Multiple Due Dates Research Articles

Scheduling a single machine with multiple due dates per job

AbstractIn this paper, we consider single-machine scheduling with multiple due dates per job. This is motivated by several industrial applications, where it is not important by how much we miss a due date. Instead the relevant objective is to minimize the number of missed due dates. Typically, this situation emerges whenever fixed delivery appointments are chosen in advance, such as in the production of individualized pharmaceuticals or when customers can only receive goods at certain days in the week, due to constraints in their warehouse operation. We compare this previously unexplored problem with classical due date scheduling, for which it is a generalization. We show that single-machine scheduling with multiple due dates is NP-hard in the strong sense if processing times are job dependent. If processing times are equal for all jobs, then single-machine scheduling with multiple due dates is at least as hard as the long-standing open problem of weighted tardiness with equal processing times and release dates $$1 \mid r_j, p_j = p \mid \sum w_j T_j$$ 1 ∣ r j , p j = p ∣ ∑ w j T j . Finally, we focus on the case of equal processing times and provide several polynomially solvable special cases as well as an exact branch-and-bound algorithm and heuristics for the general case. Experiments show that our branch-and-bound algorithm compares well to modern exact methods to solve problem $$1 \mid r_j, p_j = p \mid \sum w_{j} T_{j}$$ 1 ∣ r j , p j = p ∣ ∑ w j T j .

Spatial and temporal optimization for smart warehouses with fast turnover

With the rapid development of e-commerce and the new retail, the same-day or even same-half day delivery service is provided to compete for market share. Recently, an increased number of e-commerce companies implement the unmanned smart warehouses to improve the logistics efficiency. In order to further reduce the demand response time, a novel picking strategy is designed to firstly split the orders, and then assign the partial orders to different pickers. After all the order segments have been collected, it is shipped to the customer. Due to the inherent complexity of the problem, a two stage optimization model is introduced. In the first stage, an order splitting and batching strategy based on spatial measure is proposed. And a MIP model is constructed to minimize the total picking distance, which is then solved via a column generation based algorithm. In the second stage, the newly formed batches are considered as a priori inputs, which are then assigned to automatic pickers. The picking process is modeled as a special parallel machine scheduling problem with multiple due dates for a single item, which could reduce to a customer order scheduling problem on parallel machines, and it is unary NP-complete. A heuristic method is proposed to obtain an approximate solution. Although the order splitting technique is not new in the logistics industry, the split orders are picked according to a vehicle routing problem, which fails to address the kitting issue for fast turnovers. In the numerical analysis section, the proposed algorithm is validated through extensive testing on various scales of instances. It is observed that the optimality gap for our algorithm is within 9%, and the computation time is around 5 min. Also, the average turnover rate increases by approximately 50% in comparison with the no-splitting policy. In most cases, the average order tardiness decreases by 90% compared with order splitting and no-kitting policy.

A Model of Batch Scheduling for a Single Batch Processor with Additional Setups to Minimize Total Inventory Holding Cost of Parts of a Single Item Requested at Multi-due-date

This paper deals with a model of batch scheduling for a single batch processor on which a number of parts of a single items are to be processed. The process needs two kinds of setups, i. e., main setups required before processing any batches, and additional setups required repeatedly after the batch processor completes a certain number of batches. The parts to be processed arrive at the shop floor at the times coinciding with their respective starting times of processing, and the completed parts are to be delivered at multiple due dates. The objective adopted for the model is that of minimizing total inventory holding cost consisting of holding cost per unit time for a part in completed batches, and that in in-process batches. The formulation of total inventory holding cost is derived from the so-called actual flow time defined as the interval between arrival times of parts at the production line and delivery times of the completed parts. The actual flow time satisfies not only minimum inventory but also arrival and delivery just in times. An algorithm to solve the model is proposed and a numerical example is shown.

Production and Delivery Batch Scheduling with Multiple Due Dates to Minimize Total Cost

This paper addresses an integrated production and delivery batch scheduling problem for a make-to-order environment over daily time period, where the holding costs of in-process and completed parts at a supplier location and of completed parts at a manufacturer location are distinguished. All orders of parts with different due dates from the manufacturer arrive at the same time. The parts are produced in production batches and subsequently the completed parts are delivered in delivery batches using a capacitated vehicle in order to be received at the respective due dates. This study was aimed at finding an integrated schedule of production and delivery batches so as to meet the due date at minimum total cost consisting of the corresponding holding cost and delivery cost. The holding cost is a derivation of the so-called actual flow time (AFT), while the delivery cost is assumed to be proportional to the number of deliveries. The problems can be formulated as an integer non-linear programming model, and the global optimal solution can be obtained using optimization software. A heuristic algorithm is proposed to cope with the computational time problem using software. The numerical experiences show that the proposed algorithm yields near global optimal solutions.

A General Modeling Framework for the Long-Term Scheduling of Multiproduct Pipelines with Delivery Constraints

Common carrier pipelines are one of the most economic modes for transportation of petroleum refined products over land, especially when huge amounts of these products have to be pumped toward long-distance terminals. This paper introduces a novel Mixed Integer Linear Programming (MILP)-based approach for the long-term scheduling of a real world multiproduct pipeline connecting a unique refinery to several distribution centers. This approach allows consideration of multiple due dates for demands at period ends, flow rate limitation on pipeline segments, and simultaneous deliveries at distribution centers. The proposed model results in substantial reduction in pump operation and maintenance costs in comparison with the available models. Computational results and data are reported.

Single machine scheduling to minimize a modified total late work function with multiple due dates

In this paper, the problem of scheduling n jobs on a single machine is evaluated. We introduce a Modified Total Late Work function that allows a declining piecewise linear penalty over time. Multiple due dates for each job are identified and at each due date, the penalty is reassessed. Many instances occur when delivery urgency leads to progress metrics or dates being added to a contract. Over the life of the contract, a loss of incentives or a price decrease can occur at each of the negotiated due dates. After the final due date, the product is valueless and the penalty ceases to accrue. The number and placement of contract due dates are part of the initial negotiations. Two metaheuristics, Simulated Annealing and the Noising Method, are empirically evaluated to determine their performance when measured by this new loss function.

Single CNC machine scheduling with controllable processing times and multiple due dates

In this study, we solve the single CNC machine scheduling problem with controllable processing times. Our objective is to maximize the total profit that is composed of the revenue generated by the set of scheduled jobs minus the sum of total weighted earliness and weighted tardiness, tooling and machining costs. Customers offer multiple due dates to the manufacturer, each coming with a distinct price for the order that is decreasing as the date gets later, and the manufacturer has the flexibility to accept or reject the orders. We propose a number of ranking rules and scheduling algorithms that we employ in a four-stage heuristic algorithm that determines the processing times for each job and a final schedule for the accepted jobs simultaneously, to maximize the overall profit.

Optimal production scheduling for the dairy industry

The increasing variety of products offered by the food industry has helped the industry to respond to market trends, but at the same time has resulted in a more complex production process, which requires flexibility and an efficient coordination of existing resources. Especially in industrial yogurt production, there is a wide variety of products that differ in features like fat content, the whey used to produce the mixture, the flavor, the size of the container or the language on the label. The great diversification and the special features that characterize yogurt production lines (satisfaction of multiple due dates, variable processing times, sequence-dependent setup times and costs and monitoring of inventory levels), render generic scheduling methodologies impractical for real-world applications. In this work we present a customized Mixed Integer Linear Programming (MILP) model for optimizing yogurt packaging lines that consist of multiple parallel machines. The model is characterized by parsimony in the utilization of binary variables and necessitates the use of only a small pre-determined number of time periods. The efficiency of the proposed model is illustrated through its application to the yogurt production plant of a leading dairy product manufacturing company in Greece.

Beam search filtrado com inserção de ociosidade na programação de uma máquina em ambiente do tipo jit

Este trabalho avalia a utilização do beam search filtrado (BSF) combinado com um algoritmo de inserção de ociosidade (AIO). O caso estudado é baseado em uma única máquina, com datas de entrega múltiplas e com penalidades distintas de adiantamento e de atraso para cada ordem. O objetivo a ser alcançado é a minimização do custo total. Para isso, o BSF é utilizado para gerar as seqüências, e o AIO, para definir os programas. Assume-se que a dificuldade de solução do problema é dependente de dois parâmetros: fator de atraso médio e amplitude relativa das datas de entrega. Testes empíricos comparativos são realizados por meio de simulação computacional, no qual se mede o tempo de solução e o valor alcançado pela função-objetivo. Os resultados indicam que de uma forma geral, o procedimento proposto propicia uma diminuição no custo total e, além disso, que para a escolha de um procedimento apropriado, o ideal é se conhecer o valor dos parâmetros.

On the fixed interval due-date scheduling problem

We consider the nonpreemptive single machine scheduling problem with multiple due-dates (delivery dates), where the time between two consecutive due-dates is a constant. Given a set of jobs, we are interested in scheduling the jobs such that the sum of the total due-date cost and the total earliness cost is minimized with the constraint that each job must be finished at or before its due-date. We show that this problem is strongly NP-hard in general. We then analyze the problem where the number of due-dates is bounded by a given constant. We describe a pseudo-polynomial dynamic programming algorithm for this restricted problem. A heuristic is also provided and worst-case analysis is performed. An efficient algorithm is developed to solve the special case where all the job processing times are identical.

A Single Machine Model for Determination of Optimal Due Dates and Sequence

The problem of simultaneous determination of optimal due dates and optimal sequence for N-job single machine problem with multiple due dates is considered in this paper. The penalty for a job is assumed to be a linear function of the due date and the earliness/tardiness for the job. The objective is to minimize the total penalty for all jobs. An efficient optimal algorithm to solve the problem is developed and several results are provided.