Non-zero Setup Research Articles

Single-Machine Multi-feedstock Sustainable EPQ Models for a Biomass Direct-Fired Power Plant with Non-zero Setup Times

Single-Machine Multi-feedstock Sustainable EPQ Models for a Biomass Direct-Fired Power Plant with Non-zero Setup Times

PSO-based algorithm for solving lot splitting in unbalanced seru production systems

Seru production system is one of responsive and flexible systems to cope with uncertain demands or changes in current volatile market, and the design of this system involves many structural and operational factors. One of the most important steps is the formation of seru production system, including worker assignment and order scheduling. This paper aims to address a scheduling problem in unbalanced seru production system with lot splitting, where the non-zero setup time is also considered. After describing the problem, a comprehensive mathematical model is proposed to confirm seru formations and arrange orders to different serus. Subsequently, motivated by the particular nature of proposed model, a solution method based on PSO algorithm is designed to assign workers to each seru and determine the productivity, and the optimal assignment of sub-orders is also decided. Finally, an illustrative numerical example is presented to validate the effectiveness of proposed model and solution method.

Optimal decision-making for a single-stage manufacturing system with rework options

ABSTRACTThis study investigates a manufacturing system with a single-stage production system that sometimes produces imperfect items. In this system, we assume that the rework process can start after the regular production process (immediate rework) or when the inventory of perfect goods is equal to zero (delayed rework). Also, we assumed non-zero set-up time for rework. Two models are presented for manufacturing systems with re-workable goods. The first model deals with non-zero set-up time for immediate rework and the second model deals with non-zero set-up times for delayed rework. We also investigate special cases associated with these models wherein the set-up times are zero. A general and aggregated model that included those two models is considered. The novelty of this research lies in selecting for a decision-maker the best approach based on system conditions and solutions. This paper provides a framework for rework policies to minimise the total cost of the system, which includes the cost of manufacturing cost, set-up cost for rework and regular production, holding cost for perfect and imperfect items, and the cost of rework. Finally, we solve the aggregated model by using an exact solution algorithm, and the optimal value of production in each period is obtained.

An Imperfect Multi-Item Single Machine production system with Shortage, Rework, and Scrapped Considering Inspection, Dissimilar Deficiency Levels, and Non-Zero Setup Times

In this paper, we consider a deficient production system with permissible shortages. The production system consists of a unique machine that manufactures a number of products that a part of them are imperfect in form of rework or scrap. These defective products are identified by 100% inspection during production, then, they are whether reworked or disposed of after normal production process. Like real-world production systems, there are diverse kinds of errors creating dissimilar breakdown severity and rework. Moreover, reworks have non-zero setup times that makes the problem closer to real-world instances where machines require some preparations before starting a new production cycle. Thus, we introduce an economic production quantity (EPQ) problem for an imperfect manufacturing system with non-zero setup times for rework items. The rework items are classified into several categories based on their type of failure and rework rate. The aim of this study is to obtain optimum production time and shortage in each period that minimizes inventory system costs including setup costs in reworks, holding costs, production costs, inspection costs, disposal costs, and shortage. Finally, a numerical example is proposed to assess efficiency and validation of the proposed algorithm.

Some Observations to: Lot Sizing with Non-zero Setup Times for Rework

Haji et al. (J Syst Sci Syst Eng 17(2):230–240, 2008) proposed a single machine multiproduct economic batch quantity for an imperfect manufacturing system that includes perfect and re-workable items. They assumed the setup time in rework process is non-zero. They presented two inventory models; one for a single product and one for the case that several products manufactured on a unique machine. However, in these inventory models, there exists the possibility that shortages occur. Therefore, this technical paper identifies some inconsistencies in the research paper of Haji et al. (2008). With a numerical example, it is shown that Haji et al. (2008)’s solution is not held for all instances. Furthermore, this technical paper provides some observations and corrections to the shortcomings in order to improve two solution procedures for single product and multi-product cases.

Two-stage assembly scheduling problem for minimizing total tardiness with setup times

The two-stage assembly flowshop scheduling problem has received much attention from researchers because it is applicable to many real-life environments. The objective of minimizing total tardiness is important because the fulfillment of due dates for customers must be considered when making scheduling decisions. However, the setup times were assumed to be zero in previous studies, which may not be realistic or appropriate for some scheduling environments because treating the setup times separately from the processing times increases the level of machine utilization and reduces total tardiness. In this study, we investigate the two-stage assembly flowshop scheduling problem with separate setup times to minimize the total tardiness. We propose two new algorithms and adapt four existing algorithms, which are different versions of simulated annealing, genetic, and insertion algorithms. Moreover, we formulate the problem mathematically, where we develop a dominance relation and we utilize the dominance relation in our proposed algorithms. Extensive computational experiments indicated that one of the proposed algorithms performed much better than the others on average, i.e., the error using the best algorithm was 54% to 98% less than that with the other algorithms. Computational experiments were also conducted with zero setup times in order to compare the performance of our proposed algorithms with that of the best known previously reported algorithm in the zero setup time case. When the setup times were zero, the best proposed algorithm reduced the error of the best previously reported algorithm by 48% when both algorithms were run for the same computational time. Therefore, our best proposed algorithm can be used for both zero and non-zero setup times. Hence, for the first time, the present study considers the problem with separate setup times as well as proposing much better algorithms for the zero setup time case.

Unsold Versus Unbought Commitment: Minimum Total Commitment Contracts with Nonzero Setup Costs

We study a minimum total commitment (MTC) contract embedded in a finite‐horizon periodic‐review inventory system. Under this contract, the buyer commits to purchase a minimum quantity of a single product from the supplier over the entire planning horizon. We consider nonstationary demand and per‐unit cost, discount factor, and nonzero setup cost. Because the formulations used in existing literature are unable to handle our setting, we develop a new formulation based on a state transformation technique using unsold commitment instead of unbought commitment as state variable. We first revisit the zero setup cost case and show that the optimal ordering policy is an unsold‐commitment‐dependent base‐stock policy. We also provide a simpler proof of the optimality of the dual base‐stock policy. We then study the nonzero setup cost case and prove a new result, that the optimal solution is an unsold‐commitment‐dependent ( s, S) policy. We further propose two heuristic policies, which numerical tests show to perform very well. We also discuss two extensions to show the generality of our method's effectiveness. Finally, we use our results to examine the effect of different contract terms such as duration, lead time, and commitment on buyer's cost. We also compare total supply chain profits under periodic commitment, MTC, and no commitment.

Combined Sales Effort and Inventory Control under Demand Uncertainty

We study the joint inventory and sales effort management problems of a retailer in a broad context and investigate the optimal policies for a single item, periodic-review system. In each period, the demand is uncertain depending on the sales effort level exerted by the retailer, which incurs an associated cost. The retailer’s objective is to find a joint optimal inventory replenishment and sales effort policy to maximize the discounted profit over a finite horizon. We first consider a basic setting with zero setup cost and no batch ordering, under which the base stock list sales effort policy is optimal. Two extensions are then investigated: (1) the case with nonzero setup cost, under which we show that(s,S,e)policy is optimal; and (2) the case with batch ordering, under which we prove the optimality of the(r,Nq,e)policy. Finally, we conduct numerical studies to provide additional managerial insights.

The analysis of scheduling rules in a flexible job shop with non-zero setup costs

This paper evaluates the scheduling of parts in a Flexible Job Shop (FJS) with non-zero setup costs, varying arrival rates and multiple objective functions. The Shortest Processing Time (SPT), Longest Processing Time (LPT), First-in, First-out (FIFO) and Earliest Due Date (EDD) scheduling rules are evaluated with respect to minimising the number of early jobs and optimising the due-date performance while simultaneously approximating Just-in-Time (JIT) inventory levels. We show in this paper that when the setup costs are not zero, depending on which objective is given priority, different machine loading configurations optimise system performance.

Lot sizing with non-zero setup times for rework

In this paper we consider a single machine multi-product lot scheduling problem in which defective items are produced in any production run of each product. In each cycle after the normal production of each product the machine is setup for the rework of the defectives of the same product and then the rework process starts. We assume that the setup time for the normal production process as well as the rework process is non-zero. This paper has two objectives. The first objective is to obtain the economic batch quantity (EBQ) for a single product. The second objective is to extend the result of the first objective to the multi-product case. Adopting the common cycle scheduling policy we obtain optimal batch sizes for each product such that the total cost of the system per unit time is minimized.

Bi-objective cell loading problem with non-zero setup times with fuzzy aspiration levels in labour intensive manufacturing cells

In this study, four different bi-objective mathematical models are presented to solve the cell loading problem with setup times in labour-intensive cellular environments. The objectives of each model are minimizing the number of the tardy jobs and the minimizing the total manpower needed. Model I does the following four tasks simultaneously: (1) determine the number of cells to open; (2) determine cell size among alternatives for each opened cell; (3) assign products to cells (cell loading); (4) determine the sequence of products in each cell. The other three models are extensions of model I. Model II restricts all cells to the common cell size. Model III allows lot-splitting and model IV allows lot-splitting only if the entire job can be completed. Fuzziness stems from the fuzzy aspiration levels attained to both objective functions. Fuzzy mathematical models are developed for each crisp model and fuzzy achievement function is defined by different fuzzy operators. Experimentation is conducted in two stages. In the first stage, an example problem is solved to represent the performance of the min-operator, fuzzy and- operator and the proposed representation for the fuzzy mathematical modelling. In the second stage, another example is considered to compare the models and to investigate the behaviour of each model with different setup time levels. First, models are solved to maximize the number of the early jobs considering each possible manpower level as a constraint and then fuzzy model solutions are obtained. Experimentation shows that each model represents alternative cell loading systems requirements effectively and the fuzzy and-operator and the proposed fuzzy model representations are convenient to reach the efficient solutions for each model with non-zero setup times.

Anticipative control of switched queueing systems

The relevant dynamics of a queueing process can be anticipated by taking future arrivals into account. If the transport from one queue to another is associated with transportation delays, as it is typical for traffic or productions networks, future arrivals to a queue are known over some time horizon and, thus, can be used for an anticipative control of the corresponding flows. A queue is controlled by switching its outflow between “on” and “off” similar to green and red traffic lights, where switching to “on” requires a non-zero setup time. Due to the presence of both continuous and discrete state variables, the queueing process is described as a hybrid dynamical system. From this formulation, we derive one observable of fundamental importance: the green time required to clear the queue. This quantity allows to detect switching time points for serving platoons without delay, i.e., in a “green wave” manner. Moreover, we quantify the cost of delaying the start of a service period or its termination in terms of additional waiting time. Our findings may serve as a basis for strategic control decisions.

Analysis and solution to the single-level batch production smoothing problem

Many companies use mixed-model production systems running under the Just-in-Time philosophy in order to efficiently meet customer demands for a variety of products. Such systems require demand be stable and production sequence be leveled. The production smoothing problem aims at finding level schedules in which the appearances of products are dispersed over the horizon as uniformly as possible. In this paper, the production smoothing problem is extended to a more general manufacturing environment where a single machine can be identified as either the final or the bottleneck stage of the system and products may have arbitrary non-zero setup and processing time requirements on this single machine. An optimization model is built for the problem and a two phase solution methodology is developed. The first phase problem is shown to be NP-hard and a parametric heuristic procedure is proposed for its solution. In contrast, the second phase problem is shown to be efficiently solvable and currently available solution methods are adopted from the literature. A computational study is designed to test the proposed two phase solution methodology and also the parametric heuristic procedure. Computational results show that the proposed two phase solution methodology enables effective and efficient control of the studied manufacturing system, and the heuristic procedure developed for the first phase problem is time efficient and promises near optimal solutions for a variety of test instances.

Dynamic programming solution to the batching problem in just-in-time flow-shops

Mixed-model manufacturing systems are widely used by companies, in order to meet the customers' demand for a variety of products, in an efficient way. This paper is concerned with a special class of mixed-model manufacturing systems: flow-shops. In a flow-shop, each product has to be processed by a number of machines, following a common route. We study the production smoothing problem under presence of non-zero setup and processing times which also vary among the products. We split the master problem into two sub-problems which are concerned with determining the batch sizes and production sequences, respectively. We develop a dynamic programming procedure to solve the batching problem, and suggest using an existing method from the current literature to solve the sequencing problem. We conduct a computational study and show that our solution approach is effective in meeting the JIT goals and efficient in its computational requirements.

Batch splitting in an assembly scheduling environment

This paper presents mathematical models and algorithms for a production scheduling problem with batch splitting of assembly operations. The operation precedence is represented in an operations network, and the operations at any particular workcenter are split into suitable batch sizes on the available identical parallel processors for faster completion. The solution methodology comprises of a batch splitting algorithm followed by a batch scheduling algorithm. The batch splitting algorithm is developed based on a preemptive scheduling algorithm after incorporating non-zero setup times. The batch scheduling algorithm is based on a critical path algorithm for an operations network. The mathematical model also considers movesizes for batches which determine the threshold for the batch size that needs to be built up before it can be transferred for the successor operation. The computational results for different problem sizes show that the proposed solution scheme can satisfactorily solve this complex scheduling problem for cases where the standard solvers fail to generate solutions within practical time limits. Moreover, there is a significant reduction in makespan due to batch splitting.

A two-bottleneck system with binomial yields and rigid demand

This study considers multistage production systems where production is in lots and only two stages have non-zero setup costs. Yields are binomial and demand, needing to be satisfied in its entirety, is “rigid”. We refer to a stage with non-zero setup cost as a “bottleneck” (BN) and thus to the system as “a two-bottleneck system” (2-BNS). A close examination of the simplest 2-BNS reveals that costs corresponding to a particular level of work in process (WIP) depend upon costs for higher levels of WIP, making it impossible to formulate a recursive solution. For each possible configuration of intermediate inventories a production policy must specify at which stage to produce next and the number of units to be processed. We prove that any arbitrarily “fixed” production policy gives rise to a finite set of linear equations, and develop algorithms to solve the two-stage problem. We also show how the general 2-BNS can be reduced to a three-stage problem, where the middle stage is a non-BN, and that the algorithms developed can be modified to solve this problem.

The capacitated lot-sizing and scheduling problem with sequence-dependent setup costs and setup times

We consider the single machine capacitated lot-sizing and scheduling problem (CLSP) with sequence-dependent setup costs and non-zero setup times, with the additional feature that setups may be carried over from one period to the next, and that setups are preserved over idle periods. We provide an exact formulation of this problem as a mixed-integer program. It is well known that the CLSP is NP- hard. Therefore, we have also developed a heuristic for solving large problem instances. This is coupled with a procedure for obtaining a lower bound on the optimal solution. We carry out a computational study to test the accuracy of several different lower bounding linear relaxations and the approximate solution obtained by the heuristic. In our study, the average deviation of the heuristic solution from the corresponding exact solution depends on the size of the problem and ranges from 10 to 16%. The heuristic is more effective when there are many more products than there are planning periods. This is a desirable property from a practical viewpoint since most firms are likely to implement such a procedure on a rolling horizon basis, solving the problem repeatedly for a few periods at a time.

Optimal Scheduling of the Single Line Multi-purpose Batch Process with Re-circulation Products.

The semi-conductor integrated circuit electronic devices process has many re-circulation production paths through the stages of product manufacturing. These kinds of processes can be defined as the multi-purpose batch process with re-circulation products if they produce more than two products. In this paper, we have developed the completion time algorithms for a single line multi-purpose batch process including re-circulation products with consideration of the non-zero set-up times and transfer times. We also developed the optimization method, genetic algorithm, for optimal scheduling of a multi-purpose batch process including re-circulation products. Several randomly generated examples were tested using the proposed algorithm, and the Gantt chart results are presented. We used Genetic Algorithm for solving the scheduling problems, and optimal solutions are also presented.

A genetic algorithm of optimal scheduling for multi-purpose batch process with re-circulation products

In this paper we have developed the completion times algorithms of single line multi-purpose batch process including re-circulation products under consideration of the non-zero set-up times and transfer times. We also developed the optimization method, genetic algorithm, for optimal scheduling of mUlti-purpose batch process including re-circulation products. Finally the performance of the proposed algorithms was tested by several randomly generated examples and the Gantt chart results are presented. We used Genetic Algorithm for solving the scheduling problems and optimal solutions are also presented.

Workload allocation in multi-product, multi-facility production systems with setup times

In this article, we model the problem of assigning work to M heterogeneous servers (machines), which arises from exogenous demands for N products, in the presence of nonzero setup times. We seek a workload allocation which minimizes the total expected Work-in-Progress (WIP) inventory. Demands are assumed to arrive according to independent Poisson processes, but the setup and the processing times can have arbitrary distributions. Whenever a machine produces more than one product type, production batch sizes are determined by a group scheduling policy; which is also known as the cyclic-exhaustive polling policy. We formulate the workload allocation problem as a nonlinear optimization problem and then provide several insights gleaned from first order necessary conditions, from numerical examples, and from a close examination of the objective function. For example, we show that increasing either the load or the number of products assigned to a machine, or both, does not necessarily increase its contribution to total WIP. These insights are then used to devise a heuristic workload allocation as well as a lower bound. The heuristic allocation is further refined using a nonlinear optimization algorithm.