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A comprehensive review of the literature for the problem of lot‐size scheduling (serial and assembly) considering the uncapacitated problem and complicated capacitated assembly manufacturing structure. Analyses the different solution techniques and findings for each product set.

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.

Inventory models are quantitative ways of calculating low-cost operating systems. These models can be either deterministic or stochastic. A deterministic model hypothesizes variable quantities like demand and lead time, as certain. However, various types of research have revealed that the value of demand and lead time is still ambiguous and vary unanimously. The main purpose of this research piece is to reduce the uncertainties in such a dynamic environment of Industry 4.0.

The current study tackles the multiperiod single-item inventory lot-size problem with varying demands. The three lot sizing policies – Lot for Lot, Silver–Meal heuristic and Wagner–Whitin algorithm – are reviewed and analyzed. The suggested machine learning (ML)–based technique implies the criteria, when and which of these inventory models (with varying demands and safety stock) are best fit (or suitable) for economical production.

When demand surpasses a predicted value, variance in demand comes into the picture. So the current work considers these things and formulates the proper lot size, which can fix this dynamic situation. To deduce sufficient lot size, all three considered stochastic models are explored exclusively, as per respective protocols, and have been analyzed collectively through suitable regression analysis. Further, the ML-based Classification And Regression Tree (CART) algorithm is used strategically to predict which model would be economical (or have the least inventory cost) with continuously varying demand and other inventory attributes.

The ML-based CART algorithm has rarely been seen to provide logical assistance to inventory practitioners in making wise-decision, while selecting inventory control models in dynamic batch-type production systems.

This paper aims to give a comprehensive review, summary, and discussion on inventory models that have appeared in the literature. During these past ten decades, no seminal paper reviewing the field of inventory lot sizing has even been published. This limitation has been identified in the literature by several researchers over the years, with the sheer volume of the number of published inventory lot sizing models acting as a factor which has limited a research endeavor to review the literature on inventory lot sizing models.

This article reviews research on inventory lot size models and provides a review of previously published literature review papers on inventory models. Based on this initial review, the literature extending current research practices on inventory modeling in supply chains and in sustainable practices is presented. Directions for expanding research in these two areas are examined in light of concerns expressed in the historical use of inventory models and in light of a new inventory research paradigm.

In our paper, we have adopted a novel strategy to overcome this limitation by focusing our review on a review of inventory lot sizing review papers.

By adopting the methodology of reviewing published inventory review papers, we can contribute a comprehensive review of the inventory lot sizing literature that serves to provide in one paper a consolidation of inventory research that can serve as a single source to keep researchers up to date with the research developments in inventory lot sizing models. We also identify gaps in the field which could stimulate new research agendas in the areas of supply chain management and sustainable inventory practices.

The EOQ formula is definitely the oldest and best known single stage lot sizing technique. Its use reportedly dates back to 1904, even though it was not published until a later date. It is often looked upon with scepticism by practitioners and academicians alike, although the reasons for this may differ; it seems, however, to be the most widely used lot sizing technique overall.

The main contribution of this manuscript is to suggest new approaches in order to deal with dynamic lot-sizing and maintenance problem under aspect energetic and risk analysis. The authors introduce a new maintenance strategy based on the centroid approach to determine a common preventive maintenance plan for all machines to minimize the total maintenance cost. Thereafter, the authors suggest a risk analysis study further to unforeseen disruption of availability machines with the aim of helping the production stakeholders to achieve the obtained forecasting lot-size plan.

The authors tackle the dynamic lot-sizing problem using an efficient hybrid approach based on random exploration and branch and bound method to generate possible solutions. Indeed, the feasible solutions of random exploration method are used as input for branch and bound to determine the near-optimal solution of lot-size plan. In addition, our contribution to the maintenance part is to determine the optimal common maintenance plan for M machines based on a new algorithm called preventive maintenance (PM) periods means.

First, the authors have funded the optimal lot-size plan that should satisfy the random demand under service level requirement and energy constraint while minimizing the costs of production and inventory. Indeed, establishing a best lot-size plan is to determine the appropriate number of available machines and manufactured units per period. Second, for risk analysis study, the solution of subcontracting is proposed by specifying a maximum cost of subcontractor in the context of a calling of tenders.

For maintenance problem, the originality consists in regrouping the maintenance plans of M machines into only one plan. This approach lets us to minimize the total maintenance cost and reduces the frequent breaks of production. As a second part, this paper contributed to the development of a new risk analysis study further to unforeseen disruption of availability machines. This risk analysis developed a decision-making system, for production stakeholders, in order to achieve the forecasting lot-size plan and keeps its profitability, by specifying the unit cost threshold of subcontractor in the context of a calling of tender.

Describes a spreadsheet approach for implementing Wagner‐Whitin (WW) and Silver‐Meal (SM) methods for lotsizing time‐varying demands. Suggests that this approach manages the computation and makes tedious and repetitive tasks more interesting; consequently, the student/user can concentrate on the concepts. Outlines the methods, which involve the computation of incremental costs (inventory carrying and replenishment costs) for several alternatives in each period. Presents a spreadsheet template to compute the incremental costs for possible alternatives which is created by using only a small number of spreadsheet formulae and a series of copy commands. The costs are displayed as a matrix. Describes a step‐by‐step procedure to determine the period and the quantity of replenishment.

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 purpose of this paper is to capture the dynamic variations in sales of a product based upon the dynamic estimation of the time series data and propose a model that imitates the price discounting and promotion strategy for a product category in a retail organization.

Time series data relating to sales has been used to model the sales estimates using moving average and proportional and derivative control; thereafter a sales forecast is generated to estimate the sales of a particular product category. This provides valuable inputs for taking lot sizing decisions regarding procurement of the products and selection of suppliers. A hybrid model has been proposed and explained with a hypothetical case, which considerably impacts the sales promotion and intelligent pricing decisions.

A conceptual framework is developed for modeling the dynamic price discounting strategy in retail using fuzzy logic. The model imitates sales promotion and price discounting strategy. This has helped minimize the inventory cost thereby keeping the profitability of the retail organization intact.

There is no appropriate empirical data to verify the models. In light of the research approach (modeling based upon historical time series data of a particular product category) that was undertaken, there is a possibility that the research results may be valid for the product category that was selected. Therefore, the researchers are advised to test the proposed propositions further for other product categories.

The study provides valuable insight on how to use the real-time sales data for designing a dynamic automated model for product sales promotion and price discounting strategy using fuzzy logic for a retail organization.

The purpose of this paper is to capture the dynamic variations in sales of a product based upon the dynamic estimation of the time series data and propose a model that imitates the price discounting and promotion strategy for a product category in a retail organization. A modest attempt has been made in the study to capture the relationship between the sales promotion, price discount and the batch procurement strategy of a particular product category to maximize sales volume and profitability.

Time series data relating to sales have been used to model the sales estimates using moving average and proportional and derivative control; thereafter a sales forecast is generated to estimate the sales of a particular product category. This provides valuable inputs for taking lot sizing decisions regarding procurement of the products that considerably impact the sales promotion and intelligent pricing decisions. A conceptual framework is developed for modeling the dynamic price discounting strategy in retail using fuzzy logic.

The model captures the lag effect of sales promotion and price discounting strategy; other strategies have been formulated based upon the sales forecast that was done for taking the lot sizing decisions regarding procurement of products in the selected category. This has helped minimize the inventory cost thereby keeping the profitability of the retail organization intact.

There is no appropriate empirical data to verify the models. In light of the research approach (modeling based upon historical time series data of a particular product category) that was undertaken, there is a possibility that the research results may be valid for the product category that was selected. Therefore, the researchers are advised to test the proposed propositions further for other product categories.

The study provides valuable insight on how to use the real-time sales data for designing a dynamic automated model for product sales promotion and price discounting strategy using fuzzy logic for a retail organization.