Customer order scheduling to minimize total weighted completion time

In this paper we study the scheduling problem in which each customer order consists of several jobs of different types, which are to be processed on m facilities. Each facility is dedicated to the processing of only one type of jobs. All jobs of an order have to be delivered to the customer at the same time. The objective is to schedule all the orders to minimize the total weighted order completion time. While the problem has been shown to be unary NP-hard, we develop a heuristics to tackle the problem and analyze its worst-case performance.     

An optimal online algorithm for single machine scheduling to minimize total general completion time

We study the online problem of single machine scheduling to minimize total general completion time. General completion time is defined as C^a_j=(C_j)^aC^{\alpha}_{j}=(C_{j})^{\alpha}, where C _j denotes the completion time of job J _j and α≥1 is a constant integer. Total general completion time characterizes the feather in service that when a customer is served later in time, his dissatisfaction increases in a manner of power function. The objective function ∑(C _j ) ^α can also be viewed as a total weighted completion time, but the “weight” is no longer a constant number. Our purpose to minimize customers’ total dissatisfaction. The problem is online in the sense that all jobs arrive over time. Each job’s processing time becomes known at its arrival time. Preemption is not allowed. For this online problem, we show that a lower bound on competitive ratio is 2 ^α and prove that D-SPT (delayed shortest processing time) algorithm is optimal with a competitive ratio 2 ^α .     

Online scheduling to minimize the total weighted completion time plus the rejection cost

We consider the online scheduling on a single machine, in which jobs are released over time and each job can be either accepted and scheduled on the machine or rejected under a certain rejection cost. The goal is to minimize the total weighted completion time of the accepted jobs plus the total rejection cost of the rejected jobs. For this problem, we provide an online algorithm with a best possible competitive ratio of 2.     

A simple two-agent system for multi-objective flexible job-shop scheduling

Journal of Combinatorial Optimization - In this paper, a simple two-agent multi-objective scheduling system for flexible job-shop scheduling problem is proposed and corresponding framework is...     

Total completion time minimization in online hierarchical scheduling of unit-size jobs

This paper investigates an online hierarchical scheduling problem on m parallel identical machines. Our goal is to minimize the total completion time of all jobs. Each job has a unit processing time and a hierarchy. The job with a lower hierarchy can only be processed on the first machine and the job with a higher hierarchy can be processed on any one of m machines. We first show that the lower bound of this problem is at least \(1+\min \{\frac{1}{m}, \max \{\frac{2}{\lceil x\rceil +\frac{x}{\lceil x\rceil }+3}, \frac{2}{\lfloor x\rfloor +\frac{x}{\lfloor x\rfloor }+3}\}\), where \(x=\sqrt{2m+4}\). We then present a greedy algorithm with tight competitive ratio of \(1+\frac{2(m-1)}{m(\sqrt{4m-3}+1)}\). The competitive ratio is obtained in a way of analyzing the structure of the instance in the worst case, which is different from the most common method of competitive analysis. In particular, when \(m=2\), we propose an optimal online algorithm with competitive ratio of \(16\) \(/\) \(13\), which complements the previous result which provided an asymptotically optimal algorithm with competitive ratio of 1.1573 for the case where the number of jobs n is infinite, i.e., \(n\rightarrow \infty \).     

A two-agent single machine scheduling problem with due-window assignment and a common flow-allowance

We study a single-machine scheduling model combining two competing agents and due-date assignment. The basic setting involves two agents who need to process their own sets of jobs, and compete on the use of a common processor. Our goal is to find the joint schedule that minimizes the value of the objective function of one agent, subject to an upper bound on the value of the objective function of the second agent. The scheduling measure considered in this paper is minimum total (earliness, tardiness and due-date) cost, based on common flow allowance, i.e., due-dates are defined as linear functions of the job processing times. We introduce a simple polynomial time solution for this problem (linear in the number of jobs), as well as to its extension to a multi-agent setting. We further extend the model to that of a due-window assignment based on common flow allowance.     

A fast FPTAS for single machine scheduling problem of minimizing total weighted earliness and tardiness about a large common due date

We address the single machine scheduling problem to minimize the total weighted earliness and tardiness about a nonrestrictive common due date. This is a basic problem with applications to the just-in-time manufacturing. The problem is linked to a Boolean programming problem with a quadratic objective function, known as the half-product. An approach to developing a fast fully polynomial-time approximation scheme (FPTAS) for the problem is identified and implemented. The running time matches the best known running time for an FPTAS for minimizing a half-product with no additive constant.     

A coordination mechanism for a scheduling game with parallel-batching machines

In this paper we consider the scheduling problem with parallel-batching machines from a game theoretic perspective. There are m parallel-batching machines each of which can handle up to b jobs simultaneously as a batch. The processing time of a batch is the time required for processing the longest job in the batch, and all the jobs in a batch start and complete at the same time. There are n jobs. Each job is owned by a rational and selfish agent and its individual cost is the completion time of its job. The social cost is the largest completion time over all jobs, the makespan. We design a coordination mechanism for the scheduling game problem. We discuss the existence of pure Nash Equilibria and offer upper and lower bounds on the price of anarchy of the coordination mechanism. We show that the mechanism has a price of anarchy no more than \(2-\frac{2}{3b}-\frac{1}{3\max \{m,b\}}\).     

A note on the complexity of the problem of two-agent scheduling on a single machine

We consider a two-agent scheduling problem on a single machine, where the objective is to minimize the total completion time of the first agent with the restriction that the number of tardy jobs of the second agent cannot exceed a given number. It is reported in the literature that the complexity of this problem is still open. We show in this paper that this problem is NP-hard under high multiplicity encoding and can be solved in pseudo-polynomial time under binary encoding. When the first agent's objective is to minimize the total weighted completion time, we show that the problem is strongly NP-hard even when the number of tardy jobs of the second agent is restricted to be zero.     

Online MapReduce scheduling problem of minimizing the makespan

MapReduce system is a popular big data processing framework, and the performance of it is closely related to the efficiency of the centralized scheduler. In practice, the centralized scheduler often has little information in advance, which means each job may be known only after being released. In this paper, hence, we consider the online MapReduce scheduling problem of minimizing the makespan, where jobs are released over time. Both preemptive and non-preemptive version of the problem are considered. In addition, we assume that reduce tasks cannot be parallelized because they are often complex and hard to be decomposed. For the non-preemptive version, we prove the lower bound is \(\frac{m+m(\Psi (m)-\Psi (k))}{k+m(\Psi (m)-\Psi (k))}\), higher than the basic online machine scheduling problem, where k is the root of the equation \(k=\big \lfloor {\frac{m-k}{1+\Psi (m)-\Psi (k)}+1 }\big \rfloor \) and m is the quantity of machines. Then we devise an \((2-\frac{1}{m})\)-competitive online algorithm called MF-LPT (Map First-Longest Processing Time) based on the LPT. For the preemptive version, we present a 1-competitive algorithm for two machines.     

A note on special optimal batching structures to minimize total weighted completion time

A batch is a subset of jobs which must be processed jointly in either serial or parallel form. The algorithmic aspects of the batching scheduling problems have been extensively studied in the literature. This paper presents necessary and sufficient conditions of the existence of optimal batch sequences for the single machine, batching, total weighted completion time scheduling problems on two batching ways: (1) all jobs form one batch; (2) each batch contains a single job. This kind of conditions can help us to recognize some special optimal schedules quickly. Research supported by NSFC (10671183).     

A dynamic programming approach of finding an optimal broadcast schedule in minimizing total flow time

We study the problem of (off-line) broadcast scheduling in minimizing total flow time and propose a dynamic programming approach to compute an optimal broadcast schedule. Suppose the broadcast server has k pages and the last page request arrives at time n. The optimal schedule can be computed in O(k³(n+k)^k−1) time for the case that the server has a single broadcast channel. For m channels case, i.e., the server can broadcast m different pages at a time where m < k, the optimal schedule can be computed in O(n^k−m) time when k and m are constants. Note that this broadcast scheduling problem is NP-hard when k is a variable and will take O(n^k−m+1) time when k is fixed and m ≥ 1 with the straightforward implementation of the dynamic programming approach. The preliminary version of this paper appeared in Proceedings of the 11th Annual International Computing and Combinatorics Conference as “Off-line Algorithms for Minimizing the Total Flow Time in Broadcast Scheduling”.     

Subcontracting price schemes for order acceptance and scheduling

In this paper we study subcontracting price schemes between a subcontractor and a firm that are engaged in subcontracting of heterogeneous orders with distinct due dates, revenues, and processing times. We assume that the subcontractor proposes the subcontracting pricing and the firm follows by determining the subcontracted orders by solving its order acceptance and scheduling problem. When the subcontractor adopts a linear pricing scheme, we find the firm׳s optimal decisions and develop an algorithm to derive the subcontractor׳s own optimal pricing. We then design a fixed pricing with transfer payment scheme and a quantity discount pricing scheme to coordinate the firm׳s and subcontractor׳s decisions. We examine if the subcontractor can make a higher profit using either of these schemes than the linear pricing scheme, and if they will induce the firm to make decisions that lead to system-wide optimal outcomes.     

The effects of price subsidy and fairness concern on pricing and benefits of take-away supply chain

In this paper, from the perspective of game theory, we study the impact of price subsidy and fairness concern on the pricing strategies and benefits of members in the take-away industry. In the single-channel supply chain, we build a Stackelberg game model between the take-away platform and the restaurant for the online take-away business. By comparing and analyzing the product pricing and revenue in the cases of no price subsidy and price subsidy, we obtain the optimal pricing strategy for both parties. In the dual-channel supply chain, we explore the benefits of supply chain members under the combined effects of fairness concern and price subsidy. Under the single channel price subsidy model, we find that restaurant always raises prices, and the price increase is directly proportional to the subsidy intensity. Such a proper price increase always brings more benefits to both parties. Under the dual-channel model, consumer fairness concern may curb the price increase behavior of restaurants. Regardless of the model, in the long term, the optimal subsidy of the platform will decrease with the expansion of the online take-away market.

     

Competitive analysis for make-to-order scheduling with reliable lead time quotation

This paper makes extended studies on the discrete problem of online scheduling and reliable lead time quotation (discrete Q-SLTQ) introduced by Keskinocak et al. (Manag. Sci. 47(2):264–279, 2001). We first relax the assumption on revenue function from a linear decreasing function to any decreasing function. We present an online deterministic strategy which is optimal in competitiveness for concave revenue functions. The above results are further extended to the continuous Q-SLTQ model where orders are released at arbitrary time points. For the discrete Q-SLTQ problem, if orders are with nonuniform lengths, we prove the nonexistence of online strategies with bounded competitive ratios; otherwise if orders are with unit length but various weights, we present an optimal online strategy.     

具有最大总加权满意度的单机调度问题的dynasearch算法

研究了总加权满意程度最大化的单机调度问题.对最优解的性质进行分析和证明,提出该类问题的统治规则.提出该问题新的基于dynasearch 邻域的迭代局域搜索算法(ILS).算法主要特点:1)dynasearch 是基于多摄动的思想,即一次可以做多个相互独立的交换(或插入);2)用动态规划获得最优dynasearch移动;3)ILS采用随机kick 策略对局部最优解进行摄动,然后继续迭代.实现了该问题的两种dynaearch算法;把两种dynasearch算法与统治规则相结合;在进行kick时引入误差限制.实验表明:嵌入统治规则的算法优于没有统治规则的算法;基于dynasearch交换的ILS 优于基于dynasearch插入的ILS;dynaearch算法要优于以交换为邻域的多初始点改进算法.     

Two-agent scheduling problems on a single-machine to minimize the total weighted late work

In this paper, two-agent scheduling problems are presented. The different agents share a common processing resource, and each agent wants to minimize a cost function depending on its jobs only. The objective functions we consider are the total weighted late work and the maximum cost. The problem is to find a schedule that minimizes the objective function of agent A, while keeping the objective function of agent B cannot exceed a given bound U. Some different scenarios are presented by depending on the objective function of each agent. We address the complexity of those problems, and present the optimal polynomial time algorithms or pseudo-polynomial time algorithm to solve the scheduling problems, respectively.     

等待时间受限的置换流水车间调度启发式算法

针对等待时间受限的置换流水车间调度问题,分析了其可行解与流水车间调度最优解的关系,给出了计算最大完工时间的有向图,证明了等待时间受限的置换流水车间调度问题的可逆性,并以此为基础提出了一种启发式算法.算法首先根据等待时间受限约束与无等待(no-wait)约束的相似特征,生成初始工件序列集;然后利用问题可逆性给出了复杂度为O(n2m)的插入优化机制,进一步优化初始解.数据实验的结果验证了启发式算法的可行性和有效性.