K. L. Mak

Scheduling trucks in container terminals using a genetic algorithm

Trucks are the most popular transport equipment in most mega-terminals, and scheduling them to minimize makespan is a challenge that this article addresses and attempts to resolve. Specifically, the problem of scheduling a fleet of trucks to perform a set of transportation jobs with sequence-dependent processing times and different ready times is investigated, and the use of a genetic algorithm (GA) to address the scheduling problem is proposed. The scheduling problem is formulated as a mixed integer program. It is noted that the scheduling problem is NP-hard and the computational effort required to solve even small-scale test problems is prohibitively large. A crossover scheme has been developed for the proposed GA. Computational experiments are carried out to compare the performance of the proposed GA with that of GAs using six popular crossover schemes. Computational results show that the proposed GA performs best, with its solutions on average 4.05% better than the best solutions found by the other six GAs.

Quay crane scheduling in container terminals

The problem of scheduling identical quay cranes moving along a common linear rail to handle containers for a ship is studied. The ship has a number of container-stacking compartments called bays, and only one quay crane can work on a bay at the same time. The objective of the scheduling problem is to find the work schedule for each quay crane which minimizes the ship’s stay time in port. Finding the optimal solution of the scheduling problem is computationally intractable and a heuristic is proposed to solve it. The heuristic first decomposes the difficult multi-crane scheduling problem into easier subproblems by partitioning the ship into a set of non-overlapping zones. The resulting subproblems for each possible partition are solved optimally by a simple rule. An effective algorithm for finding tight lower bounds is developed by modifying and enhancing an effective lower-bounding procedure proposed in the literature. Computational experiments were carried out to evaluate the performance of the heuristic on a set of test problems randomly generated based on typical terminal operations data. The computational results show that the heuristic can indeed find effective solutions for the scheduling problem, with the heuristic solutions on average 4.8% above their lower bounds.

An effective heuristic for scheduling a yard crane to handle jobs with different ready times

In land-constrained port container terminals, yard cranes are commonly used for handling containers in a container yard to load containers onto or unload containers from trucks. However, yard cranes are bulky, slow and need to move frequently between their work locations. As it is common that the container flow in a terminal is bottlenecked by yard crane operations, effective work schedules of yard cranes are needed to increase the terminal’s throughput. This article studies the problem of scheduling a yard crane to perform a given set of container handling jobs with different ready times. The objective is to minimize the sum of job waiting times. It is noted that the scheduling problem is NP-complete. This research develops a heuristic to solve the scheduling problem and an algorithm to find lower bounds for benchmarking the schedules found by the heuristic. The performance of the heuristic is evaluated by a set of test problems generated on the basis of real-life terminal operations data. Indeed, the computational results show that the proposed heuristic can find effective solutions for the scheduling problem.

Yard planning for vessel services with a cyclical calling pattern

In a land-scarce container terminal, congestions in the terminal yard due to highly concentrated workload often lead to unsatisfactory terminal productivity. Currently, yard planners use their experience to design a yard template for determining the storage locations of export containers to be loaded onto vessels deployed to services with a cyclical calling pattern. This article studies the problem of designing a yard template that balances the workload in an export yard. The template design problem is formulated as an integer program. It is found that the computational time required to optimally solve realistic sizes of the template design problem is unacceptably long. This article proposes a simpler integer program as an approximate model. On the basis of the analysis on the approximate model, a heuristic is developed to solve the template design problem. Results of computational experiments show that the heuristic can find effective solutions for the template design problem.

The determination of optimal partial fill policy for an inventory system with lumpy demand items

This paper presents a mathematical model developed for the synthesis of optimal replenishment policies for items that experience lumpy demands. In order to avoid disrupting the inventory system, a cutoff point of w units is introduced such that the system would only satisfy routinely customer orders with transaction sizes less than or equal to w units. For customer orders with transaction sizes larger than w units, the system would only supply the cutoff amount (w units). The excess units would be refused. The control discipline is the (s, S) inventory policy with continuous review, and the nature of the customer orders is approximated by a discrete stuttering Poisson distribution. The optimal values of the control parameters, w, s and S, are determined. The theoretical results obtained are illustrated with a numerical example.

A Markov chain analysis of genetic algorithms with individuals having different birth and survival rates

This article studies the convergence characteristics of a genetic algorithm (GA) in which individuals of different age groups in the population possess different survival and birth rates. The inclusion of this feature into the algorithm makes the algorithm mimic the natural evolutionary process more closely than the conventional GA. Although numerical experiments have demonstrated that the proposed algorithm tends to perform better than the conventional GA when used as a function optimizer, the population size of the algorithm is affected by the survival and birth rates of the individuals, which may lead to an unstable search process. Hence, this research develops the condition which governs the birth and survival rates for maintaining a stationary population size during the search process. The Markov chain approach is also used to analyze the convergence characteristics of the algorithm. The proposed algorithm is shown to converge to the global optimal solution if the best candidate solution is maintained over time. The mathematical analysis thus provides a theoretical foundation for the application of the proposed approach as a function optimizer. The performance of the proposed algorithm is tested by solving two benchmark test problems and the results are compared to those obtained by using the conventional GA. Indeed, comparison of the results clearly shows that the proposed approach is superior to the canonical genetic algorithm in terms of the quality of the final solution. The algorithm is described in some detail in the hope of thus stimulating the use of the proposed genetic approach to the solution of important problems in industrial engineering practice.

SYNTHESIS OF KANBAN CONTROL POLICIES FOR MULTI-STAGE JUST-IN-TIME ASSEMBLY SYSTEMS

This paper studies the problem of determining the number of Kanbans that should be assigned to each production slage of a multi-stage assembly system in a just-in-time production environment. The objective is to minimize the inventory cost of the system. A new algorithm is developed as a means of solving such a problem. The approach is described in some detail and the theoretical results obtained are illustrated by using a numerical example. A set of randomly generated test problems are also included to illustrate the performance of the algorithm. The results show that the algorithm proposed in this paper is indeed superior both in terms of minimizing Ihe required amount of computational effort and improving accuracy.

MANPOWER PLANNING FOR MIXED-MODEL ASSEMBLY LINES IN JUST-IN-TIME MANUFACTURING SYSTEMS

This paper studies the problem of determining the optimal number of workers in each station and the optimal amount of overtime used to meet the workload requirements associated with a given assembly sequence for a just-in-time mixed-model assembly line. The problem is formulated as an integer program which minimizes the sum of the work force adjustment cost and the overtime cost. A polynomial time-bounded algorithm is developed to solve the problem optimally. A numerical example is used to illustrate the procedure of the algorithm.

Function optimization by using genetic algorithms with individuals having different birth and survival rates

Abstract This paper proposes an effective approach to function optimisation using the concept of genetic algorithms. The proposed approach differs from the canonical genetic algorithm in that the populations of candidate solutions consist of individuals from various age-groups, and each individual is incorporated with an age attribute to enable its birth and survival rates to be governed by predefined aging patterns. In order to ensure a stable search process, the condition that governs the relationships among the various birth and survival rates is determined. By generating tbe evolution of the populations with the genetic operators of selection, crossover and mutation, the proposed approach can provide excellent results by maintaining a better balance between exploitation and exploration of the solution space. A thorough study on the effects of the genetic parameters is carried out to examine the convergence behaviour of the proposed approach, and the findings illustrate how the convergence rate and the solutions quality are affected by the changes in the genetic parameters. The results of applying the proposed approach to solve five benchmark lest problems are compared with those obtained by using the canonical genetic algorithm. Indeed, the proposed approachs performance is shown to surpass those of the canonical genetic algorithm

SYNTHESIS OF JOINT REPLENISHMENT POLICIES FOR INVENTORY SYSTEMS WHEN DEMAND IS LUMPY

This paper is concerned with the synthesis of control policies for inventory systems in which the items experience lumpy demands. The nature of the customer demands is approximated by a discrete stuttering Poisson distribution and a continuous review (s,S) inventory policy is used to control such items. A cutoff point is also incorporated into the control policy such that customer orders with transaction sizes greater than the cutoff point will be filtered out of the inventory system and satisfied by placing a special replenishment order to a higher echelon. Customer orders with transaction sizes less than or equal to the cutoff point will be met from stock. It is also specified that if the available inventory is below the order-up-to level S at the time when a special replenishment order is placed, such a replenishment order will also raise the available inventory level to S. A search procedure is presented for determining the optimal values of the control parameters w, j and S. A numerical example is us...