Lot-sizing Policies Research Articles

Aggregated planning to solve multi-product multi-period disassembly line balancing problem by considering multi-manned stations: A generic optimization model and solution algorithms

Disassembly lines are crucial in the recovery process of end-of-life (EOL) products, facilitating the systematic extraction of parts to meet predetermined objectives. While previous studies have made significant advancements, they have not addressed the disassembly line planning and balancing problem by focusing on the real-life significance of combining long-term decision-making and short-term operational missions. This study fills this gap by combining multi-product, multi-period, and multi-manned disassembly line concepts into a novel integrated approach. Initially, a generic optimization model is formulated, incorporating the concept of multi-manned stations. Subsequently, genetic algorithm (GA)-based solution approaches are developed to address the problem’s complexity. Three tactical-level policies, including economic disassembly quantity (EDQ), just-in-time (JIT), and random (R) based lot size policies, are explored within the algorithms. Additionally, simulated annealing-based local search algorithms and two crossover operators, CR1 and CR2, are incorporated to enhance solution quality. Through computational analysis, six algorithms are evaluated, with the GACR1-JIT algorithm demonstrating significant cost reductions compared to alternatives. The findings underscore the growing importance of JIT-based lot size policies, particularly with an increasing number of periods. This research bridges theoretical and practical considerations by highlighting the strategic importance of combining long-term disassembly line planning and short-term lot sizing decisions to improve system performance.

Third-party retailer’s lot-sizing policy under credit loan considering uncertain demand and asymmetric initial budget information

Third-party retailer’s lot-sizing policy under credit loan considering uncertain demand and asymmetric initial budget information

OPTIMAL PRICING AND PRODUCTION LOT SIZE FOR TWO RATES OF PRODUCTION WITH PRICE-SENSITIVE DEMAND, PRICE BREAK-EVEN POINT, AND PROFIT MAXIMISATION IN HIGHER ORDER EQUATION

In the present study, optimal pricing and optimal lot size production policy models with price-sensitive demand of deteriorating products are considered, taking into account two distinct production rates. It is possible to begin production at one rate and then switch to a different rate after a period of time. Such a scenario is appealing, in that a big initial stock of produced goods can be avoided by starting production at a modest pace, thus reducing the initial investment and the holding cost. Further, the fifth-order equation is obtained when the equation for optimal pricing is derived. Maximising the profit is calculated based on a fifth-order equation. Both optimal pricing and production lot size are decision variables, and optimal cycle time is also one of the decision variables for determining price break-even points. As far as information is concerned, no researcher has examined optimal pricing and production lot size policies in two-rates-of-production models for their study.The objective of the present study is to examine the optimal production, optimal pricing, and optimal cycle time to reduce the total cost and to maximise the total profit. Both price break-even point and profit maximisation are considered. An appropriate mathematical model is developed. An illustrative example is provided and numerically validated using a sensitivity analysis. Microsoft Visual Basic 6.0 was used to code the model’s outcome validation.

Sequential auction for cloud manufacturing resource trading: A deep reinforcement learning approach to the lot-sizing problem

Cloud manufacturing is a rapidly growing trend in modern manufacturing, which has transformed the traditional operations and value chain structure of enterprises. It is crucial to develop a rational and effective trading mechanism of cloud manufacturing resources to meet the ever-increasing demands in this new environment. This paper proposes a sequential auction-based paradigm for the trading of manufacturing resources. The main challenge of the design of the paradigm is to determine the dynamic lot size of resources allocated to each auction considering the uncertainty of arriving demands. To achieve this, we first develop a competitive game model to identify optimal bidding strategies of arrived customers and estimate the expected revenue for each round with the given lot size. Secondly, we construct a Markov decision process (MDP) model to characterize the dynamics of the arrival of stochastic demand and the inventory transition of the manufacturing resources in sequential auctions. Lastly, we leverage a data-driven approach by integrating machine learning with an offline deep reinforcement learning (RL) approach. Specifically, we employ a long short-term memory (LSTM) model to predict forthcoming demands in the environment and develop the deep Q-network (DQN) learning algorithm to optimize lot-sizing policy by interacting with the well-learned LSTM environment model. Our simulation experiments validate the effectiveness of our approach and some management insights are given.

Efficient Formulation for Vendor–Buyer System Considering Optimal Allocation Fraction of Green Production

The classical joint economic lot-sizing (JELS) policy in a single-vendor single-buyer system generates an equal production quantity in all cycles, where the input parameters remain static indefinitely. In this paper, a new two-echelon supply chain inventory model is developed involving a hybrid production system. The proposed model simultaneously focuses on green and regular production methods with an optimal allocation fraction of green and regular productions. Unlike the classical mathematical formulation, cycles do not depend on each other, and consequently, each model parameter can be adjusted to be responsive to the dynamic nature of demand rate and/or price fluctuation. A rigorous heuristic approach is used to derive a global optimal solution for a joint hybrid production system. This paper accounts for carbon emissions from production and storage activities related to green and regular produced items along with transportation activity under a multi-level emission-taxing scheme. The results emphasize the significant impact of green production on emissions. That is, the higher the allocation fraction of green production, the lower the total amount of emissions generated by the system, i.e., the system becomes more sustainable. Adopting a hybrid production method not only decreases the greenhouse gas (GHG) emissions dramatically, but also reduces the minimum total cost per unit time when compared with regular production. One of the main findings is that the total system cost generated by the base closed-form formula of the proposed model is considerably lower in the first cycle (subsequent cycles) than that of the existing literature, i.e., 33.59% (16.13%) when the regular production method is assumed. Moreover, the optimal production rate generated by the proposed model is the one that minimizes the emissions production function. In addition, the system earns further revenue by utilizing a mixed transportation policy that combines the Truck Load (TL) and Less than Truck Load (LTL) services. Illustrative examples and special cases that reflect different realistic situations are compared to outline managerial insights.

Carbon Emissions Effect on Vendor-Managed Inventory System Considering Displaced Re-Start-Up Production Time

Background: The classical mathematical formulation of the vendor-managed inventory (VMI) model assumes an infinite planning horizon, and consequently, the solution derived ignored the impact of the first cycle. The classical formulation is associated with another implicit assumption that input parameters remain static indefinitely. Methods: This paper develops two mathematical models for VMI for a joint economic lot-sizing (JELS) policy. Each model considers investment in green production, energy used for keeping items in storage, and carbon emissions from production, storage, and transportation activities under the carbon cap-and-trade policy. The first model underlies the first cycle, while the second underlies subsequent cycles. Results: The re-start-up production time for subsequent cycles commences only at the time required to produce and replenish the first lot, which implies further cost reduction. Mathematical formulations are perceived as important both for academics and practitioners. For example, the base model of the first cycle (subsequent cycles) generates an optimal produced quantity with 18.42% (4.35%) less total system cost when compared with the pest scenario in favor of the existing literature. Moreover, such a percentage of total system cost reduction increases as the production rate increases. Further, the proposed models not only produce better results but also offer the opportunity to adjust the input parameters for subsequent cycles, where each cycle is independent from the previous one. Conclusions: The emissions generated by the system are very much related to the demand rate and the amount of investment in green production. Illustrative examples, special cases, model overview, and managerial insights are given. The discussion related to the contribution of the proposed model, the concluding remarks, and further research are also provided. The proposed model rectifies the base model adopted by the existing literature, which can be further extended to be implemented in several interesting further inquiries related to JELS inventory mathematical modeling.

Optimal Joint Pricing and Lot Sizing Policies for Perishables Under Periodic Inspections, and Trade Credit Financing Schemes

Optimal Joint Pricing and Lot Sizing Policies for Perishables Under Periodic Inspections, and Trade Credit Financing Schemes

Optimizing Supplier Selection and Order Lot-Sizing Decisions in a Two-Stage Supply Chain

This paper analyzes different lot-sizing policies for the supplier selection and order allocation problem in a two-stage supply chain. The supply chain consists of multiple candidate suppliers and a single buyer. In this system, selected suppliers produce a product in batches at finite production rates, ship it to the buyer, and the buyer sells it to the market at a constant demand rate. Our goal is to evaluate two lot-sizing policies and select the one that optimizes the supply chain by minimizing the total cost and maximizing supplier efficiency. A bi-objective mixed-integer nonlinear programming (BOMINLP) model is proposed. The first objective consists of the development of a coordination mechanism for supplier selection and order allocation that minimizes the entire supply chain cost, and the second objective comprises a data envelopment analysis (DEA) approach to evaluate the overall performance of suppliers to optimize supplier efficiency. Then, the lot-for-lot and order frequency policies are applied to the BOMINLP model separately to determine the set of selected suppliers as well as the corresponding order quantities and number of orders allocated to each selected supplier per replenishment cycle. Numerical examples that illustrate the solution approach and compare the two lot-sizing policies are provided.

Optimal pricing and production lot-size policies in imperfect production system with price-sensitive demand, reworking, scrap, and sales return

Optimal pricing and production lot-size policies in imperfect production system with price-sensitive demand, reworking, scrap, and sales return

Third-Party Retailer’s Lot-Sizing Policy Under Conditions of Trade Credit, Uncertain Demand and Asymmetric Initial Budget Information

Large retail platform has begun to provide trade credit to the capital-constrained and start-up third party retailer (3PR). Most of the 3PRs face uncertain demands with few historical data, which makes it difficult for retail platform to evaluate the rationality of 3PR’s lot-sizing decision and to design trade credit contracts. In addition, and 3PR’s initial budget is unknown to the retail platform, which further increases the risk of trade credit. There- fore, this paper considers a two-echelon supply chain consisting of a retail- platform and a 3PR, and investigates the 3PR’s lot-sizing decision and the design of trade credit contract based on uncertain demand and asymmetric initial budget information. We find that a) empirical uncertainty distribution is an effective tool for modeling uncertain demand with few historical data. b) The 3PR will place an irrational purchasing order regardless of the market condition when the retail platform does not interfere with 3PR’s decision mak- ing. 3) The 3PR will overstate its initial budget to get more loan when the retail platform interferes with 3PR’s decision making.

Unleashing an ML-based selection criteria for economic lot sizing in a smart batch-type production system

PurposeInventory 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.Design/methodology/approachThe 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.FindingsWhen 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.Originality/valueThe 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.

A sustainable supply chain under VMI-CS agreement with withdrawal policies for imperfect items

Supply Chain (SC) coordination, quality requirements, and environmental issues are the main areas of interest within the field of inventory management. Few studies have integrated these concepts into an inventory problem despite its overwhelming necessity. In this direction, this paper deals with a vendor-buyer SC under the Vendor-Managed Inventory with Consignment Stock (VMI-CS) agreement. According to the agreement, the vendor bears the buyer's financial holding cost in return for the storage of products in the buyer's warehouse. Further, each shipment involves a random fraction of repairable items, which need to be withdrawn from the inventory system. Unlike the existing literature, when repair policy is evaluated not to be profitable, these items can either be salvaged or scrapped in the present problem. In other words, this study aims at providing a decision support model to find the optimal withdrawal policy as a joint quality and lot-sizing policy. To fulfill sustainability criteria, carbon emissions are incorporated into the total cost of SC by considering carbon tax and cap-and-trade regulation. The optimum solution is found through an analytical algorithm. Finally, a numerical study is conducted to illustrate the applicability of the models and gain managerial insights. The results show that the performance of VMI-CS for all withdrawal policies is superior to traditional mechanism, but its cost-saving sharing has to improve. In addition, the sensitivity analyzes reveal that the fraction of imperfect items greatly affects the optimal withdrawal policy. Finally, adopting carbon regulations does not seriously affect the optimal withdrawal policy and inventory decisions but causes a relatively much increase in the total cost.

An integrated lot-sizing policy for the inventory management of constrained multi-level supply chains: null-space method

ABSTRACT The null-space method (NSM) for solving the nonlinear programming (NLP) is used to transform an indefinite system into a symmetric positive definite one of a smaller dimension. In this paper, an NSM optimises the constrained NLP model of the inventories in multi-level supply chains (SCs). The presented NSM can give a direct method with a predictable level of fill without pivoting, decreasing the number of taken iterations to find the optimum solution. We transform the nonlinear equations into an NLP model, which NSM can solved. We also investigate the suitability of using null-space-based factorisations to derive sparse direct methods. Accordingly, an integrated lot-sizing model of the multi-level SC is designed and then optimised using the presented NSM. The paper's objectives are to find the optimum number of stockpiles and the economic period length for inventories. Some numerical examples demonstrate the applicability of the presented NSM to optimise the integrated lot-sizing policy of the multi-level SCs. The presented NSM shows satisfactory performance in optimum solutions, the number of iterations, infeasibility, optimality error, and complementarity.

Determining Optimal Inventory Policy and Sales Price under Promotional Expenditure for Some Veblen Products

This paper focuses on determining the optimal promotional expenses as well as optimal sales price and lot-sizing policies for Veblen products, generally being luxury goods consumed conspicuously. The price-demand relationships considered for the product are the ones suggested by Leibenstein (1950). The promotion is assumed to increase the product's perceived value facilitating in increasing the selling price without sacrificing the demand. The effect of promotional expenses has been analysed for the niche and mass markets using two different relationships. For obtaining the optimal pricing, lot-sizing and promotional expenses, a mathematical model has been developed and a GA-based heuristic is also proposed. Numerical examples are taken to illustrate the use of the proposed problem solving approaches and also to carry out sensitivity analyses. The results show almost no impact of variation in setup cost and carrying cost rate on optimal inventory policy, but of the product unit cost.

Optimal lot-sizing of an integrated EPQ model with partial backorders and re-workable products: an outer approximation

In this paper, we develop and optimise the lot-sizing policy in an integrated Economic Production Quantity (EPQ) model with partial backorders and re-workable products considering linear and fixed backordering costs. Time intervals, number of lots, and lot size are the decision variables of our model. The cost function includes the set-up costs, the holding costs, the goodwill loss costs, the fixed backorder costs, the backorder costs, the costs of reworking, the production costs, the disposal costs, and the screening costs. The profit function consists of the sale profits obtained from the sold products. The goal is to minimise the cost function and maximise the profit function under stochastic constraints simultaneously. A Lexicographic method is applied for integrating the conflicting objective functions. The integrated objective function, with stochastic constraints, is a Mix Integer Nonlinear Programming (MINLP) model. Accordingly, an Outer Approximation (OA) algorithm is provided for optimal lot-sizing the integrated EPQ model. Two numerical examples and a real large-scale example demonstrate the decent and acceptable performance of the presented OA with respect to the optimality criteria such as optimum solutions, complementarity, and taken iterations.

Hybrid meta-heuristic algorithms for a supply chain network considering different carbon emission regulations using big data characteristics

Big data (BD) approach has significantly impacted on the development and expansion of supply chain network management and design. The available problems in the supply chain network (SCN) include production, distribution, transportation, ordering, and inventory holding problems. These problems under the BD environment are challenging and considerably affect the efficiency of the SCN. The drastic environmental and regulatory changes around the world and the rising concerns about carbon emissions have increased the awareness of customers regarding the carbon footprint of the products they are consuming. This has enforced supply chain managers to change strategies to reframe carbon emissions.. The decisions such as an optimization of the suitable network of the proper lot sizes can play a crucial role in minimizing the whole carbon emissions in the SCN. In this paper, a new integrated production–transportation–ordering–inventory holding problem for SCN is developed. In this regard, a mixed-integer nonlinear programming (MINLP) model in the multi-product, multi-level, and multi-period SCN is formulated based on the minimization of the total costs and the related cost of carbon emissions. The research also uses a chance-constrained programming approach. The proposed model needs a range of real-time parameters from capacities, carbon caps, and costs. These parameters along with the various sizes of BD, namely velocity, variety, and volume, have been illustrated. A lot-sizing policy along with carbon emissions is also provided in the proposed model. One of the important contributions of this paper is the three various carbon regulation policies that include carbon capacity-and-trade, the strict capacity on emission, and the carbon tax on emissions in order to assess the carbon emissions. As there is no benchmark available in the literature, this study contributes toward this aspect by proposing two hybrid novel meta-heuristics (H-1) and (H-2) to optimize the large-scale problems with the complex structure containing BD. Hence, a generated random dataset possessing the necessary parameters of BD, namely velocity, variety, and volume, is provided to validate and solve the suggested model. The parameters of the proposed algorithms are calibrated and controlled using the Taguchi approach. In order to evaluate hybrid algorithms and find optimal solutions, the study uses 15 randomly generated data examples having necessary features of BD and T test significance. Finally, the effectiveness and performance of the presented model are analyzed by a set of sensitivity analyses. The outcome of our study shows that H-2 is of higher efficiency.

Optimal lot-sizing policy for a failure prone production system with investment in process quality improvement and lead time variance reduction

<p style='text-indent:20px;'>To survive in today's competitive market, it is not enough to produce low-cost products but also quality-related issues and lead time needs to be considered in the decision-making process. This paper extends the previous research by developing a stochastic economic manufacturing quantity (EMQ) model for a production system which is subject to process shifts from an <i>in-control</i> state to an <i>out-of-control</i> state at any random time. Moreover, we consider the option of investment to increase the process quality and decrease the lead-time variability. Closed-form solutions of the proposed models are obtained by applying the classical optimization technique. Some lemmas and theorems are developed to determine the optimal solution of the decision variables. Numerical results are obtained for each of these models and compared with those of the basic <i>EMQ</i> model without any investment. From the numerical analysis, it has been observed that our proposed model can significantly reduce the cost of the system compared to the basic model.</p>

A coordination mechanism for supplier selection and order quantity allocation with price-sensitive demand and finite production rates

We study a supplier selection and order quantity allocation problem in a two-stage supply chain, which is composed of a set of potential suppliers and a single buyer/retailer trading one product. The demand at the buyer's stage is price-sensitive and suppliers have finite production rates. Within this framework, the optimization of the supply chain is evaluated by considering the performance of both stages and guaranteeing their profitability through a coordination mechanism based on profit-sharing. Two mixed integer nonlinear programming models are presented under different lot-sizing policies to determine the optimal set of selected suppliers, retail price, and order quantity and number of orders per order cycle for each selected supplier. The structure of the models' solutions is examined by deriving properties of the optimal supplier selection and order quantity allocation scheme. Numerical examples are also provided to illustrate the applicability of the proposed models.

Designing a dynamic model to evaluate lot-sizing policies in different scenarios of demand and lead times in order to reduce the nervousness of the MRP system.

ABSTRACT The aim of this study is to provide a systematic approach to reduce the total cost and nervousness in material requirement planning (MRP) system based on appropriate lot-sizing policies under different scenarios of safety stock for demand and lead time. In this study, the system dynamics (SD) approach was utilized. The MRP system has been modelled and simulated and three scenarios were introduced: (1) stochastic demand-stochastic lead time, (2) stochastic demand-deterministic lead time, and (3) suggestion of the company. Four lot-sizing policies consist of a lot for lot, fixed order quantity, fixed period ordering, and economic order quantity was also evaluated under each scenario. The results showed that in scenario 2, the nervousness of the MRP system was at the highest level. Too, the lowest total cost in the situation of scenarios 1 and 2 has happened in the lot for lot policy, while it is for the suggestion of company related to fixed period ordering policy.

Replenishment policy for an economic production quantity model considering rework and multiple shipments

Determining the optimal replenishment lot size and shipment policy for a production setup has been of greater interest during the last few years. This paper derives the optimal replenishment lot size and shipment policy for an Economic Production Quantity (EPQ) model with rework of defective items. However, in a real life situation, multi-shipment policy is used in lieu of continuous issuing policy and generation of defective items is inevitable. The proposed research assume that all imperfect quality items are reworked to perfect quality items and then all perfect quality items are delivered to the customers. Mathematical modeling is used in this study and the long-run average production–inventory-delivery cost function is derived. Convexity of the cost function is proved by using the Hessian matrix equations. The closed-form optimal replenishment lot size and optimal number of shipments that minimize the long-run average costs for such an EPQ model are derived.