Machine repairing models for production systems

In this paper we consider manufacturing systems of m identical unreliable machines producing one type of product. The operating time of each machine is exponentially distributed. The repairing process of a machine requires more than one phase. In each phase, the repair time is exponentially distributed and more than one operator may be required for fixing a broken machine. Here we consider two models of manufacturing systems. In the first model, there are r operators assigned in one server to repair a broken machine. The repairing rate in each phase depends on the number of operators there. This is a generalized model discussed in Buzacott and Shanthikumar [11]. We then consider a two-phase repairing model. Two groups of operators are assigned in the two phases. Each operator can handle one broken machine in each phase individually. This model is a generalization of Eben–Chaime's model [8]. Average profits are derived for both models and can be optimized by suitable allocation of the number of machines and operators in the systems.     

Heuristics for operational fixed job scheduling problems with working and spread time constraints

Operational fixed job scheduling problems select a set of jobs having fixed ready and processing times and schedule the selected jobs on parallel machines so as to maximize the total weight. In this study, we consider working time and spread time constrained versions of the operational fixed job scheduling problems. The working time constraints limit the total processing load on each machine. The spread time constraints limit the time between the start of the first job and the finish of the last job on each machine. For the working time constrained problem, we present a filtered beam search algorithm that evaluates the promising nodes of the branch and bound tree. For the spread time constrained problem we propose a two phase algorithm that defines the promising sets for the first jobs and finds a solution for each promising set. The results of our computational tests reveal that our heuristic algorithms perform very well in terms of both solution quality and time.     

Production planning and inventory allocation of a single-product assemble-to-order system with failure-prone machines

We consider the optimal production and inventory allocation of a single-product assemble-to-order system with multiple demand classes and lost sales. Each component is replenished by a dedicated machine that is subjected to unpredictable breakdowns. We find that the machine state not only influences the production and allocation decisions on its own component but also influences the decisions on the other components. Specifically, the optimal component production policy is a base-stock policy with the base-stock level non-decreasing in the inventory levels of the other components and the states of the other machines. The optimal component allocation policy is a rationing policy with the rationing level non-increasing in the inventory levels of the other components, the states of the other machines, and its own machine state. We use an exponential distribution to approximate the distribution of the total processing times and propose two heuristic policies to address the production and allocation decisions. The importance of taking machine failures into consideration is revealed through computational experiments.     

A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system

We analyze a two-machine flow-shop scheduling problem in which the job processing times are controllable by the allocation of resources to the job operations and the resources can be used in discrete quantities. We provide a bicriteria analysis of the problem where the first criterion is to maximize the weighted number of just-in-time jobs and the second criterion is to minimize the total resource consumption cost. We prove that although the problem is known to be NP-hard even for constant processing times, a pseudo-polynomial time algorithm for its solution exists. In addition, we show how the pseudo-polynomial time algorithm can be converted into a two-dimensional fully polynomial approximation scheme for finding an approximate Pareto solution.     

Scheduling a maintenance activity and due-window assignment based on common flow allowance

We study a due-window assignment problem on a single machine. The job-dependent due-windows are obtained by the common flow allowance criterion. The scheduler has the option to perform a maintenance activity which is rate modifying, i.e., improves the processing times of the following jobs. We consider a number of versions of this setting: (i) The maintenance requires a constant time, (ii) The maintenance duration is an increasing function of its starting time (linear deterioration), and (iii) The maintenance duration is position-dependent (general deterioration). We study the standard setting of regular job processing times, and investigate also the extension to position-dependent processing times. The set of potential optimal positions for the maintenance activity is fully characterized. Consequently, the problems based on all the combinations of these settings are shown to be solved in polynomial time.     

A hybrid approach based on the variable neighborhood search and particle swarm optimization for parallel machine scheduling problems—A case study for solar cell industry

This paper studies a solar cell industry scheduling problem which is similar to the traditional hybrid flow shop scheduling (HFS). In a typical HFS with parallel machines problem, the allocation of machine resources for each order should be scheduled in advance and then the optimal multiprocessor task scheduling in each stage could be determined. However, the challenge in solar cell manufacturing is the number of machines can be dynamically adjusted to complete the job within the shortest possible time. Therefore, the paper addresses a multi-stage HFS scheduling problem with characteristics of parallel processing, dedicated machines, sequence-independent setup time, and sequence-dependent setup time. The objective is to schedule the job production sequence, number of sublots, and dynamically allocate sublots to parallel machines such that the makespan time is minimized. The problem is formulated as a mixed integer linear programming (MILP) model. A hybrid approach based on the variable neighborhood search and particle swarm optimization (VNPSO) is developed to obtain the near-optimal solution. Preliminary computational study indicates that the developed VNPSO not only provides good quality solutions within a reasonable amount of time but also outperforms the classic branch and bound method and the current industry heuristic practiced by the case company.     

Two-machine flow shop scheduling with deteriorating jobs and chain precedence constraints

In this paper we investigate two-machine flow shop scheduling problems with deteriorating jobs and chain precedence constraints. We consider two types of precedence constraints. Under the first type constraints, a successor cannot start on any machine before its predecessor has been completed on the same machine. Under the second one, a successor cannot start on any machine before its predecessor has been completed on all machines. We show that the problem with the first type precedence constraints is polynomially solvable, and the problem with the second type precedence constraints is NP-hard in the strong sense.     

Scheduling deteriorating jobs with CON/SLK due date assignment on a single machine

This paper considers the problem of scheduling deteriorating jobs and due date assignment on a single machine. The actual processing time of a job is a linear increasing function of its starting time. The problem is to determine the optimal due dates and the processing sequence simultaneously to minimize costs for earliness, due date assignment and weighted number of tardy jobs. We present polynomial-time algorithms to solve the problem in the case of two popular due date assignment methods: CON and SLK.     

A note: Multi-machine scheduling with general position-based deterioration to minimize total load

The majority of the papers dealing with scheduling deteriorating jobs ignores general deterioration forms, and considers only special cases. Moreover, most of these papers consider deterioration, most of these papers consider deterioration based on job starting times, and only a few study position-based deterioration. Finally, very few researchers focus on the measure of total load, which becomes important in a setting of deterioration on multi-machines. In this note, we study general, non-decreasing, job-dependent and position-dependent deterioration function. The machine setting is parallel identical machines, and the objective function is total load. We introduce a polynomial time solution for this problem.     

Genetic and psychological underpinnings of motivation and satisfaction of industrial salespeople

We investigate the effects of genetic polymorphisms of salespeople on their motivation and job satisfaction. We hypothesize that psychological attachment styles (anxious, avoidance, and secure) and role conflict interact with variants of three genes (dopamine DRD4, COMT and OXTR) to influence motivation and satisfaction. Our approach follows the spirit of the emerging subfield of organizational neuroscience and biological foundations of social behavior recently introduced into the literature and is one of the first studies to uncover complex dependence of behavior on genes and to employ a large enough sample to reduce false positive inferences. Variants of the DRD4 and COMT genes are found to interact with avoidance and secure attachment style, respectively, to influence motivation, under conditions of felt role conflict. Variants of OXTR have main effects on job satisfaction, as do anxious attachment styles and felt role conflict. Hypotheses are tested on a sample of 334 salespersons selling goods and services to business customers. The role of genetic endowment represents untapped origins for research into the behavior of salespeople and has a number of managerial implications that we discuss.     

Permutation flowshop scheduling to minimize the total tardiness with learning effects

Scheduling with learning effects has received considerable attention recently. Often, numbers of operations have to be done on every job in many manufacturing and assembly facilities. However, it is seldom discussed in the general multiple-machine setting, especially without the assumptions of identical processing time on all the machines or dominant machines. With the current emphasis of customer service and meeting the promised delivery dates, we consider a permutation flowshop scheduling problem with learning effects where the objective is to minimize the total tardiness. A branch-and-bound algorithm and two heuristic algorithms are established to search for the optimal and near-optimal solutions. Computational experiments are also given to evaluate the performance of the algorithms.     

Scheduling jobs with values dependent on their completion times

The paper concerns two scheduling problems with job values and losses of job values (costs) dependent on job completion times. In the first problem, we consider scheduling jobs with stepwise values in parallel processor environment. In the stepwise value, there is given a number of moments at which the job value decreases and between them the job value is constant (thus, the value deteriorates over time). The maximized criterion is the total job value. We prove strong NP-hardness of a single processor case of the problem and construct a pseudo-polynomial time algorithm for a special case with fixed number of unrelated parallel processors and fixed number of common moments of job value changes. Additionally, for uniform and unrelated parallel processors we construct and experimentally test several heuristic algorithms based on the list strategy. The second problem is a single processor one with piecewise linear losses of job values (the loss increases over time). The minimized criterion is the total loss of job value. We prove strong NP-hardness of the problem and existence of a pseudo-polynomial time exact algorithm for its special case. We also construct some heuristic algorithms for this problem and verify experimentally their efficiency.     

Minimizing mean absolute deviation of completion time about a common due window subject to maximum tardiness for a single machine

This study deals with the problem of scheduling jobs on a single machine to minimize the mean absolute deviation of the job completion time about a large common due window subject to the maximum tardiness constraint. Using the well-known three-field notation, the problem is identified as MAD/large DueWindow/T_max. The common due window is set to be large enough to allow idle time prior to the beginning of a schedule to investigate the effect of the T_max constraint. Penalties arise if a job is completed outside the due window. A branch and bound algorithm and a heuristic are proposed. Many properties of the solutions and precedence relationships are identified. Our computational results reveal that the branch and bound algorithm is capable of solving problems of up to 50 jobs and the heuristic algorithm yields approximate solutions that are very close to the exact solution.     

A new approach to job shop scheduling problems with due date constraints considering operation subcontracts

We consider a kind of job shop scheduling problems with due-date constraints, where temporal relaxation of machine capacity constraint is possible through subcontracts. In practice, this kind of problem is frequently found in manufacturing industries where outsourcing of manufacturing operation is possible through subcontract. We present a heuristic algorithm that addresses the problem by solving a series of smaller subproblems to optimality. For the sake of efficiency, the algorithm repeatedly executes in two steps—(1) improving the sequence of operations and (2) picking out the operations to be subcontracted—on bottleneck machines. Experiments are conducted for example problems, and the result of the experiment confirms the viability of the suggested algorithm.     

Fuzzy multi-criteria decision model for evaluating reconfigurable machines

The design and configuration of manufacturing equipment require crucial decision considering optimum capacity and functionality. The equipment selection problem might be involved with choosing between large-capacity machines versus a greater number of machines with smaller capacities, and/or dedicated facilities versus multi-product facilities. This paper investigates reconfigurable machining system characteristics in order to identify the crucial factors influencing the machine selection and the machine (re)configuration. Furthermore, changeover cost and changeover time while switching from one product to the other are taken into account. In particular, a fuzzy analytical hierarchical process (FAHP) model is proposed to integrate the decisive factors for the equipment selection process under uncertainty. The expected values of the normalised fuzzy sets are determined to identify the preference values of the alternative machines. The fuzzy multi-criteria model is analysed within the fuzzy domains of the operational characteristics along with economic, quality and performance criteria. The proposed model is examined using monitoring sensitivity analysis through a case study. As a result, the alternative machines are prioritised with consideration of the inconsistency ratios. The relative performances of the alternative equipment in view of interactions of process reconfigurability and cost, and capacity and functionality are graphically illustrated.     

Entry,imperfect competition,and futures market for the input

We analyze firms' entry, production and hedging decisions under imperfect competition. We consider an oligopoly industry producing a homogeneous output in which risk-averse firms face an entry cost upon entering the industry, and then compete in Cournot with one another. Each firm faces uncertainty in the input cost when making production decision, and has access to the futures market to hedge the random cost. We provide two sets of results. First, under general assumptions about risk preferences, demand, and uncertainty, we characterize the unique equilibrium. In contrast to previous results in the literature (without entry), both production and output price depend on uncertainty and risk aversion. Specifically, when entry is endogenized and the futures price is not actuarially fair, access to the futures market does not lead to separation. Second, to study the effect of access to the futures market on entry and production, we restrict attention to constant absolute risk aversion (CARA) preferences, a linear demand, and a normal distribution for the spot price. In general, the effect of access to the futures market on the number of firms and production is ambiguous.     

Near-optimal (r,Q) policies for a two-stage serial inventory system with Poisson demand

We consider a two-stage serial inventory system whose cost structure exhibits economies of scale in both stages. In the system, stage 1 faces Poisson demand and replenishes its inventory from stage 2, and the latter stage in turn orders from an outside supplier with unlimited stock. Each shipment, either to stage 2 or to stage 1, incurs a fixed setup cost. We derive important properties for a given echelon-stock (r, Q) policy for an approximation of the problem where all states are continuous. Based on these properties, we design a simple heuristic algorithm that can be used to find a near-optimal (r, Q) policy for the original problem. Numerical examples are given to demonstrate the effectiveness of the algorithm.     

Scheduling multiple robots in a no-wait re-entrant robotic flowshop

No-wait re-entrant robotic flowshops are widely used in the electronic industry, such as PCB and semiconductor manufacturing. In such an industry, cyclic production policy is often used due to large lot size and simplicity of implementation. This paper addresses cyclic scheduling of a no-wait re-entrant robotic flowshop with multiple robots for material handling. We formulate the problem and propose a polynomial algorithm to find the minimum number of robots for all feasible cycle times. Consequently, the minimum cycle time for any given number of robots can be obtained with the proposed algorithm. The algorithm runs in O(N⁵) time in the worst case, where N is the number of machines in the robotic flowshop.     

Determination of an order-up-to policy in the stochastic economic lot scheduling model

We consider a production–inventory problem with compound renewal item demand. The model consists of stockpoints, one for each item, controlled according to (R,S)-policies and one machine which replenishes them. The replenishment orders are produced with a fixed rate on the machine with significant setup times and costs, which are stochastic and sequence dependent. The time between the release and the production of the replenishment order is called the waiting time. We develop analytical approximations for the first two moments of this waiting time, the order-up-to levels and the average physical inventory levels for all stockpoints, given the target fill rates. These analytical approximations allows for a quick evaluation of the waiting time which is important when optimization of the system is considered.