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This paper deals with finding economic order quantity, number of orders to be placed and/or the time to place each order for four different special types of problems that may be encountered in practice. The first problem (Problem 1a) assumes a fixed planning horizon and a perishable product such as Christmas trees or fashion merchandise whose value deteriorates as the item gets aged. Under constant demand assumption, solution for this type of problem is worked out by capturing the deterioration in value by increasing holding cost. The second problem (Problem 2) has the same assumption as the first, except that the demand is assumed to increase as we move forward in time. The third problem (Problem 2a) is a restricted version of the second, which allows a specific number of integer orders during the planning horizon. The fourth problem (Problem 3) allows the ordering cost to increase as time progresses. All formulae derived can be easily applied to find numerical answers. The answers may have to be adjusted to reflect container size, minimum order quantity and any other restriction not modeled, or to take into account any violation of the model assumptions.

The paper presents a methodology to utilise available information from condition monitoring systems. Before a new approach to determine optimal time for overhaul/replacement is introduced, a brief review of existing mathematical models for this purpose is presented. Unlike the usual approach of looking at failure rates and life time distributions, the focus is put on extracting information from models of continuous‐time deterioration processes. Defining a finite number of condition levels of the system, the continuous‐time deterioration process is described by a condition transition probability matrix. All input data are modelled as a function of time or system status. We have also the flexibility to include cyclic variation as for example changes in production demand.

An attempt is made to classify the lot‐sizing problem based on evidence from the literature and current research trends. For future research a mixture of a heuristic method to find a sequence and cycle time and a mathematical program to find lot sizes would be feasible even for fairly large problems. Attempts should be made to apply marginal analysis in practical lot‐sizing problems since it may result in lower cost solutions.

The aim of this paper is to present the rationale, a numerical example and a case study of the application of an algorithm to convert non‐calendar based preventive maintenance (PM) schedules into calendar‐time format for semiconductor manufacturing systems (SMS). The resulting calendar‐time PM schedules can be utilized as a baseline within a PM scheduling optimization process.

The algorithm utilizes estimations of work‐in‐process (WIP) and system parameters to estimate an equivalent calendar‐time schedule for PM schedules based on different units. A numerical example based on fictitious data illustrates the utilization of the conversion algorithm within a mixed PM scheduling scenario, including wafer, processing‐time and energy‐based PM tasks for multi‐chamber tools. In addition, a case study illustrates the accuracy of the algorithm by comparing estimated PM targets (i.e. due, warning and late dates) with historical data from a real semiconductor fabrication facility.

Results from the case study validated the conversion algorithm by showing accurate estimations of PM targets (i.e. due, warning and late dates). The accuracy of the algorithm depends, however, on good estimates for WIP levels within the planning horizon.

The conversion algorithm may be utilized not only in SMS but also in other industries that require the conversion of non‐calendar based PM schedules into calendar‐time format for PM optimization and operational purposes.

The purpose of this paper is to assess life cycle costing (LCC) of the equipment in a more realistic, precise, and applicable manner, and to apply it to a real industrial problem.

Based on the failure rates of the components of a machine, the LCC is assessed, mathematically modeled, and incorporated to the parallel machine replacement problem with capacity expansion consideration. The problem is modeled as mixed integer programming which intends to minimize the total costs incurred during a planning horizon of several periods for the machines of the same type with different ages. The decision variables are the number of machines to be purchased/salvaged in each period. A genetic algorithm (GA) is developed for solving the problem and its efficiency is verified.

In conventional models presented for calculation of LCC, corrective maintenance (CM) costs of the machines are incorporated to the model as a whole which may result in inaccurate calculations. Obtaining this value is also very difficult and it can be different for machines with different ages. By calculating the CM costs of a machine based on the failure rates of its components, the LCC can be properly estimated in a realistic and precise manner. The presented GA is also proven to be efficient for solving problems of almost any size with different number of machines, components, and planning periods.

The presented model and GA are applied to a real case of a construction company that needs to determine a purchase/salvage schedule for its loaders in the next ten years. Results of the calculated schedule imply that employing new loaders rather than maintaining the aged ones generally results in the minimum LCC.

This paper presents a novel approach for precise, meaningful, and practical LCC calculation. The mathematical model and its solving method can be utilized by both the manufacturers and buyers of equipment as a tool which determines a parallel machine purchase/salvage schedule for a planning horizon of several periods which incurs minimum overall cost. The presented material can be also applied to other industrial problems and cases.

Presents a mathematical model for determining Economic Production Quantity (EPQ) in a multistage flow‐shop production system for the case where the demand for items per unit time is deterministic and the planning horizon is finite. Solves an example problem to illustrate the model.

Two lot‐sizing heuristics are proposed for deterministic time‐varying demands, a case commonly encountered in requirements planning systems. The first heuristic simplifies the stopping rule of the Silver‐Meal (SM) heuristic so that difficult cases may be solved nearly optimally. The second combines the merits of both the SM and the Least‐Unit‐Cost heuristic Both perform favourably even when compared to recent modifications to the basic SM algorithm.

Lot-sizing is among the most important problems in the production and inventory management field. The purpose of this paper is to move one step forward in the direction of the real environment of the dynamic, multi-period, lot-sizing problem. For this purpose, a two-warehouse inventory system, imperfect quality and supplier capacity are simultaneously taken into consideration, where the aim is minimization of the system costs.

The problem is formulated in a novel continuous nonlinear programming model. Because of the high complexity of the lot-sizing model, invasive weed optimization (IWO), as a population-based metaheuristic algorithm, is proposed to solve the problem. The designed IWO benefits from an innovative encoding–decoding procedure and a heuristic operator for dispersing seeds. Moreover, sequential unconstrained minimization technique (SUMT) is used to improve the efficiency of the IWO.

Taking into consideration a two-warehouse system along with the imperfect quality items leads to model nonlinearity. Using the proposed hybrid IWO and SUMT (SUIWO) for solving small-sized instances shows that SUIWO can provide satisfactory solutions within a reasonable computational time. In comparison between SUIWO and a parameter-tuned genetic algorithm (GA), it is found that when the size of the problem increases, the superiority of SUIWO to GA to find desirable solutions becomes more tangible.

Developing a continuous nonlinear model for the concerned lot-sizing problem and designing a hybrid IWO and SUMT based on a heuristic encoding–decoding procedure are two main originalities of the present study.

Production is defined as the mission of creating wealth (economic goods and services) from a variety of resources (human and non‐ human) by adding values (intrinsic and extrinsic) through transformation (physical and conceptual) so as to derive utilities (form, place, time, economic, non‐economic). This mission is organised through a system. Basically, what a production system looks like is as Fig.1. It is basically the flow of various resources that defines the nature and characteristic of the production system.

This paper offers an introduction to dynamic economic planning under uncertainty, i.e. the use of econometric models together with mathematical optimization methods for the analysis and quantitative determination of optimal economic policies. The corresponding basic methodology (optimal feedback stochastic control of linear econometric models given a quadratic cost functional) is presented with particular regard to its practical application. The method is then applied for demonstration purposes to an econometric model of the Federal Republic of Germany.