Production Setup Cost Research Articles

An efficient approximation to the pull policy for hybrid manufacturing and remanufacturing systems with setup costs

We consider a continuous-review inventory control problem for a hybrid manufacturing and remanufacturing system with product recovery and setup costs. A pull policy has been proposed in the literature, however, finding its optimal parameters requires an exhaustive search and a single cost function evaluation is itself complex. We propose a tractable approach to finding these parameters using an interim policy called double (r, Q) with parameters ( r m , Q m , r r , Q r ) . When the inventory position of the serviceable item reaches rr , a remanufacturing lot size Qr is setup if recoverable inventory is sufficient. Otherwise, we allow the inventory position to decrease further. As it drops to rm , a manufacturing lot size Qm is placed. Unlike the pull policy, this interim policy suspends the remanufacturing option when the inventory position is less than rr . This facilitates an efficient approximation of the recoverable inventory which decouples the double (r, Q) problem into two standard (r, Q) problems. It can then be efficiently solved using a modification of existing (r, Q) algorithms for two instances. Numerical studies show that our approach performs well relative to the optimal pull policy with parameters estimated from an extensive Simulation-Optimization method and other heuristics found in the literature. The approach is also extended to correlated demand and return arrivals.

Improvement to an existing multi-level capacitated lot sizing problem considering setup carryover, backlogging, and emission control

This paper presents a multi-level, multi-item, multi-period capacitated lot-sizing problem. The lot-sizing problem studies can obtain production quantities, setup decisions and inventory levels in each period fulfilling the demand requirements with limited capacity resources, considering the Bill of Material (BOM) structure while simultaneously minimizing the production, inventory, and machine setup costs. The paper proposes an exact solution to Chowdhury et al. (2018)'s[1] developed model, which considers the backlogging cost, setup carryover & greenhouse gas emission control to its model complexity. The problem contemplates the Dantzig-Wolfe (D.W.) decomposition to decompose the multi-level capacitated problem into a single-item uncapacitated lot-sizing sub-problem. To avoid the infeasibilities of the weighted problem (WP), an artificial variable is introduced, and the Big-M method is employed in the D.W. decomposition to produce an always feasible master problem. In addition, Wagner & Whitin's[2] forward recursion algorithm is also incorporated in the solution approach for both end and component items to provide the minimum cost production plan. Introducing artificial variables in the D.W. decomposition method is a novel approach to solving the MLCLSP model. A better performance was achieved regarding reduced computational time (reduced by 50%) and optimality gap (reduced by 97.3%) in comparison to Chowdhury et al. (2018)'s[1] developed model.© 2023 Society of Manufacturing Engineers (SME). Published by Elsevier Ltd. All rights reserved.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)Peer-review under responsibility of the Scientific Committee of the NAMRI/SME.

Analysing a lean manufacturing inventory system with price-sensitive demand and carbon control policies

Production lot-sizing techniques used by lean practitioners to lower waste inventories and increase production efficiency in the manufacturing industry, are the subject of this paper’s speculation. Lean manufacturing aims to incorporate innovative tools into the manufacturing process to improve productivity and reduce processing time. In view of this, the model anticipates a flexible production rate based on labor, energy, and tool/die costs, to meet the demand while minimizing wastage. Moreover, a discrete investment in set-up costs is considered to lower the initial set-up cost since it is a critical component of smooth manufacturing operations. Further, it is found that price plays a significant role in stimulating a product’s demand; consequently, demand is presumed to be price-sensitive. Besides this, to reduce the carbon footprint in the production systems, two methods namely “Carbon tax” and “Cap-and-trade”, have been employed. The purpose of the developed model is to maximize total profit by jointly optimizing the production rate, selling price, and set-up cost. Numerical experiments are performed to validate the model findings. Results suggest that manufacturers’ production time decreases simultaneously with the introduction of advanced labor and technologies. With respect to carbon policies, the cap-and-trade policy performs better with an increase in total profit and a higher production rate as compared to a carbon tax. Also, sensitivity analysis is performed to support the manufacturer in the decision-making process for ancillary benefits of the optimal policy.

Modelling and optimising the capacity and production network planning in plastics processing factories

ABSTRACT This paper deals with the capacity planning and production network planning in plastics processing factories. We lay emphasis on the opportunity and – potentially – necessity to move machines, tools and material. Furthermore, we consider the option to outsource production to external suppliers. Demand is deterministic and has to be satisfied in the same period. We present a linear mixed integer programming model representing the problem to find a minimum-cost production plan where total cost accounts for variable production cost, setup cost, transportation cost, relocation cost and cost caused by machine purchases. The decisions to be made are the allocation of machines to plants. This includes to decide for investments or relocating machines between plants. In addition, the allocation of products to machines and the determination of the corresponding optimal quantities of production, purchase and transportation within the network of suppliers, plants and customers are decided. We provide a computational study validating the model and conduct a sensitivity analysis of the run time using an off-the-shelf solver. Finally, we present a real-world case of an international automobile supplier. Tackling the instance with an off-the-shelf solver the problem cannot be solved in reasonable time. Thus we apply a simple decomposition scheme to provide decision support for the real-world case.

Sustainable production lot sizing problem: A sensitivity analysis on controlling carbon emissions through green investment

Improving inventory decisions and developing better approaches to invest green technology have been the prime contributions in the existing relevant literature. Besides proposing better inventory decisions and investing on green technologies, the financial performance of a business have also been considered as a focal point. However, none of the existing works on sustainable lot-sizing has considered a simultaneous reduction of carbon emission, product deterioration rate and set-up costs to maximize total profit. Thence, a sustainable lot-sizing model is proposed in this work by incorporating strategies to reduce the setup cost, to optimize the inventory of a greenhouse farm and simultaneous investments in green and preservation technologies to deal with the carbon emission and waste. This study shows the variation of total profit due to changes in investment level and production cycle length. The numerical examples demonstrates the threshold for green technology investment. The study also proves the vital role of preservation technology in deteriorating product inventory, as it gives a higher impact than the other investments.

Integrated lot-sizing and pricing problem under cross-price demand model

This paper addresses a multi-product integrated lot-sizing and pricing problem for an entity which produces and sells different products under a finite production capacity constraint. The demands for each product is assumed to be linear and takes into account the complementarity or substitution characteristics of the products. The objective is to find prices and the production planning (productions quantities, inventory level, setups configuration) for each product during several time periods to maximize the profit. The problem is formulated as a mixed integer nonlinear model with the consideration of different constraints related to production capacity and setup costs. Some new theoretical properties regarding the convexity of the problem and its relaxation are established. Finally, numerical examples are presented to illustrate the obtained results.

Who carries strategic inventory? Manufacturer or retailer

AbstractIt is widely accepted that the retailer's use of strategic inventory can mitigate double marginalization and improve supply chain coordination. However, the recent literature of channel coordination only considers the effects of the retailer's strategic inventory, leaving the manufacturer's incentive to hold strategic inventory mostly unexplored. In reality, there are situations where the manufacturer's inventory can be observed or inferred by the retailer and hence affects the vertical interaction. In our two‐period dynamic model, we show that the manufacturer in equilibrium may carry a positive amount of inventory, which yields a significant impact on the equilibrium decisions and the supply chain players' profits. Specifically, we find that the manufacturer's use of strategic inventory commits a lower propensity to resume production in the second period, thereby encouraging the retailer to carry more strategic inventory at a higher wholesale price in the first period. The manufacturer's use of strategic inventory always hurts the retailer's profit but may enhance channel profit, consumer surplus, and social welfare. Moreover, we show that the manufacturer can earn an even higher profit by directly committing to no replenishment in the second period, observed in industries with longer production lead time and higher production setup costs.

Multi-Product Shipment and Production Scheduling Mathematical Model under Different Distribution Policies

Nowadays, integration of production and distribution has been important in the supply chain. Besides, due to their limited lifespan, integration in the supply chain of perishable items has led to more studies. This study aims to present integrated production and shipment models under full truckload capacity (TL) and less than truckload (LTL) policies combining perishable and non-perishable products in a supply chain, simultaneously. The optimization objective is to minimize the total relevant cost of manufacturer such as the production setup, inventory holding, and transportation costs per time unit. After presenting the models, different numerical example has been used to evaluate based on the change of truck capacity, lifespan as well as costs, and increasing the number of perishable products via Gams software. The results obtained illustrate that the priority of policies TL and LTL depends on the capacity of the truck and shipping costs.

Global optimisation for a developed price discrimination model: A signomial geometric programming-based approach

This paper presents a price discrimination model for a manufacturer who acts in two different markets. In order to have a fair price discrimination model and compare monopoly and competitive markets, it is assumed that there is no competitor in the first market (monopoly market) and there is a strong competitor in the other market (competitive market). The manufacturer’s objective is to maximise the total benefit in both markets. The decision variables are selling price, lot size, marketing expenditure, customer service cost, flexibility and reliability of production process, set-up costs, and quality of products. The proposed model in this paper is a signomial geometric programming problem which is difficult to solve and find the globally optimal solution. So, this signomial model is converted to a posynomial geometric type and using an iterative method, the globally optimal solution is found. To illustrate the capability of the proposed model, a numerical example is solved and the sensitivity analysis is implemented under different conditions.

Investment for process quality improvement and setup cost reduction in an imperfect production process with warranty policy and shortages

Cost reduction for setup and improvement of processes quality are the main target of this research along with free minimal repair warranty for an imperfect production System. This paper deals with the effect of setup cost reduction and process quality improvement on the optimal production cycle time for an imperfect production process with free product minimal repair warranty. Here the production system is subject to a random breakdown from ancontrolledsystem to anout-of-controlstate. Shortages are fully backlogged. The main target to minimize the total cost by simultaneously optimizing the production run time, setup cost, and process quality. A solution algorithm with some numerical experiments are provided such as the proposed model can illustrate briefly. Sensitivity analysis section is decorated for the optimal solution of the model with respect to major cost parameters of the system are carried out, and the implications of the analysis are discussed.

A genetic regulatory network based method for multi-objective sequencing problem in mixed-model assembly lines.

This research proposes a genetic regulatory network based sequencing method that minimizes multiple objectives including utility work costs, production rate variation costs and setup costs in mixed-model assembly lines. After constructing mathematical model of this multi-objective sequencing problem, the proposed method generates a set of genes to represent the decision variables and develops a gene regulation equation to describe decision variable interactions composed of production constraints and some validated sequencing rules. Moreover, a gene expression procedure that determines each gene's expression state based on the gene regulation equation is designed. This enables the generation of a series of problem solutions by indicating decision variable values with related gene expression states, and realizes the minimization of weighted sum of multiple objectives by applying a regulatory parameter optimization mechanism in regulation equations. The proposed genetic regulatory network based sequencing method is validated through a series of comparative experiments, and the results demonstrate its effectiveness over other methods in terms of solution quality, especially for industrial instances collected from a diesel engine assembly line.

The Uncapacitatied Dynamic Single-Level Lot-Sizing Problem under a Time-Varying Environment and an Exact Solution Approach

The dynamic lot-sizing problem under a time-varying environment considers new features of the production system where factors such as production setup cost, unit inventory-holding cost, and unit price of manufacturing resources may vary in different periods over the whole planning horizon. Traditional lot-sizing theorems and algorithms are no longer fit for these situations as they had assumed constant environments. In our study, we investigated the dynamic lot-sizing problem with deteriorating production setup cost, a typical time-varying environment where the production setup is assumed to consume more preparing time and manufacturing resources as the production interval lasts longer. We proposed new lot-sizing models based on the traditional lot-sizing model considering the changing setup cost as a new constraint, called uncapacitatied dynamic single-level lot-sizing under a time-varying environment (UDSLLS-TVE for short). The UDSLLS-TVE problem has a more realistic significance and higher research value as it is closer to reality and has higher computational complexity as well. We proposed two mathematical programming models to describe UDSLLS_TVE with or without nonlinear components, respectively. Properties of the UDSLLS-TVE models were extensively analyzed and an exact algorithm based on forward dynamic programming (FDP) was proposed to solve this problem with a complexity of O (n2). Comparative experiments with the commercial MIP solver CPLEX on synthesized problem instances showed that the FDP algorithm is a global optimization algorithm and has a high computational efficiency.

Modeling and solving the constrained multi-items lot-sizing problem with time-varying setup cost

The dynamic lot-sizing problem is highly complex and very important for the planning systems of manufacturing enterprises in time-varying environment, where production factors such as the production setup costs, unit storage costs, and production capacities may constantly rise or fall in different planning periods over the entire planning horizon. This paper proposed an extension model of the dynamic multi-product lot-sizing problem considering time-varying production setup cost and with dual constraints on dynamic capacities and resource limits, which carters for the actual situation of modern production and manufacturing systems in time-varying environments. Comparative experiments on synthesized problem instances were conducted by using the AMPL/CPLEX solver, which showed that the new model is efficiently on finding solutions with high qualities and the maximum size of test problems can be more than 500 products.

Optimal decision-making for a single-stage manufacturing system with rework options

ABSTRACTThis study investigates a manufacturing system with a single-stage production system that sometimes produces imperfect items. In this system, we assume that the rework process can start after the regular production process (immediate rework) or when the inventory of perfect goods is equal to zero (delayed rework). Also, we assumed non-zero set-up time for rework. Two models are presented for manufacturing systems with re-workable goods. The first model deals with non-zero set-up time for immediate rework and the second model deals with non-zero set-up times for delayed rework. We also investigate special cases associated with these models wherein the set-up times are zero. A general and aggregated model that included those two models is considered. The novelty of this research lies in selecting for a decision-maker the best approach based on system conditions and solutions. This paper provides a framework for rework policies to minimise the total cost of the system, which includes the cost of manufacturing cost, set-up cost for rework and regular production, holding cost for perfect and imperfect items, and the cost of rework. Finally, we solve the aggregated model by using an exact solution algorithm, and the optimal value of production in each period is obtained.

A multi-stage stochastic programming for lot-sizing and scheduling under demand uncertainty

A stochastic lot-sizing and scheduling problem with demand uncertainty is studied in this paper. Lot-sizing determines the batch size for each product and scheduling decides the sequence of production. A multi-stage stochastic programming model is developed to minimize overall system costs including production cost, setup cost, inventory cost and backlog cost. We aim to find the optimal production sequence and resource allocation decisions. Demand uncertainty is represented by scenario trees using moment matching technique. Scenario reduction is used to select scenarios with the best representation of original set. A case study based on a manufacturing company has been conducted to illustrate and verify the model. We compared the two-stage stochastic programming model to the multi-stage stochastic programming model. The major motivation to adopt multi-stage stochastic programming models is that it extends the two-stage stochastic programming models by allowing revised decision at each period based on the previous realizations of uncertainty as well as decisions. Stability test and weak out-of-sample test are applied to find an appropriate scenario sample size. By using the multi-stage stochastic programming model, we improved the quality of solution by 10–13%.

A multi-phase heuristic for the production routing problem

This study considers the production routing problem where a plant produces and distributes a single item to multiple retailers over a multi-period time horizon. The problem is to decide on when and how much to produce and stock at the plant, when and how much to serve and stock at each retailer, and vehicle routes for shipments such that the sum of fixed production setup cost, variable production cost, distribution cost, and inventory carrying cost at the plant and retailers is minimized. A multi-phase heuristic is proposed for the problem. The proposed heuristic is a mathematical programming-based heuristic that relies on formulating and solving restricted versions of the problem as mixed integer programs. The computational experiments on benchmark instances show favorable results with regard to the quality of the solutions found at the expense of higher computing times on large instances. In particular, the heuristic managed to find new best solutions for the 65% of benchmark instances.

Model EPQ Multi Item yang Dimodifikasi untuk Dua Permintaan secara Simultan

Inventory is one of many factors of the business operation that need to be controlled by industries in order to improve efficiency, enhance productivity, and decrease the holding cost. The holding cost of inventories in supply chain contribute to 20% - 40% of the product value. It can be controlled by applying appropriate inventory model, such as EPQ/Economic Production Quantity and EOQ/Economic Order Quantity. EPQ is an inventory model that used to determine the optimum production lot size with balanced the production setup cost and holding cost. Even the classic EPQ has applied widely in industries, the assumption used by this model differed between the researchers whether it is continuous or discrete demand, because the multi delivery or discrete demand is mostly used by industries. Even so, there are industries that used both continuous and discrete demand simultaneously. Based on previous research, there was an advanced EPQ model that synchronizing both assumptions simultaneously, but it still addressed single item problem. Since almost the industries produced multi item, this model has lack of applicability. Therefore, this research proposed a multi item EPQ Model that synchronizing continuous and discrete demand simultaneously. The solution procedure that used in this proposed model are classical calculus method/differential calculus and simultaneous approach. A numerical example is given to show the effectiveness of the proposed approach based on the data from the literature.

A hybrid imperialist competitive algorithm for solving economic lot and delivery scheduling problem in a four-stage supply chain

In this article, we study the economic lot and delivery scheduling problem for a four-stage supply chain that includes suppliers, fabricators, assemblers, and retailers. All of the parameters such as demand rate are deterministic and production setup times are sequence-dependent. The common cycle time and integer multipliers policies are adapted as replenishment policies for synchronization throughout the supply chain. A new mixed integer nonlinear programming model is developed for both policies, the objective of which is the minimization of inventory, transportation, and production setup costs. We propose a new hybrid algorithm including a modified imperialist competitive algorithm which is purposed to the assimilation policy of imperialist competitive algorithm and teaching learning–based optimization which is added to improve local search. A hybrid modified imperialist competitive algorithm and teaching learning–based optimization is applied to find a near-optimum solution of mixed integer nonlinear programming in large-sized problems. The results denoted that our proposed algorithm can solve different size of problem in reasonable time. This procedure showed its efficiency in medium- and large-sized problems as compared to imperialist competitive algorithm, modified imperialist competitive algorithm, and other methods reported in the literature.

A fuzzy periodic review integrated inventory model involving stochastic demand, imperfect production process and inspection errors

In this study, we investigate an integrated production-inventory system consisting of a single-vendor and single-buyer. The buyer manages its inventory level periodically at a certain period of time. We consider a fuzzy annual demand, imperfect production, inspection errors, partial backordering, and adjustable production rate in the proposed model. Additionally, it is assumed that the protection interval demand follows a normal distribution. The model contributes to the current literature by allowing the inclusion of fuzzy annual demand, adjustable production rate and imperfect production and inspection processes. Our objective is to optimize the number of deliveries from vendor to buyer, the buyer’s review period, and the vendor’s production rate, so that the joint expected total annual cost incurred has the minimum value. Furthermore, an iterative procedure is proposed to find the optimal solutions of the model. We also provide a numerical example and conduct a simple sensitivity analysis to illustrate the model’s behaviour and feasibility. The results from the sensitivity analysis show that the defective rate, type I inspection error, fuzzy annual demand, fixed production cost, variable production cost and setup cost give impacts to both the review period and production rate. Finally, it is concluded that the proposed model can be applied by managers or practitiones for managing inventories across the supply chain involving a vendor and a buyer.

Production planning in the molded pulp packaging industry

Production planning in molded pulp packaging companies involves decisions about setting up appropriately the production process to meet the demands of different products. This production process comprises stages such as blending, molding and drying, and the major challenges for the production planning occur in the molding stage, where the mix of products manufactured simultaneously depends on the combination of molds attached to the molding machine, called molding pattern. Thus, the problem lies in deciding which molding patterns should be used, how long each pattern should be used and the production sequence that they should be scheduled. In this study we propose a novel optimization approach to deal with this problem by considering some possible settings for the molding machine based on specific technological constraints. These preset settings are included into a mixed integer programming model to define the molding patterns and to deal with the production lot sizing and scheduling decisions. Since the molding patterns are defined by the approach, three types of production setup times and costs (some of then are sequence-dependent) must be also calculated and taken into account in the planning decisions. Computational tests with real data from a Brazilian molded pulp plant show that the production plans generated by this approach are suitable in practical settings, as well as define molding patterns different from those commonly used and simultaneously reduce setup times and costs, when compared to the production plans of the company.