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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.

This paper aims to present a novel bi-objective mathematical model for a production-inventory system under uncertainty.

This paper addresses agile and lean manufacturing concepts alongside with green production methods to design an integrated capacitated lot sizing problem (CLSP). From a methodological perspective, the problem is solved in three phases. In the first step, an FM/M/C queuing system is used to minimize the number of customers waited to receive their orders. In the second step, an effective approach is applied to deal with the fuzzy bi-objective model and finally, a hybrid metaheuristic algorithm is used to solve the problem.

Some numerical test problems and sensitivity analyzes are conducted to measure the efficiency of the proposed model and the solution method. The results validate the model and the performance of the solution method compared to Gams results in small size test problems and prove the superiority of the hybrid algorithm in comparison with the other well-known metaheuristic algorithms in large size test problems.

This paper presents a novel bi-objective mathematical model for a CLSP under uncertainty. The proposed model is conducted on a practical case and several sensitivity analysis are conducted to assess the behavior of the model. Using a queue system, this problem aims to reduce the items waited in the queue to receive service. Two objective functions are considered to maximize the profit and minimize the negative environmental effects. In this regard, the second objective function aims to reduce the amount of emitted carbon.

The capacitated lot sizing problem (CLSP) is one of the most important production planning problems which has been widely studied in lot sizing literature. The CLSP is the extension of the Wagner-Whitin problem where there is one product and no capacity constraints. The CLSP involves determining lot sizes for multiple products on a single machine with limited capacity that may change for each planning period. Determining the right lot sizes has a critical importance on the productivity and success of organizations. The paper aims to discuss these issues.

This study focuses on the CLSP with setup carryover and backordering. The literature focusing on this problem is rather limited. To fill this gap, a number of problem-specific heuristics have been integrated with fix-and-optimize (FOPT) heuristic in this study. The authors have compared the performances of the proposed approaches to that of the commercial solver and recent results in literature. The obtained results have stated that the proposed approaches are efficient in solving this problem.

The computational experiments have shown that the proposed approaches are efficient in solving this problem.

To address the solution of the CLSP with setup carryover and backordering, a number of heuristic approaches consisting of FOPT heuristic are proposed in this paper.

The purpose of this paper deals with a capacitated multi-item dynamic lot-sizing problem with the simultaneous sequence-dependent setup scheduling of the parallel resource under complex uncertainty.

An improved chance-constrained method is developed, in which confidence level of uncertain parameters is used to process uncertainty, and based on this, the reliability of the constraints is measured. Then, this study proposes a robust reconstruction method to transform the chance-constrained model into a deterministic model that is easy to solve, in which the robust transformation methods are used to deal with constraints with uncertainty on the right/left. Then, experimental studies using a real-world production data set provided by a gearbox synchronizer factory of an automobile supplier is carried out.

This study has demonstrated the merits of the proposed approach where the inventory of products tends to increase with the increase of confidence level. Due to a larger confidence level may result in a more strict constraint, which means that the decision-maker becomes more conservative, and thus tends to satisfy more external demands at the cost of an increase of production and stocks.

Joint decisions of production lot-sizing and scheduling widely applied in industries can effectively avert the infeasibility of lot-size decisions, caused by capacity of lot-sing alone decision and complex uncertainty such as product demand and production cost. is also challenging.

This study provides more choices for the decision-makers and can also help production planners find bottleneck resources in the production system, thus developing a more feasible and reasonable production plan in a complex uncertain environment.

Dynamic lot sizing is the problem of determining the quantity and timing of ordering items while satisfying the demand over a finite planning horizon. This paper considers the problem with two practical considerations: minimum order size and lost sales. The minimum order size is the minimum amount of items that should be purchased and lost sales involve situations in which sales are lost because items are not on hand or when it becomes more economical to lose the sale rather than making the sale. The objective is to minimize the costs of ordering, item , inventory holding and lost sale over the planning horizon. To solve the problem, we suggest a heuristic algorithm by considering trade-offs between cost factors. Computational experiments on randomly generated test instances show that the algorithm quickly obtains near-optimal solutions.

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.

Surveys multiple‐stage production planning literature to reveal that this sizeable body of research is largely inspired by single‐item production planning. Suggests several promising research opportunities, including the possible development of scheduling techniques not derived from older, single‐item procedures. Highlights the need for further comparative testing between existing “improved” techniques, as well as the wealth of work yet to be done in multiple‐stage production planning with limited resources and possible extensions to supply‐chain management.

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 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.

The purpose of this paper is to find the best approximation algorithm for solving the more general case of single‐supplier multi‐retailer capacitated economic lot‐sizing (SM‐CELS) problem in deterministic inventory theory, which is the non‐deterministic polynomial (NP)‐hard problem.

Since few theoretical results have been published on polynomial time approximation algorithms for SM‐CELS problems, this paper develops a fully polynomial time approximation scheme (FPTAS) for the problem with monotone production and holding‐backlogging cost functions. First the optimal solution of a rounded problem is presented as the approximate solution and its straightforward dynamic‐programming (DP) algorithm. Then the straightforward DP algorithm is converted into an FPTAS by exploiting combinatorial properties of the recursive function.

An FPTAS is designed for the SM‐CELS problem with monotone cost functions, which is the strongest polynomial time approximation result.

The main limitation is that the supplier only manufactures without holding any products when the model is applied.

The paper presents the best result for the SM‐CELS problem in deterministic inventory theory.

The LP‐rounding technique, an effective approach to design approximation algorithms for NP‐hard problems, is successfully applied to the SM‐CELS problem in this paper.