A note on a single-machine lot scheduling problem with indivisible orders

In this paper, a lot scheduling problem on a single machine with indivisible orders is studied. The objective is to minimize the total completion time of all orders. We show that the problem is NP-hard in the strong sense. Then, a binary integer programming approach and four simple heuristics are proposed to solve the problem. The binary integer programming approach with running time limit is considered as one heuristic method. As compared to a lower bound, the average performances of the heuristic method are really good and better than those of the four simple heuristics.     

Production and vehicle scheduling for ready-mix operations

This paper deals with the problem of selecting and scheduling the orders to be processed by a ready-mix manufacturing plant for immediate delivery to the customer site. Orders have a fixed due date and must be prepared in a single plant with limited capacity. The objective is to maximize the total value of orders served. We first describe the problem as it occurs in practice in some industrial environments, and then present two scenarios to be considered: arbitrary and uniform profit margins for orders. The first scenario corresponds to the fixed job scheduling problem, which is solved by a minimum cost flow problem. A new scheme that reduces the number of nodes in the graph is proposed in this paper. The second scenario on the other hand requires more computationally expensive approaches as a second objective of minimizing the number of vehicles is to be considered. An exact graph-based method and a heuristic branch-and-bound based scheme are described. Computational experiences show that the optimal approach is not feasible for large problems and that the proposed heuristic approach gives high-quality solutions in short running times.     

Maximum lifetime data sensing and extraction in energy constrained networked sensor systems

We focus on data gathering problems in energy constrained networked sensor systems. The system operates in rounds where a subset of the sensors generate a certain number of data packets during each round. All the data packets need to be transferred to the base station. The goal is to maximize the system lifetime in terms of the number of rounds the system can operate. We show that the above problem reduces to a restricted flow problem with quota constraint, flow conservation requirement, and edge capacity constraint. We further develop a strongly polynomial time algorithm for this problem, which is guaranteed to find an optimal solution. We then study the performance of a distributed shortest path heuristic for the problem. This heuristic is based on self-stabilizing spanning tree construction and shortest path routing methods. In this heuristic, every node determines its sensing activities and data transfers based on locally available information. No global synchronization is needed. Although the heuristic cannot guarantee optimality, simulations show that the heuristic has good average case performance over randomly generated deployment of sensors. We also derive bounds for the worst case performance of the heuristic.     

Finding optimal solutions to the graph partitioning problem with heuristic search

As search spaces become larger and as problems scale up, an efficient way to speed up the search is to use a more accurate heuristic function. A better heuristic function might be obtained by the following general idea. Many problems can be divided into a set of subproblems and subgoals that should be achieved. Interactions and conflicts between unsolved subgoals of the problem might provide useful knowledge which could be used to construct an informed heuristic function. In this paper we demonstrate this idea on the graph partitioning problem (GPP). We first show how to format GPP as a search problem and then introduce a sequence of admissible heuristic functions estimating the size of the optimal partition by looking into different interactions between vertices of the graph. We then optimally solve GPP with these heuristics. Experimental results show that our advanced heuristics achieve a speedup of up to a number of orders of magnitude. Finally, we experimentally compare our approach to other states of the art graph partitioning optimal solvers on a number of classes of graphs. The results obtained show that our algorithm outperforms them in many cases.     

Completion time variance minimization in single machine and multi-machine systems

In this paper we consider the problem of minimizing the completion time variance of n jobs on a single machine with deterministic processing times. We propose a new heuristic and compare the results with existing popular heuristics for the problem. We also propose a method based on genetic algorithms to solve the problem. We present the worst case performance analysis of the proposed heuristic. We also consider the problem of minimizing the completion time variance of n jobs on m identical parallel machines in both restricted and unrestricted versions. A heuristic method and a method based on genetic algorithms are presented for both the cases and results of computational testing are provided. It is concluded that the proposed methods provide better results compared to existing methods for the single machine case as well as for the multi-machine case.     

The inventory-routing problem with transshipment

This paper introduces the Inventory-Routing Problem with Transshipment (IRPT). This problem arises when vehicle routing and inventory decisions must be made simultaneously, which is typically the case in vendor-managed inventory systems. Heuristics and exact algorithms have already been proposed for the Inventory-Routing Problem (IRP), but these algorithms ignore the possibility of performing transshipments between customers so as to further reduce the overall cost. We present a formulation that allows transshipments, either from the supplier to customers or between customers. We also propose an adaptive large neighborhood search heuristic to solve the problem. This heuristic manipulates vehicle routes while the remaining problem of determining delivery quantities and transshipment moves is solved through a network flow algorithm. Our approach can solve four different variants of the problem: the IRP and the IRPT, under maximum level and order-up-to level policies. We perform an extensive assessment of the performance of our heuristic.     

Scheduling algorithms for a semiconductor probing facility

This paper focuses on a scheduling problem in a semiconductor wafer probing facility. In the probing facility, wafer lots with distinct ready times are processed on a series of workstations, each with identical parallel machines. We develop a heuristic algorithm for the problem with the objective of minimizing total tardiness of orders. The algorithm employs a bottleneck-focused scheduling method, in which a schedule at the bottleneck workstation is constructed first and then schedules for other workstations are constructed based on the schedule at the bottleneck. For scheduling wafer lots at the bottleneck workstation, we consider prospective tardiness of the lots as well as sequence-dependent setup times required between different types of wafer lots. We also present a rolling horizon method for implementation of the scheduling method on a dynamic situation. The suggested methods are evaluated through a series of computational experiments and results show that the methods work better than existing heuristic methods.     

New approximate algorithms for the customer order scheduling problem with total completion time objective

In this paper, we study a customer order scheduling problem where a number of orders, composed of several product types, have to be scheduled on a set of parallel machines, each one capable to process a single product type. The objective is to minimise the sum of the completion times of the orders, which is related to the lead time perceived by the customer, and also to the minimisation of the work-in-process. This problem has been previously studied in the literature, and it is known to be NP-hard even for two product types. As a consequence, the interest lies on devising approximate procedures to obtain fast, good performing schedules. Among the different heuristics proposed for the problem, the ECT (Earliest Completion Time) heuristic by Leung et al. [6] has turned to be the most efficient constructive heuristic, yielding excellent results in a wide variety of settings. These authors also propose a tabu search procedure that constitutes the state-of-the-art metaheuristic for the problem. We propose a new constructive heuristic based on a look-ahead mechanism. The computational experience conducted shows that it clearly outperforms ECT, while having both heuristics the same computational complexity. Furthermore, we propose a greedy search algorithm using a specific neighbourhood that outperforms the existing tabu search procedure for different stopping criteria, both in terms of quality of solutions and of required CPU effort.     

Minimizing maximum earliness on parallel identical machines

This paper addresses the scheduling problem of minimizing maximum earliness (or more generally — maximizing minimum lateness) on parallel identical machines. We prove that the two-machine case is NP-hard in the ordinary sense, and introduce a pseudo-polynomial dynamic programming algorithm for this case. When the number of machines is arbitrary, the problem is shown to be NP-hard in the strong sense. Then we introduce an efficient heuristic and two simple upper bounds on the optimal minimum lateness value. Finally we provide an extensive numerical study which indicates that the heuristic performs well in various job and machine settings.Scope and purposeIn recent years many researchers have focused on minimizing both earliness and tardiness costs. Only a few studies have considered problems with (maximum or total) earliness as the sole performance measure. We believe that the earliness measure is appropriate for many real-life settings, where the main cost component is the earliness (inventory) cost, and the tardiness (positive lateness) cost component is negligible. Our paper studies the scheduling problem of minmax earliness on parallel identical machines: we analyze the complexity of the problem, and introduce an efficient heuristic and simple bounds on the optimal cost.     

A bi‐objective mathematical model for product allocation in block stacking warehouses

Put‐away and picking operations in warehouses play a critical role in determining operating costs and customer response time. While the place where products are put away has an important effect on picking efficiency due to accessibility, it also affects space usage, which is critical for space availability and space costs. Hence, this study focuses on put‐away operations in pallet‐in pallet‐out block stacking warehouses. We develop a unique bi‐objective mathematical model and a constructive heuristic algorithm to allocate products to storage lanes while considering two objectives simultaneously: minimizing total travel distance and maximizing average storage usage. We test our model and heuristic through a real company case study and randomly generated large‐sized problem instances. We show that the model and heuristic offer better storage usage with reduced travel distance than the company's approach when the two objectives have equal weight. We also present a set of nondominated solutions for each problem instance. We present that the heuristic seems beneficial for the warehouse industry due to its short run time and effective solutions.     

A tabu search algorithm for order acceptance and scheduling

We consider a make-to-order production system, where limited production capacity and order delivery requirements necessitate selective acceptance of the orders. Since tardiness penalties cause loss of revenue, scheduling and order acceptance decisions must be taken jointly to maximize total revenue. We present a tabu search algorithm that solves the order acceptance and scheduling problem on a single machine with release dates and sequence dependent setup times. We analyze the performance of the tabu search algorithm on an extensive set of test instances with up to 100 orders and compare it with two heuristics from the literature. In the comparison, we report optimality gaps which are calculated with respect to bounds generated from a mixed integer programming formulation. The results show that the tabu search algorithm gives near optimal solutions that are significantly better compared to the solutions given by the two heuristics. Furthermore, the run time of the tabu search algorithm is very small, even for 100 orders. The success of the proposed heuristic largely depends on its capability to incorporate in its search acceptance and scheduling decisions simultaneously.     

An improved NEH heuristic to minimize makespan in permutation flow shops

For over 20 years the NEH heuristic of Nawaz, Enscore, and Ham [A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega, The International Journal of Management Science 1983;11:91–5] has been commonly regarded as the best heuristic for solving the NP-hard problem of minimizing the makespan in permutation flow shops. The strength of NEH lies mainly in its priority order according to which jobs are selected to be scheduled during the insertion phase. Framinan et al. [Different initial sequences for the heuristic of Nawaz, Enscore and Ham to minimize makespan, idle time or flowtime in the static permutation flowshop problem. International Journal of Production Research 2003;41:121–48] presented the results of an extensive study to conclude that the NEH priority order is superior to 136 different orders examined. Based upon the concept of Johnson's algorithm, we propose a new priority order combined with a simple tie-breaking method that leads to a heuristic that outperforms NEH for all problem sizes.     

A vendor managed inventory model under contractual storage agreement

Vendor managed inventory (VMI) is a supply chain partnership strategy that allows a supplier to place orders on behalf of its customers. This paper considers a supply chain composed of a single vendor and multiple retailers operating under a VMI contract that specifies limits on retailers' stock levels. We address the problem of synchronizing the vendor's cycle time with the buyers' unequal ordering cycles by developing a mixed integer non-linear program that minimizes the joint relevant inventory costs under storage restrictions. We also propose a cost efficient heuristic to solve the developed optimization problem. We conducted computational experiments to assess the reduction in the total supply chain costs resulting from relaxing the restriction of equal ordering cycles. It is found that the heuristic generates greater cost savings in cases of increased variability in retailers' demand and cost parameters.     

A storage assignment heuristic method based on genetic algorithm for a pick-and-pass warehousing system

An order storage assignment problem (SAP) is to find an effective way to locate products in a warehouse in order to improve the operational efficiency of order picking. Since SAP is an NP-hard problem, many heuristic algorithms have been proposed. Most of previous researches focused on picker-to-parts warehousing systems or automated storage and retrieval systems. However, pick-and-pass systems play an important role for the faster delivery of small and frequent orders of inventory with the rise of e-commerce and e-business in the global supply chain. Two factors lead to idle time of pickers in a pick-and-pass system: picking line imbalance and shortage replenishment of products. This paper develops a genetic based heuristic method to solve SAP for a pick-and-pass system with multiple pickers to determine the appropriate storage space for each product and balance the workload of each picking zone so that the performance of the system can be improved. A simulation model based on FlexSim is used to implement the proposed heuristic algorithm and compare the throughput for different storage assignment methods as well. The results indicate that the proposed heuristic policy outperforms existing assignment methods in a pick-and-pass system.     

参数化系统安全性的启发式符号验证

参数化系统(paramterized system)是指包含特定有限状态进程多个实例的并发系统,其中的参数是指系统内进程实例的数目,即系统的规模.反向可达性分析(backward reachability analysis)已被广泛用于验证参数化系统是否满足以向上封闭(upward-closed)集合表示的安全性(safety property).与有限状态系统验证相类似,参数化系统的验证同样也面临着状态爆炸(state explosion)问题,并且模型检测算法的有效性依赖于如何采用有效的数据结构表示状     

Service Sharing for Streaming Video Multicast

In a general context, the sharing of intermediate service results among different processes is seldom feasible because parameters are often different and there may be transactional and side effects. However, in a streaming video multicast environment, a large number of users often request various similar processing on the same stream. Therefore, service sharing is feasible, with a large potential of savings in processing cost. In this paper, we study the problem of determining the service invocation orders for multiple service composition requests in a streaming video multicast with the aim of maximizing the service sharing. We first formally define the problem. After proving the problem is NP-Complete, we develop an optimal algorithm for the base case of two requests. Then for the general case, we develop two heuristic algorithms, namely, a global greedy algorithm and a local greedy algorithm using the optimal algorithm for the base case as the building block. The global greedy algorithm is designed for a system where the existing service composition requests can be recomposed with the arrival of a new request. The local greedy algorithm can be used in a system where the existing service composition requests do not change their service composition solutions with the arrival of a new request. We prove that the global greedy algorithm is a 2-approximation algorithm in terms of maximizing service sharing. Simulation results show that the greedy algorithms can save more service costs compared with a naive algorithm, and are effective compared with the cost lower bound.      

Heuristics for tactical time slot management: a periodic vehicle routing problem view

In this study, we consider a tactical problem where a time slot schedule for delivery service over a given planning horizon must be selected in each zone of a geographical area. A heuristic search evaluates each schedule selection by constructing a corresponding tactical routing plan of minimum cost based on demand and service time estimates. At the end, the schedule selection leading to the best tactical routing plan is selected. The latter can then be used as a blueprint when addressing the operational problem (i.e., when real customer orders are received and operational routes are constructed). We propose two heuristics to address the tactical problem. The first heuristic is a three‐phase approach: a periodic vehicle routing problem (PVRP) is first solved, followed by a repair phase and a final improvement phase where a vehicle routing problem (VRP) with time windows is solved for each period of the planning horizon. The second heuristic tackles the problem as a whole by directly solving a PVRP with time windows. Computational results compare the two heuristics under various settings, based on instances derived from benchmark instances for the VRP with time windows.     

Integrated order acceptance and supply chain scheduling problem with supplier selection and due date assignment

The importance, benefits, and impact of integration of decisions within supply chains have long been investigated by many researchers. Order acceptance and supplier selection are two of the most critical decisions for supply chain managers. Throughout the process of order acceptance, a manufacturer has to decide which orders to be accepted and processed and based on the accepted orders, the volume of required raw material is determined. On the other hand, a manufacturer aims to choose one or several suppliers among all possible choices to provide sufficient raw material for the accepted orders, subject to different criteria such as list price, transportation cost, etc. This paper addresses an integrated framework for profit maximization in an integrated supplier selection, order acceptance and scheduling problem in a single-machine environment with multiple customers. There is substantial literature on the problems of supplier selection and order acceptance; however, to the best of our knowledge, this paper is the first research that integrates these essential decisions in the form of a mathematical model to maximize the total profit. The problem is NP-hard in nature; therefore, solving to optimality is not practically possible for problems with medium and large size. For that purpose, we developed a Heuristic Algorithm (HA) to solve the problem above in a reasonable time, with proper accuracy. Results from this heuristic algorithm are compared with that of a commercial solver (GAMS) and the well-known Genetic Algorithm (GA) and Variable Neighborhood Search (VNS). Computational experiments demonstrate that the developed heuristic algorithm is more efficient in comparison with other tested methods.     

Planning for Agricultural Forage Harvesters and Trucks: Model,Heuristics, and Case Study

In this paper we study an actual problem proposed by an agricultural cooperative devoted to harvesting corn and grass. The cooperative uses harvesters for harvesting the crop and trucks for carrying it from the smallholdings to the landowners’ silos. The goal is to minimize the total working time of the machinery. Therefore, the cooperative needs to plan both the harvesters and trucks routing. This routing problem simultaneously incorporates the following characteristics: time windows, nested decisions, processing times required to service each facility and the fact that facilities must be visited in clusters. A binary integer linear programming model is proposed to solve this problem. However, since approaches dealing directly with such formulation lead to considerable computation times, we propose a heuristic alternative solution approach for the problem. The heuristic is applied to the case of the cooperative “Os Irmandiños” with a large number of landowners and smallholdings. We report on extensive computational tests to show that the proposed heuristic approach can solve large problems effectively in reasonable computing time.     

钢铁企业合同计划与余材匹配的集成优化方法

钢铁企业的合同计划和余材匹配的集成优化是解决钢铁企业面向订单生产的关键技术.由于该问题复杂,涉及因素多,求解难度大,对此提出一个带有提前拖期惩罚的联合计划优化的数学模型,并提出一种嵌有"优先适合启发式"的遗传算法.该方法利用背包问题的求解思路改进了染色体的性能,从而加快了遗传算法的求解速度.将该模型及算法应用于实际钢铁企业的计划编排中,取得了满意的效果.