Tardiness Penalty Cost Research Articles

A deep reinforcement learning based algorithm for a distributed precast concrete production scheduling

The environmental-friendly production demands higher manufacturing efficiency and lower energy cost; therefore, time-of-use electricity price constraint and distributed production have attracted more attention. For concrete precast architecture construction, the tardiness penalty and warehouse cost cannot be ignored, which should be optimized for lower cost. In this study, the concrete precast process is investigated as the group scheduling of a distributed flexible job shop problem. Each concrete precast is managed in a group, the setup time between different groups is considered. Two objectives, total weighted earliness and tardiness and total time-of-use electricity cost are minimized, simultaneously. To solve the integrated problem, three coordinated double deep Q-networks (DQN) are applied, which are organized as a learn-to-improve reinforcement learning approach. For distributed scheduling problem, operators in a single factory or in multiple factories differs in solution improvement; so selection DQN is designed to decide the type of the operators according to scheduling circumstances. Other two DQNs, i.e., local DQN and global DQN, are to select the optimization operators in one factory or in multiple factories, respectively. Furthermore, two solution refinement strategies are designed to decrease the objectives after reinforcement learning component. Numerical experiment and statistical analysis suggest that the proposed deep reinforcement learning based algorithm has superiority in solving the considered problem.

Exact and matheuristic methods for the parallel machine scheduling and location problem with delivery time and due date

The scheduling and location (ScheLoc) problem is a new and important research topic with a wide range of practical applications. It jointly optimizes machine locations, job assignments, and sequence decisions to yield a globally optimal solution. Current studies on the ScheLoc problem are limited, and most have focused on makespan minimization. This paper investigates a new variant of the parallel-machine ScheLoc problem with job delivery time and due date considerations. This is motivated by practical situations where jobs must be transported back to their original locations upon completion of processing, and a specific due date is associated with each job. The objective is to minimize the total weighted sum of location, transportation, and tardiness penalty costs incurred if a job is delivered after its due date. We propose three models adapted from classic ones for scheduling problems. We then develop an exact logic-based Benders decomposition method, which decomposes the problem into a master problem (MP) for determining machine locations and job assignments, and a subproblem (SP) for determining job sequences on each machine. The MP is augmented by dynamically adding optimality cuts generated by solving the SP. We also develop a matheuristic (MH) and its variant to achieve near-optimal solutions. An approximate model with predetermined job processing sequences on each machine is formulated and solved to determine the machine locations and job assignments. The obtained solutions are further improved by solving a series of single-machine scheduling problems. The variant combines a kernel search framework to make MH more efficient. Computational experiments on 720 randomly generated instances show the effectiveness and efficiency of both the exact and matheuristic methods.

Multi-project scheduling with multi-skilled workforce assignment considering uncertainty and learning effect for large-scale equipment manufacturer

This study addresses a resource-constrained multi-project scheduling and multi-skilled workforce assignment problem for the large-scale equipment manufacturing industry. The goal is to help the production manager perform effective planning and decrease the production cost under delivery constraints. The deterministic duration is used in most past investigations in resource-constrained multi-project scheduling problems. Uncertainty in project execution is neglected. Additional related factors are included in the current study to be close to practical circumstances. The required processing duration and material arrival time are modeled as stochastic variables. The heterogeneous skill efficiency of the internal workforce is considered with the learning effect. Skill efficiency grows with the accumulation of experience. Actual processing time is calculated on the basis of skill efficiency and stochastic process duration. The external workforce is hired when the internal workforce fails to satisfy processing demand. The objective is to minimize the expected integrated cost, which is the sum of tardiness penalty and external workforce cost. A genetic algorithm with a heuristic workforce assignment method is also developed, and a case study is illustrated to explain the scheduling result. The proposed approach with uniform crossover and local search mechanism outperforms other comparative methods by approximately 10.34% considering total costs. Furthermore, the Taguchi method of design of the experiment is conducted to find the optimal parameter setting efficiently. Afterward, the sensitivity analysis of production-related parameters is discussed.

Integrated Production and Maintenance Scheduling with Environmental and Operational Considerations

In this paper, we present an integrated production-maintenance scheduling problem with economic and ecological considerations. The contribution of our study consists in developing a new analytical model which determines, an optimal sequence of production and maintenance minimizing earliness and tardiness penalty costs as well as harmful emissions (CO2) cost due to degradation of production system. This study addresses the problem of the single machine where the machine follows a failure law. Each time the machine's degradation rate reaches a predefined threshold (λthreshold), preventive maintenance (PM) is carried out throughout optimal periods. The maintenance strategy adopted makes it possible to define the age of preventive maintenance T* corresponding to a minimum total cost of preventive and corrective maintenance. We consider the result of this strategy as a strong constraint in order to determine an optimal integrated scheduling of production and maintenance. We provide illustrative numerical examples as well as sensitivity analysis to show the applicability of our approaches and provide.

Parallel-Machine Scheduling to Minimize Tardiness Penalty and Energy Cost by using Evolutionary Algorithms

Parallel-Machine Scheduling to Minimize Tardiness Penalty and Energy Cost by using Evolutionary Algorithms

A production and distribution framework: Manufacturer dominates

This paper presents a two-stage supply chain problem at the operational level involving a manufacturer and a third-party logistics provider (3PL provider). The integrated problem consists of two subproblems: An m-machine permutation flow shop with inventory considerations for the manufacturer and a routing problem for the 3PL provider. Both agents face tardiness penalty costs in case of late delivery to the customer locations. Assuming imperfect information sharing between the two agents and independence in their own decisions, we investigate the scenario in which the manufacturer dominates the negotiation.In this scenario, the manufacturer imposes the number and composition of vehicles as well as the vehicle departure dates on the 3PL provider. However, lacking the information regarding the actual delivery times he is forced to estimate delivery times at the customer locations in the context of his planning. Following the planning of the manufacturer, the 3PL provider decides on the optimal routing of the vehicles. Both agents aim to minimise their total costs. After formulating the problems as a mixed integer linear program, two metaheuristic algorithms are proposed to solve the scenario. The performance of the heuristics is evaluated on a set of randomly generated instances. The results show that the genetic algorithm is the best performing method.

Optimal berth allocation under regular and emergent vessel arrivals

This research proposes two optimization models to deal with the berth allocation problem. The first model considers the berth allocation problem under regular vessel arrivals to minimize the flow time of vessels in the marine container terminal, minimize the tardiness penalty costs, and maximize the satisfaction level of vessels’ operators on preferred times of departure. The second model optimizes the berth allocation problem under emergency conditions by maximizing the number of assigned vessels, minimizing the vessel’s waiting time, and maximizing the satisfaction level on the served ships. Two real examples are provided for model illustration under regular and emergent vessel arrivals. Results show that the proposed models effectively provide optimal vessel scheduling in the terminal, reduce costs at an acceptable satisfaction level of vessels’ operators, decrease the waiting time of vessels, and shorten the delay in departures under both regular and emergent vessel arrivals. In conclusion, the proposed models may provide valuable assistance to decision-makers in marine container terminals on determining optimal berth allocation under daily and emergency vessel arrivals. Future research considers quay crane assignment and scheduling problems.

Minimizing Tardiness Penalty Costs in Job Shop Scheduling under Maximum Allowable Tardiness

In many manufacturing or service industries, there exists maximum allowable tardiness for orders, according to purchase contracts between the customers and suppliers. Customers may cancel their orders and request compensation for damages, for breach of contract, when the delivery time is expected to exceed maximum allowable tardiness, whereas they may accept the delayed delivery of orders with a reasonable discount of price within maximum allowable tardiness. Although many research works have been produced on the job shop scheduling problem relating to minimizing total tardiness, none of them have yet considered problems with maximum allowable tardiness. In this study, we solve a job shop scheduling problem under maximum allowable tardiness, with the objective of minimizing tardiness penalty costs. Two kinds of penalty costs are considered, i.e., one for tardy jobs, and the other for canceled jobs. To deal with this problem within a reasonable time at actual production facilities, we propose several dispatching rules by extending well-known dispatching rules for the job shop scheduling problem, in cooperation with a probabilistic conception of those rules. To evaluate the proposed rules, computational experiments were carried out on 300 test instances. The test results show that the suggested probabilistic dispatching rules work better than the existing rules and the optimization solver CPLEX, with a time limit.

Multitasking scheduling with batch distribution and due date assignment

This study addresses the multitasking scheduling problems with batch distribution and due date assignment (DDA). Compared with classical scheduling problems with due date-related optimization functions, the job due dates are decision variables rather than given parameters. The jobs completed are distributed in batches, and the sizes of all batches are identical, which may be bounded or unbounded. The jobs in every batch are scheduled one by one. Each batch incurs a fixed cost. Under multitasking environment, it allows the machine to put an uncompleted job on hold and turn to another uncompleted job. The goal is to identify the optimal primary job sequence, the optimal job due dates, and the optimal batch production and distribution strategy so that one of the following two optimization functions is minimised: the total cost composed of the earliness penalty, DDA cost, tardiness penalty and batch distribution cost, and the total cost composed of the earliness penalty, weighted number of late jobs, DDA cost and batch distribution cost. We devise efficient exact algorithms for the problems we consider, and perform numerical experiments to check how multitasking affects the scheduling cost or value, the results of which can assist decision-makers to justify the extent to put to use or refrain from multitasking.

Scheduling two projects with controllable processing times in a single-machine environment

We consider two single-machine scheduling problems in which two competing projects share one common resource. Each project has multiple interim assessments, and its own jobs are ordered completely. A tardy job incurs a tardiness penalty cost which can be avoided by compressing some jobs, which requires an additional cost. The performance measure of each project is the total tardiness penalty cost plus the total compression cost. The first problem minimizes the weighted sum of the performance measures of two projects, and the second problem minimizes the performance measure of one project with a constraint on that of the other. We show that the first problem is solvable in strongly polynomial time and the second is weakly NP-hard. Furthermore, we analyze how the computational complexity of each problem changes if the number of projects is more than two.

Solving a flexible job shop lot sizing problem with shared operations using a self-adaptive COA

This paper deals with lot sizing decisions in a flexible job shop manufacturing system considering dependencies between lot sizing decisions. A novel mathematical model is developed to optimise lot sizing and scheduling simultaneously using a product-oriented approach as opposed to the job-oriented approach which has been prevalently considered in the literature. Moreover, the proposed model considers further underlying assumptions such as assembly operations, sequence-dependent setup times, initial inventory and safety stock levels, as well as lots with unequal and variable sizes. The objective is to minimise the total production, setup, and tardiness penalty costs of the system. To solve the formulated problem, a self-adaptive Cuckoo Optimisation Algorithm (COA) embedded with three new immigration mechanisms is developed. Numerical experiments are conducted to demonstrate the validity of the model and investigate the efficiency and effectiveness of the employed optimisation algorithm.

Production Scheduling Optimization Algorithm for the Steel-Making Continuous Casting Processes

This paper investigates steel-making continuous casting (SCC) scheduling problem. SCC is a high temperature and large-scale logistics machining process with batch production at the last stage that was identified as the key process of modern iron and steel enterprises. This paper presents a mathematical model for scheduling SCC process. The model is developed as a Mixed Zero- One Linear programming (MZOLP) based on actual production situations of SCC. The objective is to schedule a set of charges (jobs) to minimize the earliness and tardiness penalty costs as well as the charge waiting time cost. The solution methodology is developed based on a branch-and-bound algorithm. A heuristic method is presented at the beginning of the search in order to compute an initial upper bound. A lower bound and an upper bound are developed and a method for reducing branches is established based on the batch production in the continuous casting (CC) stage. Moreover, branching schemes are proposed. The branch- and- bound algorithm incorporating the initial upper bound, the lower and upper bound, the method for reducing branches, and branching schemes is tested on a set of instances. The analysis shows the efficiency of the proposed features for the algorithm.

Multi-agent supply chain scheduling problem by considering resource allocation and transportation

Today in the global market competition, integration issue in supply chain is considered as an important principle. In this study, for the first time, different requirements of the customers and different aims of the manufacturer are simultaneously addressed in an integrated problem of production scheduling, transportation, and resource allocation. The problem consists of two types of customers, considered as the agents. The first agent accepts tardiness in delivery of orders provided that the manufacturer pays the tardiness penalty; whereas, the second agent does not accept the tardy orders. The purpose is to minimize the sum of batch delivery cost, resource allocation, tardiness penalty cost, and lost sale cost (the total number of tardy orders). To solve the problem, two mathematical programming models, including a Mixed Integer Non-Linear Programming (MINLP) and a Mixed Integer Linear Programming (MILP) are proposed. Also, due to NP-hard nature of the problem, two meta-heuristic algorithms of Adaptive Genetic Algorithm (AGA) and Ant Lion Optimization (ALO), as well as a heuristic algorithm are proposed. To assess the merits of the solution methods, small and large-scale tests are designed. The results indicate the superiority of adaptive genetic algorithm in comparison with other algorithms.

Optimal procurement strategies for contractual assembly systems with fluctuating procurement price

We consider a multi-component assembly system that produces a single end product in order to satisfy the one-time demand at a (known) future time with an exogenous selling price. Components can be outsourced from outside suppliers with positive leadtimes under either time-inflexible or time-flexible contracts. One of these components, say component 1, faces an uncertainty in its procurement price, depending on the spot market price that is governed by a geometric Brownian motion, while the prices of other components are constant. Given supply contracts, the assembler needs to determine the procurement strategy to maximize the total expected profit that equals the expected revenue minus procurement cost, holding cost, and tardiness penalty cost. Under time-inflexible contracts, the problem is static and a variant of the classic newsvendor problem. We show that leadtime uncertainty will cause the assembler to be more conservative in procurement quantity, but more aggressive in procurement timing than if the leadtime is deterministic. For time-flexible contracts, we show that under certain conditions, the original problem is equivalent to an optimal single stopping problem whose optimal strategies follow either upward or downward base-price procurement policies. Under the general condition, we propose an efficient Monte Carlo simulation method to calculate the optimal solutions. Numerical studies also provide several interesting insights: first, both procurement quantity and profit are non-monotone in the leadtime length; second, the value of time-flexible contracts compared to time-inflexible contracts is close to zero if the price of component 1 has a decreasing trend, but otherwise significant.

A linear time-cost tradeoff problem with multiple interim assessments within multiple projects in parallel

We consider a project scheduling problem in which the jobs can be compressed by using additional resources to meet the corresponding due dates. The project consists of multiple independent subprojects with completely ordered jobs. Some jobs have their own due dates for interim assessments of whole project. A penalty cost arises from the tardiness of a job, but it can be avoided through the compression of some jobs, which requires an additional cost. The objective is to minimize the total tardiness penalty and compression costs. We investigate optimality properties and develop an algorithm to find an optimal schedule in strongly polynomial time.

Multi-objective fuzzy parallel machine scheduling problems under fuzzy job deterioration and learning effects

This paper investigates a multi-objective parallel machine scheduling problem under fully fuzzy environment with fuzzy job deterioration effect, fuzzy learning effect and fuzzy processing times. Due dates are decision variables for the problem and objective functions are to minimise total tardiness penalty cost, to minimise earliness penalty cost and to minimise cost of setting due dates. Due date assignment problems are significant for Just-in-Time (JIT) thought. A JIT company may want to have optimum schedule by minimising cost combination of earliness, tardiness and setting due dates. In this paper, we compare different approaches for modelling fuzzy mathematical programming models with a local search algorithm based on expected values of fuzzy parameters such as job deterioration effect, learning effect and processing times.

New Properties for Solving the Single-Machine Scheduling Problem with Early/Tardy Jobs

AbstractThis paper presents a mathematically enhanced genetic algorithm (MEGA) using the mathematical properties of the single-machine scheduling of multiple jobs with a common due date. The objective of the problem is to minimize the sum of earliness and tardiness penalty costs in order to encourage the completion time of each job as close as possible to the common due date. The importance of the problem is derived from its NP-hardness and its ideal modeling of just-in-time concept. This philosophy becomes very significant in modern manufacturing and service systems, where policy makers emphasize that a job should be completed as close as possible to its due date. That is to avoid inventory costs and loss of customer’s goodwill. Five mathematical properties are identified and integrated into a genetic algorithm search process to avoid premature convergence, reduce computational effort, and produce high-quality solutions. The computational results demonstrate the significant impact of the introduced properties on the efficiency and effectiveness of MEGA and its competitiveness to state-of-the-art approaches.

A multi-period facility location problem with modular capacity adjustments and flexible demand fulfillment

We consider a multi-period facility location problem that takes into account changing trends in customer demands and costs. To this end, new facilities can be established at pre-specified potential locations and initially existing facilities can be closed over a planning horizon. Furthermore, facilities operate with modular capacities that can be expanded or contracted over multiple periods. A distinctive feature of our problem is that two customer segments are considered with different sensitivity to delivery lead times. Customers in the first segment require timely demand satisfaction, whereas customers in the second segment tolerate late deliveries. A tardiness penalty cost is incurred to each unit of demand that is satisfied with delay. We propose two alternative mixed-integer linear formulations to redesign the facility network over the planning horizon at minimum cost. Additional inequalities are developed to enhance the original formulations. A computational study is performed with randomly generated instances and using a general-purpose solver. Useful insights are derived from analyzing the impact of several parameters on network redesign decisions and on the overall cost, such as different demand patterns and varying values for the maximum delivery delay tolerated by individual customers.

Resource Tardiness Weighted Cost Minimization in Project Scheduling

In this paper, we study a project scheduling problem that is called resource constrained project scheduling problem under minimization of total weighted resource tardiness penalty cost (RCPSP-TWRTPC). In this problem, the project is subject to renewable resources, each renewable resource is available for limited time periods during the project life cycle, and keeping the resource for each extra period results in some tardiness penalty cost. We introduce a branch and bound algorithm to solve the problem exactly and use several bounding, fathoming, and dominance rules in our algorithm to shorten the enumeration process. We point out parameters affecting the RCPSP-TWRTPC degree of difficulty, generate extensive sets of sample instances for the problem, and perform comprehensive experimental analysis using the customized algorithm and also CPLEX solver. We analyze the algorithm behavior with respect to the changes in instances degree of difficulty and compare its performance for different cases with the CPLEX solver. The results reveal algorithm efficiency.

A robust multi-trip vehicle routing problem of perishable products with intermediate depots and time windows

Distribution of products within the supply chain with the highest quality is one of the most important competitive activities in industries with perishable products. Companies should pay much attention to the distribution during the design of their optimal supply chain. In this paper, a robust multi-trip vehicle routing problem with intermediate depots and time windows is formulated to deals with the uncertainty nature of demand parameter. A mixed integer linear programming model is presented to minimize total traveled distance, vehicles usage costs, earliness and tardiness penalty costs of services, and determine optimal routes for vehicles so that all customers' demands are covered. A number of random instances in different sizes (small, medium, and large) are generated and solved by CPLEX solver of GAMS to evaluate the robustness of the model and prove the model validation. Finally, a sensitivity analysis is applied to study the impact of the maximum available time for vehicles on the objective function value.