Fleet routing position-based model for inventory pickup under production shutdown

This paper addresses the problem of collecting inventory of production at various plants having limited storage capacity, violation of which forces plant shutdowns. The production at plants is continuous (with known rates) and a fleet of vehicles need to be scheduled to transport the commodity from plants to a central storage or depot, possibly making multiple pickups at a given plant to avoid shutdown. One operational objective is to achieve the highest possible rate of product retrieval at the depot, relative to the total travel time of the fleet. This problem is a variant (and generalization) of the inventory routing problem. The motivating application for this paper is barge scheduling for oil pickup from off-shore oil-producing platforms with limited holding capacity, where shutdowns are prohibitively expensive. We develop a new model that is fundamentally different from standard node-arc or path formulations in the literature. The proposed model is based on assigning a unique position to each vehicle visit at a node in a chronological sequence of vehicle-nodal visits. This approach leads to substantial flexibility in modeling multiple visits to a node using multiple vehicles, while controlling the number of binary decision variables. Consequently, our position-based model solves larger model instances significantly more efficiently than the node-arc counterpart. Computational experience of the proposed model with the off-shore barge scheduling application is reported.     

A risk management system for sustainable fleet replacement

This article analyzes the fleet management problem faced by a firm when deciding which vehicles to add to its fleet. Such a decision depends not only on the expected mileage and tasks to be assigned to the vehicle but also on the evolution of fuel and CO₂ emission prices and on fuel efficiency. This article contributes to the literature on fleet replacement and sustainable operations by proposing a general decision support system for the fleet replacement problem using stochastic programming and conditional value at risk (CVaR) to account for uncertainty in the decision process. The article analyzes how the CVaR associated with different types of vehicle is affected by the parameters in the model by reporting on the results of a real-world case study.     

Shipment planning at oil refineries using column generation and valid inequalities

In this paper we suggest an optimization model and a solution method for a shipment planning problem. This problem concerns the simultaneous planning of how to route a fleet of ships and the planning of which products to transport in these ships. The ships are used for moving products from oil refineries to storage depots. There are inventory levels to consider both at the refineries and at the depots. The inventory levels are affected by the process scheduling at the refineries and demand at the depots. The problem is formulated using an optimization model including an aggregated representation of the process scheduling at the refineries. Hence, we integrate the shipment planning and the process scheduling at the refineries. We suggest a solution method based on column generation, valid inequalities, and constraint branching. The solution method is tested on data provided by the Nynas oil refinery company and solutions are obtained within 4 hours, for problem instances of up to 3 refineries, 15 depots, and 4 products when considering a time horizon of 42 days.     

The impact of fleet size on performance-based incentive management

Performance-based contracting (PBC) is envisioned to lower the asset ownership cost while ensuring desired system performance. System availability, widely used as a performance metric in such contracts, is affected by multiple factors such as equipment reliability, spares stock, fleet size, and service capacity. Prior studies have either focussed on ensuring parts availability or advocating the reliability allocation during design. This paper investigates a single echelon repairable inventory model in PBC. We focus on reliability improvement and its interaction with decisions affecting service time, taking into account the operating fleet size. The study shows that component reliability in a repairable inventory system is a function of the operating fleet size and service rate. A principal-agent model is further developed to evaluate the impact of the fleet size on the incentive mechanism design. The numerical study confirms that the fleet size plays a critical role in determining the penalty and cost sharing rates when the number of backorders is used as the negative incentive scheme.     

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.     

A computational comparison of algorithms for the inventory routing problem

The inventory routing problem is a distribution problem in which each customer maintains a local inventory of a product such as heating oil and consumes a certain amount of that product each day. Each day a fleet of trucks is dispatched over a set of routes to resupply a subset of the customers. In this paper, we describe and compare algorithms for this problem defined over a short planning period, e.g. one week. These algorithms define the set of customers to be serviced each day and produce routes for a fleet of vehicles to service those customers. Two algorithms are compared in detail, one which first allocates deliveries to days and then solves a vehicle routing problem and a second which treats the multi-day problem as a modified vehicle routing problem. The comparison is based on a set of real data obtained from a propane distribution firm in Pennsylvania. The solutions obtained by both procedures compare quite favorably with those in use by the firm.Part of this work was performed while this author was visiting the University of Waterloo.     

A heuristic algorithm for a production planning problem in an assembly system

This paper focuses on a production planning problem in an assembly system operating on a make-to-order basis. Due dates are considered as constraints in the problem, that is, tardiness is not allowed. The objective of the problem is to minimise holding costs for final product inventory as well as work-in-process inventory. A non-linear mathematical model is presented and a heuristic algorithm is developed using a solution property and a network model for defining solutions of the problem. A series of computational tests were done to compare the algorithm with a commercial planning/scheduling software and backward finite-loading methods that employ various priority rules. The results showed that the suggested algorithm outperformed the others.     

A fuzzy goal programming approach to integrated loading and scheduling of a batch processing machine

This paper concerns a real-life problem of loading and scheduling a batch-processing machine. The integrated loading and scheduling problem is stated as a multicriteria optimization problem where different types of objectives are included: (1) short-term objectives of relevance to the shop floor, such as throughput maximization and work-in-process inventory minimization, and (2) long-term objectives such as balancing of end product inventory levels and meeting financial targets imposed by the higher production planning level. Two types of uncertainty are considered: (1) uncertainty inherent in loading and scheduling objective targets (goals) such as the allocated budget and end product demand, and (2) uncertainty in importance relations among the objectives. These two types of uncertainty are modelled using fuzzy sets and fuzzy relations, respectively. A fuzzy goal programming model and the corresponding method are developed which handle both fuzzy and crisp goals and fuzzy importance relations among the goals. Numerical examples are given to illustrate the effectiveness of the developed model.     

The scheduling of deliveries in a production-distribution system with multiple buyers

In a real production and distribution business environment with one supplier and multiple heterogeneous buyers, the differences in buyers’ ordering cycles have influence on production arrangements. Consequently, the average inventory level (AIL) at the supplier’s end is affected by both the production policy and the ordering policy, typically by the scheduling of deliveries. Consequently, the average inventory holding cost is most deeply affected. In this paper, it is proposed that the scheduling of deliveries be formulated as a decision problem to determine the time point at which deliveries are made to buyers in order to minimize the supplier’s average inventory. A formulation of the average inventory level (AIL) in a production cycle at the supplier’s end using a lot-for-lot policy is developed. Under the lot-for-lot policy, the scheduling of deliveries (SP) is formulated as a nonlinear programming model used to determine the first delivery point for each buyer with an objective to minimize the sum of the product of the individual demand quantity and the first delivery time for each buyer. Thus, the SP model determines not only the sequence of the first deliveries to individual buyers, but also the time when the deliveries are made. An iterative heuristic procedure (IHP) is developed to solve the SP model assuming a given sequence of buyers. Six sequence rules are considered and evaluated via simulation.     

The Vehicle Scheduling Problem with Multiple Vehicle Types

The vehicle scheduling problem is specified in terms of a set of tasks to be executed with a fleet of multiple vehicle types. The purpose of this paper is to formulate the problem and to show that the heuristic and exact methods developed for the vehicle scheduling problem with time windows and with a single type of vehicle can be extended in a straightforward fashion to the multiple-vehicle-types problem.     

A multicut L-shaped based algorithm to solve a stochastic programming model for the mobile facility routing and scheduling problem

This paper considers the mobile facility routing and scheduling problem with stochastic demand (MFRSPSD). The MFRSPSD simultaneously determines the route and schedule of a fleet of mobile facilities which serve customers with uncertain demand to minimize the total cost generated during the planning horizon. The problem is formulated as a two-stage stochastic programming model, in which the first stage decision deals with the temporal and spatial movement of MFs and the second stage handles how MFs serve customer demands. An algorithm based on the multicut version of the L-shaped method is proposed in which several lower bound inequalities are developed and incorporated into the master program. The computational results show that the algorithm yields a tighter lower bound and converges faster to the optimal solution. The result of a sensitivity analysis further indicates that in dealing with stochastic demand the two-stage stochastic programming approach has a distinctive advantage over the model considering only the average demand in terms of cost reduction.     

Vehicle dispatching system based on Taguchi-tuned fuzzy rules

This paper presents the development of a dispatching system for a fleet of automated guided vehicles in a flexible manufacturing environment which is based on a hybrid Fuzzy–Taguchi approach. A fuzzy decision-making system emulates the human behavior necessary for multi-objective directed decision making in a dynamically evolving environment. A statistical approach based on the Taguchi method tunes the fuzzy rules to achieve near optimal performance. Simulation results demonstrate the effectiveness of this marriage of computational tools in dealing with the well-known NP-complete scheduling problem.     

Optimal purchasing policy in a two-component assembly system with different purchasing contracts for each component

This paper considers an assembly system where a firm produces a single product which is assembled using two types of components (component 1 and component 2). The components are provided by individual suppliers (supplier 1 and supplier 2). We assume that the firm makes different procurement contracts with supplier 1 and supplier 2. To supplier 1, the firm specifies the maximum inventory level of component 1 and makes a commitment to purchase the component as long as its inventory level is below this target level. To supplier 2, the firm has the option of purchasing or rejecting component 2 at each instant supplier 2 provides it. Formulating our model as a Markov decision problem, we identify a component 2 purchasing policy which maximizes the firm’s profits subject to the costs of rejecting component 1, holding component 2, and purchasing component 2. We also investigate how the changes in the sales price and cost parameters affect the optimal purchasing policy. Finally, we present numerical study for the optimal performance evaluation.This material is based upon work supported by the Korea Science and Engineering Foundation (KOSEF) through the Northeast Asia e-Logistics Research Center at University of Incheon.     

Multi-level lotsizing and scheduling by batch sequencing

We consider a single-machine scheduling problem with a multi-level product structure. Setups are required if the machine changes production from one product type to another, and the scheduling decision must satisfy dynamic demand. We propose a lotsizing as well as a scheduling model, and we compare solution procedures for both models on a very restricted set of instances. As a result the multi-level structure complicates the inventory balance constraints in the lotsizing model. In the scheduling model, however, the multi-level structure translates into precedence constraints between jobs (leading to a smaller search space) which allows it to solve the scheduling model to optimality.     

考虑机器调整次数和产品质量的卷烟批量计划和柔性流水车间调度集成问题

针对卷烟企业生产中的批量计划和柔性流水车间调度集成问题,构建了整数规划模型,目标函数由卷烟生产时间、生产线调整次数、卷烟质量、库存成本四部分组成。鉴于该问题的NP-hard性,设计遗传算法进行求解,通过合理设计遗传算子,避免不可行解出现。应用某卷烟企业数据得到优化排产结果,与该企业之前依照经验排产方案进行对比,发现优化排程结果在减少品牌转换次数,提高生产的连续性方面具有明显优势。该算法已作为某卷烟企业排产人员的排产参考,应用于排产决策中,取得了良好的效果,对卷烟企业制定排产计划具有一定的实际指导意义。     

Economic ordering policy for deteriorating items over an infinite time horizon

In this paper a total cost model is presented for the inventory problem of deteriorating items. A constant fraction of on hand inventory at the beginning of a period deteriorates during the period. The demand for the items during a period is supplied at the end of the period. However, shortages accumulated during a scheduling period are supplied at the start of the next scheduling period. An approach is suggested for determining economic ordering policy for the case of time varying demand and a search procedure is developed when demand is constant in each period.     

Competitive production scheduling: A two-firm,noncooperative finite dynamic game

In this paper, we study the production scheduling problem in a competitive environment. Two firms produce the same product and compete in a market. The demand is random and so is the production capacity of each firm, due to random breakdowns. We consider a finite planning horizon. The scheduling problem is formulated as a finite dynamic game. Algorithms are developed to determine the security, hazard, and Nash policies. Numerical examples are discussed. A single-firm optimization model is also analyzed and it is observed that the production control policy from the single-firm optimization model may not perform well in a competitive environment.     

A developed slope order index (SOI) for bottlenecks in projects and production lines

This paper finds a sequence of m jobs on one processor with the minimum total cost as a solution to the sequencing problem where the raw materials are either expensive to buy or carry. There have been numerous studies considering m jobs on one processor which consider various cost factors such as the total penalty cost. One of the important, but less investigated cost factors, in the previous studies, is the inventory carrying and its relevant capital costs. The inventory costs such as the holding cost and capital cost must be considered in proposing a solution to the sequencing problem. In this paper, by taking those costs into account to address the sequencing problem, a developed slope order index is computed to enable decision makers to a sufficient cost saving sequence of m jobs on one processor. This paper contributes the current knowledge by proposing a new sequencing solution in which some previously less observed costs are considered. The result of this paper can also be employed in scheduling of m jobs where there is a bottleneck and the inventories are expensive or their holding costs are considerable.     

A framework for decision support systems for scheduling problems

Considering a decision support system as a tool where executive's judgment can be included along with the mathematical tool kit of the management scientist, this paper shows the need to include problem management as an integral component of the decision support system for scheduling problems. A methodology based on the resolution of conflicts among various constraints in scheduling problems is proposed to implement the problem management system in a decision support system for these problems. The paper concludes with some guidelines to create a workable framework for providing effective decision support to solve scheduling problems and the identification of some fruitful directions for future research.     

A new model and hybrid approach for large scale inventory routing problems

This paper studies an inventory routing problem (IRP) with split delivery and vehicle fleet size constraint. Due to the complexity of the IRP, it is very difficult to develop an exact algorithm that can solve large scale problems in a reasonable computation time. As an alternative, an approximate approach that can quickly and near-optimally solve the problem is developed based on an approximate model of the problem and Lagrangian relaxation. In the approach, the model is solved by using a Lagrangian relaxation method in which the relaxed problem is decomposed into an inventory problem and a routing problem that are solved by a linear programming algorithm and a minimum cost flow algorithm, respectively, and the dual problem is solved by using the surrogate subgradient method. The solution of the model obtained by the Lagrangian relaxation method is used to construct a near-optimal solution of the IRP by solving a series of assignment problems. Numerical experiments show that the proposed hybrid approach can find a high quality near-optimal solution for the IRP with up to 200 customers in a reasonable computation time.