Constant Processing Time Research Articles

Optimal threshold control in discrete failure-prone manufacturing systems

Bielecki and Kumar (1988) show that the threshold or hedging-point production policies are optimal in a continuous manufacturing system, even if production ability is uncertain. Their analysis assumes constant demand and processing time. In this paper, we consider a discrete manufacturing system in which production capacity, demand, and processing time are all nondeterministic. We formulate the problem into a discrete Markovian production model, and explore the most cost-effective control policy for such a system. With two more sources of uncertainty, we find that the threshold control policies are optimal among all feasible policies when the long run average cost is to be minimized. This extends Bielecki and Kumar's result which shows that the threshold policies are optimal among a subset of feasible policies.

Multicyclic hoist scheduling with constant processing times

Proposes an exact algorithm for the multicyclic schedules of hoist moves in a printed circuit board (PCB) electroplating facility, where exactly r(r>1) parts enter and r parts leave the production line during each cycle, and the processing time at each production stage is a given constant. The multicyclic scheduling problem is transformed into enumeration of intervals for linear functions of decision variables. This enumeration is accomplished with a branch and bound procedure. At each node of the search tree, by solving a linear programming problem (LPP), either the corresponding partial solution is proved to be unable to lead to a feasible solution, or a lower bound is computed. Due to its particular structure, this LPP is equivalent to a cycle time evaluation problem in a bivalued graph which can be solved efficiently. The proposed algorithm is polynomial in the number of tanks for a fixed r, but exponential if r is arbitrary. Computational experience with both benchmark and randomly generated test instances is presented.

Makespan minimization for flow-shop problems with transportation times and a single robot

In a flow-shop problem with transportation times and a single robot n jobs consisting of m operations have to be processed in the same order on m machines. Additionally, transportation times are considered if a job changes from one machine to another. We assume that unlimited buffer space exists between the machines and all transportations have to be done by a single robot. The objective is to determine a feasible schedule with minimal makespan. New complexity results are derived for special cases where the processing or transportation times are constant values. Some of these may also be interpreted as new results for special cases of the classical 3-machine flow-shop F3|| C max with constant processing times at certain stages.

TWO‐ AND THREE‐STAGE FLOWSHOP SCHEDULING WITH NO‐WAIT IN PROCESS

In this paper we study the time complexities of some two‐ and three‐stage no‐wait flowshop makespan scheduling problems where, in some stage, all the jobs require a constant processing time and the stage may consist of parallel identical machines. Polynomial time algorithms are presented for certain problems, while several others are proved to be strongly NP‐complete.

Flexible kanban system

Just‐in‐time (JIT) systems were originally designed for deterministic production environments such as constant processing times and smooth and stable demand. However, once implemented, JIT is fraught with numerous types of uncertainties, including variations in processing time and demand, planned interruptions such as preventive maintenance and unplanned interruptions such as equipment failure. These uncertainties lead to lowered production throughput, decreased machine utilization, increased order completion time and greater backlogs and overtime requirements. In this paper, we introduce a newly developed system, which we refer to as the flexible kanban system (FKS), to cope with uncertainties and planned/unplanned interruptions. We demonstrate the superiority of the new system by considering four case examples covering various uncertainties, conducting numerous studies and comparing the overall performances of the FKS with that of the traditional JIT system. In all the cases considered, the performance of the FKS was, indeed, superior to that of the traditional JIT system.

Stochastically minimizing total flowtime in flowshops with no waiting space

The problem of scheduling n jobs in a two-machine flowshop with constant and known processing times is considered with the total flowtime performance measure. The machines are subject to random breakdowns and there is no waiting space between them. The problem is formulated and an expression for the completion time of the jobs is obtained in terms of the processing times and the breakdown elements. Provided that the counting processes associated with both machines have stationary increments property, a sequence that stochastically minimizes the performance criterion is established for the cases when only the first or the second machine suffers breakdowns.

The effect of sudden material handling system breakdown on the performance of a JIT system

In this paper we explore the impact of sudden breakdown of the material handling system on the performance of a traditional kanban system (TKS). TKS, which is an element of the just-in-time system, is designed to operate in an ideal environment such as constant processing times and uninterrupted processing. However, in a real life environment, the TKS could be subjected to various unpredictable factors including stochastic processing times and process interruption due to equipment failure. These factors would seriously strain the performance of TKS. We consider a TKS in which some stations are dependent on a material handling system to move parts between them. We study the effect of a sudden breakdown of such a material handling system on the performance of the TKS. In addition, we also study a newly developed kanban system (which dynamically and systematically manipulates the number of kanbans in order to offset the blocking and starvation caused by these factors during a production cycle) under the same conditions. We refer to the new system as the 'flexible kanban system' (FKS). We compare the overall performances of the TKS and FKS by considering a variety of cases. We present the solution procedure, results and discussion for these cases.

Adapting just-in-time manufacturing systems to preventive maintenance interruptions

The just-in-time (JIT) system is designed to operate in an ideal environment such as with constant processing times, smooth and stable demand and uninterrupted processing. However, in a real-life environment, the JIT system is subjected to various uncertain factors including stochastic processing times, variable demand and process interruption due to planned preventive maintenance. These factors seriously compromise the performance of JIT. In this paper, we present a newly developed JIT system which uses an algorithm to dynamically and systematically manipulate the number of Kanbans in order to offset the blocking and starvation caused by the said factors during a production cycle. We refer to the new system as the flexible Kanban system (FKS). We provide steps of the algorithm and demonstrate the effectiveness of FKS using a case example. For the case example, we present the solution procedure, results and discussion.

Scheduling of an unreliable manufacturing system with nonresumable setups

This paper considers the scheduling of a manufacturing system with nonresumable setup changes. The system considered involves an unreliable machine that can produce two part types. The switchover from one part type to the other incurs a given constant setup time. The setups are nonresumable, i.e. after a machine repair completion, a setup decision has to be made. The parts have specified constant processing time and constant demand rate. We give a continuous dynamic programming formulation of the problem, which is solved numerically. The optimal setup switching policies are shown to be hedging corridors. Two heuristics, for the determination of the hedging levels, are provided. We show, through simulation, that the two heuristics exhibit good performance.

Optimal production control of a dynamic two-product manufacturing system with setup costs and setup times

This paper deals with the optimal control of a one-machine two-product manufacturing system with setup changes, operating in a continuous time dynamic environment. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a feedback control problem. The objective is to minimize the total backlog, inventory and setup costs incurred over a finite horizon. The optimal solution provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady state, the optimal cyclic schedule is determined. To solve the transient case, the system's state space is partitioned into mutually exclusive regions such that with each region, the optimal control policy is determined analytically.

Optimal production and setup control of a dynamic two-product manufacturing system: Analytical solution

This paper deals with the optimal control of a one-machine two-product manufacturing system with setup changes, operating in a continuous time dynamic environment. The system is deterministic. A known constant setup time is incurred when production is switched from one product to the other. Each product or part has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a feedback control problem. The objective is to minimize the sum total of backlog and inventory costs incurred over a finite horizon. The optimal solution provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady state, the optimal cyclic schedule is determined. To solve the transient case, the system's state space is partitioned into mutually exclusive regions, such that, with each region the optimal control policy is determined analytically.

Transient and steady-state analysis of a manufacturing system with setup changes

This paper deals with the optimal scheduling of a one-machine two-product manufacturing system with setup, operating in a continuous time dynamic environment. The machine is reliable. A known constant setup time is incurred when switching over from a part to the other. Each part has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a production flow control problem. The objective is to minimize the sum of the backlog and inventory costs incurred over a finite planning horizon. The global optimal solution, expressed as an optimal feedback control law, provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady-state, the optimal cyclic schedule (Limit Cycle) is determined. This is equivalent to solving a one-machine two-product Lot Scheduling Problem. To solve the transient case, the system's state space is partitioned into mutually exclusive regions such that with each region is associated an optimal control policy. A novel algorithm (Direction Sweeping Algorithm) is developed to obtain the optimal state trajectory (optimal policy that minimizes the sum of inventory and backlog costs) for this last case.

Hierarchical production control for a flow shop with dynamic setup changes and random machine breakdowns

In this paper, we study a manufacturing system consisting of two machines separated by two intermediate buffers, and capable of producing two different products. Each product requires a constant processing time on each of the machines. Each machine requires a constant non-negligible setup change time from one product to the other. The demand rate for each product is considered to be piecewise constant. Each machine undergoes failure and repair. The time-to-failure and time-to-repair are exponentially distributed random variables. The setup change and processing operations are resumable. We model our system as a continuous time, continuous flow process. An optimal control problem is formulated for the system to minimize the total expected discounted cost over an infinite horizon. To determine the optimal control policy structure, a discrete version of the problem is solved numerically using a dynamic programming formulation with a piecewise linear penalty function. A real-time control algorithm is then developed with the objective of maintaining low work-in-process inventory and keeping the production close to the demand. The algorithm uses a hierarchical control structure to generate the loading times for each product on each machine in real time and to respond to random disruptions in the system. The system is simulated using this algorithm to study its performance. The performance of the algorithm is also compared to alternative policies.

Mixed-Model Sequencing to Minimize Utility Work and the Risk of Conveyor Stoppage

This paper investigates the problem of sequencing N products on an assembly line with two objectives: minimizing (1) the risk of conveyor stoppage and (2) the total utility work. For a single station with arbitrary processing times, this problem is proved NP-hard in the strong sense for each of the two objectives. For a single station with two product types, each of which has a constant processing time, a sequence minimizing both objectives can be found in O(log N) computation time.

ROUTING ALGORITHMS FOR DOUBLE LOOP NETWORKS

We give a new routing algorithm for double loop networks with n nodes which requires O(log n) time for preprocessing and constant processing time at each node on the route. A simple modification of the algorithm works for the case of a single fault (either node or link). The routing is always through a shortest path and the only information needed by a node to process is the address of the destination.

A polynomial algorithm for a one machine batching problem

A problem of batching identical jobs on a single machine is studied. Constant processing times and batch setup times are assumed. An algorithm is presented to minimize the sum over all jobs of the batched completion times, and shown to run in time polynomial in the logarithms of the problem parameters.

Periodically sampled queues with multiserver and finite waiting room

AbstractThis paper evaluates the effect of periodic data transfer from an input processor to internal processors in a distributed‐control, real‐time system. Two models comprising N (≧ 1) call processors (CP) and M (≧ 0) common buffers (CPB) are analyzed and compared. In one model data transfer from the input processor is accepted at any sampling point by the CP subsystem. In the other model data transfer is not allowed if one or more calls are being processed in the CP subsystem at the time of sampling. Steady‐state distributions of calls in the system immediately after the sampling points and maximum traffic to be carried (a0) for the above two models are derived under such conditions as constant sampling period (T), Poisson arrival and negative exponential processing time distribution (mean value h). Furthermore, using such distribution, the distributions of calls in the system at any arbitrary instant are obtained to formulate various performance measures such as the average number of waiting calls in and out of the system and the average waiting time (w). Finally, the following results are shown from some examples of numerical calculation. When T/h is small, although the system with call rejection gives lower performance in terms of a0 and w, it exhibits remarkable behavior in reducing the frequency of data transfer. As T/h which is determined by the sampling period.

Design of complex flow line system by simulation

During the last two decades or so, there have been several attempts to gain insights into the operational behaviour of mechanical and manual flow lines. However, an area which has received very little attention is the area of manual flow lines with more than one type of product input with constant or variable processing times. Such lines are more complex because each product entering into the system has a different work content which causes an uneven work flow and consequent station idle time and/or congestion of semi-finished products. In this paper, a flow line with mixed product supply which is deterministicin the number of arriving units and probabilistic in the structure of the product mix is considered. No buffer stocks between service stations are provided; queue formation of limited length is allowed; the stations are located in series on the line, and each station is allowed to use multiple servers working in parallel. The service times are assumed to be normally distributed with known mean times and variances. The objective is to design a flow line system which would provide an even flow of work where over or under utilization of servers is avoided. This is achieved by increasing or decreasing the number of service stationsby several simulations until a utilization level is achieved which is feasable for the management. GERTS III Q network modeling and simulation technique is used for the solution of the design problem. This technique leads effectively to the achievement of the objective set forth for the solution of the problem.