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In this paper, we consider an inventory–routing problem (IRP) in a large petroleum and petrochemical enterprise group. Compared to many other IRPs, the problem in this paper includes some special aspects due to the operational constraints, such as hours-of-service regulations of the company and the industry. Also, in some cases, it is more important to avoid stock out for any station, rather than purely focusing on transportation cost minimization. The objective is to minimize the maximum of the route travel time, which is not addressed in the literature so far. We present a tabu search algorithm to tackle the problem, which builds in an efficient and effective procedure to improve the search quality in each iteration. Moreover, lower bounds of reasonable sized problems, which are intractable in the formulated mathematical model by existing optimization software, are obtained via Lagrangian relaxation technique. Computational results indicate that the lower bounds are tight and the tabu search is capable of providing near optimal, close-to-lower-bound solutions in a computational time effective manner.

In this research, we study a supply chain which consists of a firm and a set of customer groups, where the demand (order quantity) from each customer group depends on the quoted delivery time. The prices of the product are determined and different to each customer group. The firm's objective is to maximize the profit by quoting different delivery times for all customer groups. A mathematical model is developed, which is proved to be NP hard. Both a mixed integer programming (MIP) formulation and the branch-and-bound algorithm are proposed to study the moderate size of the problem. Also, a heuristic algorithm is developed which is able to obtain the optimal solution quickly in most of cases when customer size is less than 20.

We consider a two-stage manufacturing system composed of a batch processor and its upstream processor. Jobs exit the upstream processor and join a queue in front of the batch processor, where they wait to be processed. The batch processor has a finite capacity Q, and its processing time is independent of the number of jobs loaded into the batch processor. In certain manufacturing systems (including semiconductor wafer fabrication), a processing time window exists from the time instance the job exits the upstream processor till the time instance it enters the batch processor. If a job is not processed before reaching the end of its processing time window, job rework or validation is required. We model this drawback by assigning a reward R for each successfully processed job by the upstream processor, and a penalty C for each job that reaches the end of its processing time window without being processed by the batch processor. We initially assume an infinite job source in front of the serial processor and also assume that the batch processor is operated under a threshold policy. We provide a method for controlling the production of the serial processor, considering the processing time window between the upstream processor and the downstream batch processor. We then show how the serial processor control policy can be modified when the serial processor also experiences intermittent job arrival.

We examine the problem of minimizing the mean cycle time of a batch processor with incompatible job families and future job arrivals. Batch processors frequently found in wafer fabrication include oxidation and diffusion ovens. When the problem is deterministic with a fixed number of job arrivals, the problem is NP-hard; an optimal dynamic program formulation is developed and empirically tested on small problem instances. For larger problem instances with possibly infinite job arrivals, an online heuristic based on model predictive control (MPC) is proposed. The proposed heuristic has two parameters: the number of job families considered f, and the number of future job arrivals L. Statistical analysis of simulation results shows that the MPC-based heuristic has significantly lower mean cycle time than a benchmark look-ahead method under the assumption that the arrival time is deterministic and job families of consecutive job arrivals are uncorrelated. These observations also hold true when the predicted arrival times can be erroneous, indicating that the suggested MPC-based heuristic is as robust as the benchmark with respect to errors in forecasted arrival times. When the job families of future job arrivals are positively correlated, the mean cycle time of jobs passing through the batch processor is significantly reduced, regardless of control policy. We infer that the introduction of correlation generates less improvement for policies that foresee events longer into the future. For this reason, when the correlation is high, the MPC-based heuristic, which considers events that occur farther into the future, may have worse performance than the benchmark. The results suggest two ways to improve the performance of the batch processor. First, we can use a heuristic that has better mean performance, which may entail much larger computational costs. Another option is to continue using a simple look-ahead policy at the batch processor, and focus attention on controlling the upstream processors, such that the batch processor arrival process exhibits correlated job families between consecutive arrivals. This introduction of correlation causes a significant reduction of cycle time regardless of system parameter and batch processor control policy.

Nowadays, it is popular to outsource transportation and distribution of finished products to third-party logistics (3PL) providers in many industries. In order to shorten the response time from order receipt to delivery, and also to improve on-time delivery accuracy, the decision of manufacturing scheduling and transportation scheduling should consider the constraints between manufacturing and transportation. In this paper, we study a coordinated scheduling problem of parallel machine assembly manufacturing and multi-destination transportation in the make-to-order (MTO) consumer electronics supply chain (CESC). By considering the constraints between parallel machine assembly and 3PL transportation, the overall problem is decomposed into a parallel machine scheduling sub-problem and a 3PL transportation sub-problem. The 3PL transportation problem is proved to be NP-complete. Heuristic algorithms are proposed to solve the parallel machine assembly scheduling problem.

In this paper, we study the problem of synchronized scheduling of assembly and air transportation to achieve accurate delivery with minimized cost in consumer electronics supply chain. This problem was motivated by a major PC manufacturer in consumer electronics industry. The overall problem is decomposed into two sub-problems, which consist of an air transportation allocation problem and an assembly scheduling problem. The air transportation allocation problem is formulated as an integer linear programming problem with the objective of minimizing transportation cost and delivery earliness tardiness penalties. The assembly scheduling problem seeks to determine a schedule ensuring that the orders are completed on time and catch the flights such that the waiting penalties between assembly and transportation is minimized. The problem is formulated as a parallel machine scheduling problem with earliness penalties. The computational complexities of the two sub-problems are investigated. The air transportation allocation problem with split delivery is shown to be solvable. The parallel machine assembly scheduling problem is shown to be NP-complete. Simulated annealing based heuristic algorithms are presented to solve the parallel machine problem.

This paper addresses a specific class of scheduling parallel batching problem, which is observed in steel casting industries. The focus of this research is to minimize the total weighted tardiness on heterogeneous batch processing machines under conditions of dynamic job arrivals, incompatible job families and non-identical job sizes. This type of parallel batching problem arises in a number of different settings, including diffusion in wafer fabrication, heat treatment operations in aircraft industries, and metal working. The problem is viewed as a three stage-decision-problem: the first stage involves selecting a machine from the heterogeneous batch processing machines for scheduling; the second stage involves the selection of a job family from the available incompatible job families; and the third stage involves the selection of a set of jobs to create a batch from the selected job family based on the capacity of the selected batch-processing machine. Since the problem is NP-hard, a few greedy heuristics are proposed. The computational experiments show that the proposed greedy heuristic algorithms are capable of consistently obtaining near-optimal solutions (statistically estimated) in very reasonable computational time on a Pentium III 650 Mz with 128 MB RAM.

This paper presents a preliminary analysis of the typical scheduling environment in semiconductor manufacturing involving multiple job families, and where more than one objective such as cycle time, machine utilization and the due-date accuracy needs to be simultaneously considered. In this study, the NP-hard problem of scheduling N independent jobs on a single testing machine with due dates and sequence-dependent setup times is addressed, where the multiple objectives are to minimize average cycle time, to minimize average tardiness, and to maximize machine utilization. A Pareto optimal solution, which is not inferior to any other feasible solutions in terms of all objectives, is generated combining the analytically optimal and conjunctive simulated scheduling approach. First, the machine-scheduling problem is modeled using the discrete event simulation approach and the problem is divided into simulation clock based lot selection sub-problems. Then, a Pareto optimal lot is selected using the compromise programming technique for multiobjective optimization at each decision instant in simulated time. With the help of a broad experimental design, this developed solution is then compared with common heuristic-dispatching rules such as SPT and EDD, which show better results for all the objectives over a wide range of problems. The developed scheduling method shows approximately 16.7% reduction in average cycle time, 25.6% reduction in average tardiness, and 21.6% improvement in machine utilization over the common dispatching rules, SPT and EDD.

The scheduling of highly complex job shops, such as those found in semiconductor manufacturing, involves multiple types of work centers, large and changing varieties of the products, sequence dependent set up times, reentrant process flow, dynamically changing environment, etc. These complexities make the job shop scheduling problem very strongly nondeterministic polynominally (NP)-hard and intractable to solve by the traditional scheduling approaches. This paper presents the concept and applications of the conjunctive simulated scheduling (CSS) approach, which incorporates the benefits of discrete event simulation in scheduling the shop and avoids the NP-hard formulation of these complex scheduling problems. The differences between CSS and typical simulation studies and its application to online simulation are also presented.

A key performance parameter of a manufacturing network or supply chain is its cycle time; the time that a typical item spends in the network. A previous simulation study on a semiconductor assembly and test facility showed that cycle times could be reduced by having smooth input and service rates. This suggested that there is a “cycle time principle” that, for a system with a specified throughput or input rate, the shortest cycle times are obtained when the input and service rates do not vary over time. We prove that this principle is true for the M/G/1 and M/M/s queueing systems and Jackson networks. The analysis involves establishing several results on the concavity of waiting time probabilities and the convexity of expected waiting times and queue lengths, as functions of input and service rates. These results also have natural uses in other optimization problems.

This paper deals with a flow-shop scheduling problem with limited intermediate buffer. Jobs are grouped in incompatible job families. Each job has to be processed by a batch processor followed by a discrete processor in the same order. The batch processor can process several jobs simultaneously so that all jobs of the same batch start and complete together. We assume that the capacity of batch processor is bounded. The batch processing time is identical for batches of the same family. A batch which has completed processing on the batch processor may block the processor until there is a free unit in the buffer. The objective is to determine a batching and scheduling for all jobs so as to minimise mean completion time. A lower bound and two heuristics algorithm are developed. Moreover, a two-stage method embedded with a Differential Evolution (DE) algorithm is also developed. DE is one of the latest evolutionary computation algorithms, which implements mutation, crossover, and selection operators to improve the candidate solutions iteratively. Three variants of DE are first compared with a continuous Genetic Algorithm employing the random key representation. Then, one variant of the DE with the best convergence speed is selected. Numerical experiments are conducted to evaluate the performances of the selected two-stage meta-heuristic and two heuristics.

We analyse the problem of minimising the mean cycle time of a batch processing stage containing K > 1 batch processors in parallel with incompatible job families and future job arrivals. We provide an integer linear programming formulation and a dynamic program formulation for small problem instances. For larger problem instances, we propose an online heuristic policy MPC_REPEAT. At each instance a decision has to be made, MPC_REPEAT decomposes the problem of simultaneously assigning multiple batches to multiple processors into sequentially assigning multiple batches to multiple processors. When job families are uncorrelated, we show via simulation experiments that MPC_REPEAT has significantly lower mean cycle time than a previously proposed look-ahead method except when: (MPC_REPEAT ignores some job families AND the traffic intensity is high.) Our experiments also reveal that increasing the job family correlation of consecutive job arrivals results, with a few exceptions, in a mean cycle-time reduction, for both policies evaluated. This reduction in cycle time generally increases with: increasing number of job families, decreasing number of processors, and increasing time between job arrivals. Our findings imply that controlling the upstream processors, such that job families of consecutive job arrivals are correlated, can reduce the cycle time at the batch processing stage. Furthermore, the expected mean cycle time reduction due to this strategy can be substantially larger than that expected from switching to a more complex batch processing stage policy, under less stringent conditions.

This paper addresses the problem of minimizing makespan for a given set of n jobs to be processed on each of m machines in a static jobshop, subject to the minimum completion time variance (CTV). A lower bound on CTV is developed for the static jobshop problem. A backward scheduling approach is proposed using the observations on the development of lower bound for hierarchical minimization of CTV and makespan. A lower bound on makespan subject to minimum CTV is also presented for this problem. Finally, we present two simulated annealing heuristic approaches using the concepts of forward and backward scheduling. Their performances are compared against each other through the use of the lower bounds established in this work. The simulated annealing heuristic based on backward scheduling is shown to perform well by evaluating the developed heuristics on 82 jobshop problems taken from literature. � 2005 Elsevier Ltd. All rights reserved.

Batch processors can concurrently process more than one job, and are commonly used in complex manufacturing systems such as wafer fabrication facilities (wafer fabs). Previous work has shown that there can be a significant reduction in cycle time when the control of the upstream serial processor is dependent on the batch processor. We wish to determine whether this is also true when the upstream processor is also a batch processor, with smaller capacity. We model a two-stage system with an upstream batch processor and a downstream batch processor under differing simple control policies as a continuous time-discrete state Markov chain. In doing so, we show that the concept of constraining the production of the upstream processor in accordance to the anticipated needs of the downstream batch processor can similarly reduce mean system cycle time when the upstream processor is a smaller batch processor. We also perform simulation experiments, using parameters close to those found in wafer fabs, and confirm that the strategy of prioritising the formation of larger batches for the downstream batch processor typically results in substantial cycle time reductions for the two-stage system.

Routing traffic across a capacitated hub-and-spoke network is very common in freight transportation and telecommunications. Most of the hub-and-spoke network models available in the literature assume a fully inter-connected hub network and allow traffic to pass through a maximum of two hubs. In the absence of a fully inter-connected hub network, the traffic may have to be routed through more than two hubs. In this paper, we develop a mathematical model and a simulated annealing (SA)-based solution methodology for routing freight through not more than three hubs in a given capacitated network. We generate test problem instances to evaluate the efficacy of the mathematical model and the meta-heuristic procedure. The effect of each network parameter on the performance of the SA procedure is analysed thoroughly with extensive computational experiments and relevant statistical tests. The results show that near-optimal solutions for large problem instances can be derived in little computational time.

Batch processors can concurrently process more than one job. In wafer fabrication, the processing time of a batch is independent of batch size, and only jobs from the same job family can be batched together. We consider a two-stage subsystem of a wafer fabrication facility (wafer fab), comprised of the diffusion furnace (a batch processor) and its upstream serial processor, with random job arrivals. We hypothesise that allowing the serial processor to anticipate the job family preference of the batch processor will reduce the overall cycle time of jobs passing through this system. To evaluate this hypothesis, we model the performance of the two-stage system under different system parameters and processor control policies as discrete state continuous time Markov chains. We characterise the system performance and show that the concept of constraining the production of the upstream processor according to the anticipated needs of the batch processor can reduce the mean cycle time of jobs being processed. We also perform simulation experiments to show that a simple heuristic based on this insight can translate to substantial cycle time reductions for systems with assumptions closer to those found in wafer fabs.

We consider the problem of scheduling semiconductor burn-in operations, where burn-in ovens are modelled as batch processing machines. Most of the studies assume that ready times and due dates of jobs are agreeable (i.e., ri < rj implies di ≤ dj). In many real world applications, the agreeable property assumption does not hold. Therefore, in this paper, scheduling of a single burn-in oven with non-agreeable release times and due dates along with non-identical job sizes as well as non-identical processing of time problem is formulated as a Non-Linear (0-1) Integer Programming optimisation problem. The objective measure of the problem is minimising the maximum completion time (makespan) of all jobs. Due to computational intractability, we have proposed four variants of a two-phase greedy heuristic algorithm. Computational experiments indicate that two out of four proposed algorithms have excellent average performance and also capable of solving any large-scale real life problems with a relatively low computational effort on a Pentium IV computer.

In this paper, we consider the problem of scheduling semiconductor burn-in operation, where the burn-in oven is modelled as a batch processing machine. In this study, both oven capacity and the number of boards available are taken as constraints. The objective measure of the problem is minimising the total completion time of all jobs. The computational difficulty in getting optimal solution is shown empirically. Since the problem under study is NP-hard, two variants of Tabu Search method are proposed. A series of computational experiments show that the proposed variants of Tabu Search method outperforms the existing heuristic for most system configurations in very meagre CPU times on P4 machine.

Motivated by a major PC manufacturer in the consumer electronics industry, we study the problem of synchronisation of assembly manufacturing and final deliveries using air transportation to achieve accurate delivery with minimised delivery cost in consumer electronics supply chain (CESC). The customer orders are shipped to the customers by cargo flights. Orders are allocated to the available flight capacities based on customer delivery dates. Synchronisation is considered to match the assembly completion of each order with the departure time of its predetermined allocated flights. We break the synchronisation problem down into two sub-problems consisting of an air transportation allocation problem and an assembly scheduling problem. The first sub-problem is formulated as an Integer Linear Programming (ILP) model. Two solution methodologies are proposed for the second sub-problem. Computational results indicate that the proposed methodologies can achieve considerable cost reduction compared to the existing industry practice.