problem introduced in this paper, we develop a hybrid metaheuristic approach that uses a Genetic Algorithm for vendor selection and allocation, and a modified savings algorithm for the capacitated VRP with multiple pickup, single delivery and time windows (CVRPMPDTW). The proposed Genetic Algorithm guides the search for optimal vendor pickup location decisions, and for each generated solution in the genetic population, a corresponding CVRPMPDTW is solved using the savings algorithm. We validate our solution approach against published VRPTW solutions and also test our algorithm with Solomon instances modified for CVRPMPDTW.     

Sensible decisions based on QoS

Network Quality of Service (QoS) criteria of interest include conventional metrics such as throughput, delay, loss, and jitter, as well as new QoS criteria based on power utilization, reliability and security. Variable and adaptive routing have again become of interest in networking because of the increasing importance of mobile ad-hoc networks. In this paper we develop a probability model of adaptive routing algorithms which use the expected QoS to select paths in the network. Our objective is not to analyze QoS, but rather to design randomized routing policies which can improve QoS. We define QoS metrics as non-negative random variables associated with network paths which satisfy a sub-additivity condition along each path. We define the QoS of a path, under some routing policy, as the expected value of a non-decreasing measurable function of the QoS metric. We discuss sensitive and insensitive QoS metrics, the latter being dependent on the routing policy which is used. We describe routing policies simply as probabilistic choices among all possible paths from some source to some given destination. Incremental routing policies are defined as those which can be derived from independent decisions taken at certain points (or nodes) along paths. Sensible routing policies are then introduced: they take decisions based simply on the QoS of each available path. Sensible policies, which make decisions based on the QoS of the paths, are introduced. We prove that the routing probability of a sensible policy can always be uniquely obtained. A hierarchy of m-sensible probabilistic routing policies is then introduced. A 0-sensible policy is simply a random choice of routes with equal probability, while a 1-sensible policy selects a path with a probability which is inversely proportional to the (expected) QoS of the path. We prove that an m + 1-sensible policy provides better QoS on the average than an m-sensible policy, if the QoS metric is insensitive. We also show that under certain conditions, the same result also holds for sensitive QoS metrics.Accepted: May 2003, This work was supported by the U.S. Army and Navy under contracts N611339-00-K-0002, N61339-02-C0050, N61339-02-C0080, N61339-02-C0117, and by NSF grants EIA0086251, EIA0203446, ECS0216381.     

Optimization model for a production,inventory, distribution and routing problem in small furniture companies

Production and distribution are two key decisions in supply chain planning. In order to achieve an effective operational performance, it is important for these two decisions to be integrated, especially in supply chains with low inventory levels. In this paper, we propose a mixed integer programming model to integrate production, inventory, distribution and routing decisions in a single framework. The model was inspired by small Brazilian furniture companies and focuses on production and distribution decisions at an operational level. In particular, we consider a scenario in which only one production line and one vehicle, which makes multiple trips over the planning horizon, are available to produce items and deliver final products, respectively. We also take into account some features rarely considered in the literature, but commonly found in real-world applications, such as producing and stocking multiple items, distribution routes extending over one or more periods, multiple time windows and customers’ due dates. Computational tests on a set of randomly generated instances were carried out using a well-known optimization software and six relax-and-fix heuristics, which explore different criteria for partitioning and fixing variables. We also implemented two hybrid heuristics in which an initial solution is first constructed and then fed into the optimization software to improve it. The results showed that one relax-and-fix and the two hybrid heuristics performed better than the solver on the largest instances.