Disassembly line balancing and sequencing (DLBS) problem has received considerable attention from both enterprises and researchers, driven by its significant impact on end-of-life (EOL) product processing efficiency. Most existing studies focus on parallel lines with shared workstations, handling different products simultaneously. However, the consecutive connected lines, implemented in practice for processing complex EOL products, remain unexplored in the existing literature. This study addresses the parallel DLBS problem considering line consecutive connectivity, where products undergo initial disassembly on the main line before being transferred to branch lines for further processing, aiming to minimize the overall system cost. We propose a mixed-integer linear programming (MILP) model and then develop a customized logic-based Benders decomposition (LBBD) approach to improve computational efficiency. The LBBD method divides the problem into a master task assignment problem, which is enhanced by some valid inequalities and solved in the branch-and-cut framework, and a task sequencing subproblem, tackled via the dynamic programming approach. Numerical results demonstrate the effectiveness and efficiency of our proposed LBBD algorithm.

This paper studies a single-machine scheduling problem with learning dates to minimize the makespan. Each job has a distinct learning date, and its processing time differs before and after the learning date. All jobs have the same learning ratio, i.e., the ratio of the processing time after learning to that before learning is ρ(0<ρ<1) for each job. We consider two variants of the problem according to whether the jobs are preemptible, namely the preemptive model and the non-preemptive model. For the preemptive case, we develop an O(nlogn)-time solution algorithm with at most one preemption. For the non-preemptive case, we show that the problem is NP-hard and design an approximation algorithm whose worst-case ratio is no greater than 1+ρ1+ρ2, with a time complexity of O(nlogn).

To address the issues of inaccurate expert weight allocation in existing large-group decision-making methods and information loss in multi-attribute group emergency decision-making processes, we propose a clustering-based method using the probabilistic hesitant fuzzy set. Recognizing the diverse contributions of the decision makers within each cluster-to-cluster consistency and the varied impacts of preferences in different clusters on overall group preference, we introduce a two-layer weight model. Specifically, from a two-dimensional viewpoint, we determine the weights of decision members within each cluster using an expert evaluation distance formula and the weights of each cluster using fuzzy entropy. Subsequently, by incorporating the Maclaurin symmetric mean operator (MSMO), we establish the ranking of decision alternatives. Finally, we assess the effectiveness and applicability of the proposed method by applying it to analyze the case of the Tonga volcanic eruption.

This article considers a parallel-machine scheduling problem in which machines are unavailable to process jobs for a specified period. The objective is to maximize the total amount of early work, where the early work of a job is the amount of processing time performed before its due date. Since this problem is NP-hard, we propose a pseudo-polynomial time dynamic programming algorithm, and based on it, we further provide a fully polynomial time approximation scheme. The time complexity of these two algorithms is relatively high; to this end, we also offer a 2-approximation ratio heuristic algorithm to help solve large-scale problems, and we show that the bound is tight.

Emergency logistics, as a specialized activity for providing support during emergencies, is gaining research attention worldwide. However, the existing research on the selection of emergency logistics suppliers often fails to fully consider the impact of the decision-maker’s psychological behavior on the decision outcome in a complex decision-making environment. We propose a decision-making framework based on the probabilistic hesitant fuzzy sets TODIM (PHFSs-TODIM) method and weighted models with different decision-makers and indicators to fill this gap. It extends the existing expert weights to incorporating both expert weights and ordered weights. Building upon this foundation, we introduce and enhance the TODIM method, enabling it to better integrate and prioritize the decision information. We validate the improved TODIM method through an example of flood prevention and relief in the Beijing-Tianjin-Hebei region, confirming its feasibility, rationality, and applicability, while showing the superiority of the proposed approach over two existing approaches.

While there is much research on coordinating the dual-channel supply chain using the revenue-sharing contract, it is unclear if there is a better mechanism design in the buy-online-and-pickup-in-store (BOPS) mode. In this channel integration environment, the customer service provided by the bricks-and-mortar store is critical to the chain's success. Based on a stackable game model, we analyze the contract methods for the cases of revenue sharing and no revenue sharing, where the latter is classified into two types: All the credit goes to the offline or online channel. Focusing on improving consumer service and supply chain performance in the BOPS mode, we observe that revenue sharing is not necessarily the best contract type, while the non-revenue-sharing contract of a lump-sum subsidy plus quantity discount can coordinate the supply chain. We also analyze the impacts of some endogenous parameters and derive the conditions for the equilibrium outcomes. We find that revenue sharing cannot effectively stimulate the offline channel to improve its service effort as the offline channel is more concerned about service cost sharing than revenue sharing. The results are similar to those of revenue allocation to the online or offline channel in the BOPS mode, but the conditions are slightly different. Conducting numerical studies to gain insights from the analytical findings, we find that the subsidy contract is better than the revenue-sharing approach under various market conditions.

We consider non-preemptive online parallel-machine scheduling with a common due date to maximize the total early work of all the jobs, i.e., the total processing time of the jobs (or parts) completed before the common due date. For the general case of m machines, we provide a parameter lower bound with respect to m. For the online algorithm, we first show that the tight competitive ratio of the classical list scheduling (LS) algorithm is 43. We then improve the upper bound on the competitive ratio for the previous algorithm, EFFm, to 1.2956. Additionally, we present a formula to compute the upper bound on the competitive ratio for any given m. For the case of three machines, we improve the lower bound to 1.1878 and propose an improved online algorithm with a tight competitive ratio of 1.2483.

In modern manufacturing and service industries, urgent orders and service tasks are common, and the speed of handling such urgent tasks is an important indicator of production and service efficiency. In this study, we consider scheduling jobs on two parallel machines with the random arrival of an emergency job. The objective is to minimise the makespan, subject to a given maximum waiting time of the emergency job. We first show that the worst-case ratio of the existing algorithm LPTl-SPTm-l is at least 3/2 when m = 2. We then analyse some properties of the optimal schedule and derive lower bounds on the optimal makespan. Finally, we present an improved approximation algorithm with a tight worst-case ratio of 4/3. We also provide numerical results showing that our proposed algorithm outperforms algorithm LPTl-SPTm-l.

Yield uncertainty presents great challenges to supply chain management, which affects market supply and thus the profits of all the supply chain parties. In the context of a supply chain comprising a retailer and multiple potential suppliers with random yields, we examine the impact of yield uncertainty on the suppliers' entry decisions, and how it affects the retailer's profit and consumer surplus. We find that yield uncertainty initially increases the number of suppliers entering the market, then decreases, and it is negatively correlated with consumer surplus. We also analyze how the retailer's purchasing price strategy influences the suppliers' decisions to enter the market. We find that retailer subsidies can improve the performance of and coordinate the supply chain. In addition, the subsidy contract is in the forms of production subsidy and surplus subsidy when the suppliers do not make and make production decisions, respectively.

In this paper, we study a single machine scheduling problem with group-dependent due window assignment and further incorporate autonomous and induced learning effects. Here, autonomous learning refers to learning by doing, while induced learning denotes that proactive investments can promote the learning effect, i.e., the learning effect is controllable. The proactive spending could include any management efforts like professional training programs, among others. The objective is to find optimal strategies of due window assignments, sequence of groups and jobs, and level of induced learning that optimize the total cost comprising the due window-related penalty costs and the investment cost. We present a polynomial-time algorithm capable of solving this problem and an improved idea to further reduce the time complexity. In addition, a detailed numerical example is conducted. Our study shows that the learning effect can be tuned to fit the demand of the manufacturing system better and lead to a more flexible operating system.

We present a unified approach to single-machine scheduling with position-based processing times, an availability constraint, and job rejection. The approach uses two general position-based processing time functions to model both the learning and aging effects in scheduling. In addition, taking machine availability and job rejection into consideration, the models are more realistic, which seek to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. We present fully polynomial-time approximation schemes to address the two NP-hard problems.

As commonly observed in practice, firms can accelerate job processing by adding additional resources to the manufacturing system while striving to sustain on-time delivery. In this paper we consider due date assignment and scheduling with a learning effect that can be invoked by proactive investment at the beginning, known as induced learning in the literature. The objective is to find the optimal decisions on due date assignment, job sequencing, and level of induced learning to minimize a cost function consisting of the total weighted number of tardy jobs, due date penalty, and investment cost. We find a novel property of the optimal solution that although the due date penalty may be larger, the number of on-time jobs will not decrease with the increasing induced learning effect, which is a breakthrough to solve the problem. Exploiting the property, we present a polynomial-time algorithm that generates an approximation solution with a gap less than LE compared with the optimal result, where c can tend to be infinitesimal, and L is a constant.

We consider bi-objective parallel-machine scheduling in green manufacturing to minimize the makespan and total processing cost. Each machine has a different constant processing cost per unit time. For the objective of minimizing the makespan, given a total cost budget, we provide an approximation algorithm with a worst-case ratio of 33+14≈1.686, which improves the previous bound of 2. For the objective of minimizing the total processing cost, subject to all the jobs must be completed before a given common deadline, we provide an approximation algorithm with a worst-case ratio of 2+r3, where r is the ratio of the maximum to the minimum processing cost per unit time on a machine.

Motivated by behavioural and psychological phenomena that occur in human operators, we study single-machine multitasking scheduling with job efficiency promotion. In traditional multitasking scheduling, the primary task is assumed to be interrupted by every waiting task. In this paper we take into account job efficiency promotion that helps reduce the actual interruption time. We propose two functions to model job efficiency promotion based on the job positions in a given schedule. The objective is to minimize the makespan, total completion time, and total absolute difference in completion times. We show that the problem is polynomially solvable for each objective. We also provide efficient solutions for some special cases.

We consider parallel-machine scheduling in the context of shared manufacturing where each job has a machine set to which it can be assigned for processing. Such a set is called the processing set. In the shared manufacturing setting, a job can be assigned not only to certain machines for processing, but can also be processed on the remaining machines at a certain cost. Compared with traditional scheduling with job rejection, the scheduling model under study embraces the notion of sustainable manufacturing. Showing that the problem is NP-hard, we develop a fully polynomial-time approximation scheme to solve the problem when the number of machines is fixed.

研究带有共同交货期的三台平行机排序问题.工件在加工过程中不允许中断,目标是极大化所有工件的提前完工量,即在交货期前所加工工件(或部分)的总加工时长.由于该问题是NP-难问题,本文应用经典LPT算法来解决该问题.我们证明了LPT算法求解该问题的最坏情况界至多为15,并给出实例说明最坏情况界的下界为27-25.

We consider parallel-machine scheduling with identical machine resource capacity limits and DeJong's learning effect. Each job has a resource consumption requirement and a normal processing time. The actual processing time of a job is a function of its normal processing time, subject to DeJong's learning effect, while the resource consumption of a job is a function of its actual processing time. Each machine has the same resource capacity limit. The objective is to maximise the minimum machine load. Considering three resource consumption functions, namely, linear, concave, and convex, we show that all three scheduling models are NP-hard and propose two approximation algorithms for the models and analyse their worst-case ratios.

We consider a two-echelon supply chain network where the downstream retailers procure products from the upstream unreliable suppliers to sell in the end market. In the decentralized setting, the suppliers consider whether to enter the market and simultaneously set their wholesale prices if they enter, and then the retailers make ordering decisions and engage in quantity-based Cournot competition in the end market where each retailer can sell exactly the products purchased from the supplier. We analyze the system as a Stackelberg game where the suppliers are the leaders and the retailers are the followers. For the case where the random yields of the suppliers are independent, we derive the unique equilibrium of the game in which the suppliers with higher reliability set higher wholesale prices and obtain more profits. We then coordinate the supply chain with the spanning revenue-sharing (SRS) contract and derive the conditions under which the SRS contract achieves the win-win outcome, i.e., all the members of the supply chain network sign a single revenue-sharing contract together. Then considering the case where the random yields are correlated, we show that some suppliers may not join the game in equilibrium even if all the suppliers have the same purchasing cost. Moreover, we show that a high correlation of supplier defaults dampens suppliers’ competition, which differs from the finding in the extant literature because we consider price-sensitive demand.

This paper considers the problem of scheduling on two identical machines to maximize the total early work with a common due date of all the jobs. Chen et al. (2020) showed that the worst-case ratio of the classical LPT algorithm for the problem is at most 10/9 and provided an instance to show that the bound of LPT is at least 12/11. In this note we show that the tight bound of LPT is exactly 12/11.