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The purchasing function is growing in importance in today's industrial economy. In many purchasing situations there are a number of conflicting considerations that influence the final purchasing decision. The professional purchasing person must make profitable buying decisions under these circumstances. The single item purchase lot sizing literature in the past has served as the foundation for developing and studying the requirements planning based models and techniques. The purchasing manager's methods for making quantity (lot size) decisions are examined. Significant literature on the subject is classified and a taxonomy provided. Variations within the purchase lot sizing literature are discussed. Purchase lot sizing literature has important limitations by focusing exclusively on lot sizing as the relevant criterion for making economic order size decisions. A logical extension would be to include, the economic performance of alternative lot size procedures in a capacitated Materials Requirement Planning (MRP) environment. Another extension should consider the economics of jointly ordering from one vendor.

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.

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.

Recently several authors have concentrated their efforts in developing models to determine the economic lot size for multi‐stage systems. This is due to the fact that an increasing number of organisations are implementing material requirements planning systems. Numerous models have been developed and tested on problems with finite and rolling horizons and with deterministic time varying demand patterns.

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.

Most of the literature published regarding the performance of lot‐sizing algorithms has been in a deterministic environment. The first objective of this article is to propose a way to incorporate fuzzy sets theory into lotsizing algorithms for the case of uncertain demand in a fuzzy master production schedule. Triangular fuzzy numbers are used to represent uncertainty in the master production schedule. It is shown that the fuzzy sets theory approach provides a better representation of fuzzy demand and more information to aid the determination of lot size. The second objective is to evaluate three lot sizing methods: part‐period balancing, Silver‐Meal, and Wagner‐Whitin. The performance of each lot‐sizing algorithm was calculated over nine examples. The results indicate that the part‐period balancing algorithm may be a better overall choice to determine lot sizes.

Much has been published in the production and operations management literature regarding the performance of lot sizing rules in Material Requirements Planning (MRP). Most of this literature has been concerned with performance of these rules in a deterministic environment. In this research, the authors add uncertain demand and compare the performance of three lot sizing techniques. These techniques are economic order quantity, part‐period balancing and Wagner‐Whitin. Performance is compared using total inventory cost and computer time as criteria. In this research with stochastic demand, part‐period balancing proves to be the best lot sizing rule, overall. In many of the 128 problems generated, part‐period balancing and Wagner‐Whitin are very close to equal on total cost, but part‐period balancing uses far less computer time. Also included in the results is a discussion of particular situations where each of the lot sizing rules works best.

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.

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.

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.