An inventory control model with consideration of remanufacturing and product life cycle

This paper investigates inventory control policies in a manufacturing/remanufacturing system during the product life cycle, which consists of four phases: introduction, growth, maturity, and decline. Both demand rate and return rate of products are random variables with normal distribution; the mean of the distribution varies according to the time in the product life cycle. Closed-form formulas of optimal production lot size, reorder point, and safety stock in each phase of the product life cycle are derived. A numerical example is presented with sensitivity analysis. The result shows that different inventory control policies should be adopted in different phases of the product life cycle. It is also found that the optimal production lot size and reorder point are not sensitive to the phase length and the demand changing rate.     

An iterative approach to item-level tactical production and inventory planning

In this paper, we propose an iterative approach to jointly solve the problems of tactical safety stock placement and tactical production planning. These problems have traditionally been solved in isolation, even though both problems operate in the same decision making space and the outputs of one naturally serve as the inputs to the other. For simple supply chain network structures, two stages and one or many products, we provide sufficient conditions to guarantee the iteration algorithm’s termination. Through examples, we show how the algorithm works and prove its applicability on a realistic industrial-scale problem.     

An inventory and order admission control policy for production systems with two customer classes

In this paper we examine a Markovian single-stage system producing a single item to satisfy demand of two different customer classes. A simple threshold type heuristic policy is proposed for the joint control of inventories and backorders. Explicit forms of the steady-state probabilities under this policy are derived and used to assess the average profit rate of the system and determine the optimal control parameters. Certain properties of the average profit rate are established and used to develop computationally efficient algorithms for finding the optimal control parameter values. Numerical results show that the proposed policy is a very good approximation of the optimal policy and outperforms other commonly used policies.     

An extended production/recycling model with stationary demand and return rates

A production–recycling system is investigated. A constant demand can be satisfied with production and recycling. The used items are bought back and then recycled. The non-recycled products are disposed of. Two types of models will be analyzed. The first model examines the EOQ-related costs and minimizes the relevant costs. The second model generalizes the first model with the introduction of the cost function with linear waste disposal, recycling, production and buyback costs. It is asked whether the pure (either production or recycling) or mixed strategies are optimal and it will be shown that under these circumstances the mixed strategies are dominated by the pure strategies. The paper generalizes a former model proposed by the authors for the case of one recycling and one production batch to the case of arbitrary batch numbers.     

Optimal policies in hybrid manufacturing/remanufacturing systems with product substitution

In hybrid control systems for simultaneous remanufacturing of used products and manufacturing of new ones, the two operations are not directly interconnected if remanufactured items are downgraded and have to be sold in markets different from those for new products. Sometimes a connection between these markets is given by a downward substitution property which allows the producer to offer a new item instead of a remanufactured one in case of a shortage of a remanufactured product. Thus, shortage costs can be avoided, but a loss in profit due to sale of a high-graded product at the price of a low-graded one has to be accepted. For a single-period problem with stochastic returns of used products and stochastic demands of serviceable ones, it is shown how the manufacturing and remanufacturing decisions have been coordinated in order to maximize the total expected profit. It turns out that under strictly proportional costs and revenues a medium-simple ‘order-up-to policy’ with two parameters and two parameter functions is optimal. However, optimal policies in situations where manufacturing leadtimes exceed leadtimes for remanufacturing turn out to be different from those in the opposite leadtime case. The research presented combines methods for policy analysis in stochastic manufacturing/remanufacturing problems and in stochastic inventory control problems with substitutable products.     

Optimization of a vendor managed inventory supply chain with guaranteed stability and robustness

In this work we address the steady state optimization of a supply chain model that belongs to the class of vendor managed inventory, automatic pipeline, inventory and order based production control systems (VMI-APIOBPCS). The supply chain is optimized with the so-called normal vector method, which has specifically been developed for the economic optimization of uncertain dynamical systems with constraints on dynamics. We demonstrate that the normal vector method provides robust optimal points of operation for a number of scenarios. Since the method strictly distinguishes economic optimality, which is treated as the optimization objective, from dynamical requirements, which are incorporate by appropriate constraints, it provides a measure for the cost of stability and robustness as a desired side-effect.     

Joint determination of inventory replenishment and sales effort with uncertain market responses

An optimal joint operational and marketing decision is crucial for robust supply chain management. This paper addresses concurrent determination of inventory replenishment and sales effort decisions such as price, incentives to salesforce, and short-term promotions, or a combination of them. Market responses to sales efforts are typically highly uncertain, and demand in each period has its distribution dependent on the selected sales effort. In each period a replenishment order may be issued, which incurs both fixed and variable ordering costs, and at the same time the sales effort is also determined, the execution of which may incur costs. For such a model, the previously developed methods which are used for the joint inventory-pricing models become inadequate. A computational procedure for obtaining an optimal joint policy is addressed, and the conditions for the optimality of that policy are identified.     

Supply network capacity planning for semiconductor manufacturing with uncertain demand and correlation in demand considerations

A semiconductor supply network involves many expensive steps, which have to be executed to serve global markets. The complexity of global capacity planning combined with the large capital expenditures to increase factory capacity makes it important to incorporate optimization methodologies for cost reduction and long-term planning. The typical view of a semiconductor supply network consists of layers for wafer fab, sort, assembly, test and demand centers. We present a two-stage stochastic integer-programming formulation to model a semiconductor supply network. The model makes strategic capacity decisions, (i.e., build factories or outsource) while accounting for the uncertainties in demand for multiple products. We use the model not only to analyze how variability in demand affects the make/buy decisions but also to investigate how the correlation between demands of different products affects these strategic decisions. Finally, we demonstrate the value of incorporating demand uncertainty into a decision-making scheme.     

An economic production and remanufacturing model with learning effects

Managing inventory in reverse logistics has been receiving much attention in recent years. One inventory problem that has been of interest to researchers is the production and remanufacturing model, where used items are collected and remanufactured to satisfy customer demand. The available models in the literature do not discuss the learning effects in production and remanufacturing processes. This may not be true in industries where labour costs and learning costs are expensive. By modelling these learning effects, management may use established learning models to better utilize capacity, manage inventories, and coordinate production and distribution throughout the chain.This paper extends the production, remanufacture, and waste disposal model by assuming learning to occur in both production and remanufacturing processes. However, this paper also assumes that improvements due to learning require capital investment. Mathematical models are developed, numerical examples are provided, and results are discussed.     

Exact and approximate calculation of the cycle service level in periodic review inventory policies

The parameters of stock policies are usually determined to minimize costs while satisfying a target service level. In a periodic review policy the time between reviews can be selected to minimize costs while the order-up-to-level is based on the fulfilment of a target service level. Generally, the calculation of this service measurement is obtained using approximations based on an additional hypothesis related to the demand pattern. Previous research has shown that there is a substantial difference between exact and approximate calculations in some general circumstances, so in these cases the service level is not accomplished or the stock level is overestimated. Although an exact calculation of CSL was developed in previous work, the computational effort required to apply it in practical environments leads to the proposal of two approximate methods (PI and PII) that, with the classic approximation, are analysed and evaluated in this paper. This analysis points out the risks of using the classic approximation and leads one to suggest PII as the most suitable and accurate enough procedure to compute the CSL straightforwardly in practice. Additionally, a heuristic approach based on PII is proposed to accept or reject an inventory policy in terms of fulfilling a given target CSL. This paper focuses on uncorrelated, discrete and stationary demand with a known distribution pattern and without backlog.     

Derivation of confidence intervals of service measures in a base-stock inventory control system with low-frequent demand

We explore a base-stock system with backlogging where the demand process is a compound renewal process and the compound element is a delayed geometric distribution. For this setting it holds that the long-run average service measures order fill rate (OFR) and volume fill rate (VFR) are equal in values. However, though equal ex ante one will ex post observe differences as actual sample paths are different. By including a low-frequency assumption in the model, we are able to derive mathematical expressions of the confidence intervals one will get if OFR and VFR are estimated in a simulation using the regenerative method. Through numerical examples we show that of the two service measures it is OFR that in general can be estimated most accurately. However, simulation results show that the opposite conclusion holds if we instead consider finite-horizon service measures, namely per-cycle variants of OFR and VFR.     

Modeling and simulation of order-driven planning policies in build-to-order automobile production

In adopting build-to-order order fulfillment systems, automotive companies strive to better synchronize their production output with market demand. This essentially gives rise to a new paradigm in production planning. Since all business is linked to customer orders, the operational performance is substantially determined by order-driven planning. Therefore, a clear understanding of the associated planning tasks, order promising and master production scheduling, as well as their dynamic interaction is essential. Based on the analysis of the decision situation of order-driven planning in build-to-order settings, we provide a framework comprising separate interlinked quantitative models for order promising and master production scheduling. The focus of the contribution is on the modeling and evaluation of both models in a dynamic setting. The approach is evaluated by means of a simulative analysis using empirical data from the automotive industry. Conclusions regarding the potentials of such systems with respect to customer service, the leveling of resource utilization, and holding are presented.     

A production/remanufacture model with returns’ subassemblies managed differently

This paper considers a production-remanufacturing inventory model for a single product, where constant demand is satisfied from the inventory of newly produced and remanufactured items. Although the available models in the literature imply that collected used units (or returns) are disassembled for recovery purposes, these models really do not treat them as such. Contrary, the returns are assumed to be recovered as whole units, perhaps, for simplicity. This assumption may not capture the benefits reaped from product recovery programs. This paper addresses this limitation in the literature and assumes that each unit of a used product is collected and disassembled into components, where these components are sorted into subassemblies, which are fed back into the production-remanufacturing process. The returned subassemblies are remanufactured and reassembled to represent a second source of as-good-as-new units of the end-product. For this multi-component inventory problem, the question that needs to be answered is whether, or not, extreme strategies of either pure remanufacturing or pure production are more economical than a mixed strategy (one that combines both strategies). A mathematical model is developed that accounts for the inventories of subassemblies. The results suggested that not accounting for the disassembled components of a product leads to inappropriate inventory decisions that are not environmentally sound.     

Optimal pricing and order policies with B2B product returns for fashion products

We study optimal pricing and order policies in supply chain management of fashion products (e.g., a fashion apparel category) with consideration of product returns between supply chain partners (B2B). In order to study channel performance and optimal policies, two stochastic models for centralized channel and decentralized channel are, respectively, developed to handle new fashion and off-season product sales. In the centralized channel, closed-form solutions for optimal order and pricing decisions are proposed for new fashion products. Further, in a decentralized channel, the Stackelberg game model is proposed to derive the optimal Stackelberg equilibrium solution, and then a buy-back contract is designed to coordinate the channel. We also perform parameter analysis on performance of the two channel models. Numerical analysis is finally presented to validate our theoretical results and compare channel performances.     

Integrated production planning with sequence-dependent family setup times

This paper proposes an integrated optimization model of aggregate production planning (APP), family disaggregation planning, and family scheduling problems in hierarchical production planning (HPP) systems considering sequence-dependent family setup times. The model obtains the optimal production plan for each product type and product family in each period, together with the globally optimal production sequence of product families in all planning periods. The proposed model is tested with randomly generated experimental data consistent with what is prevalent in the manufacturing industry and its results are compared with those of the traditional HPP models. Our results show that the integrated model realizes greater cost savings.     

An improved algorithm and solution on an integrated production-inventory model in a three-layer supply chain

Ben-Daya et al. (2010) established a joint economic lot-sizing problem (JELP) for a three-layer supply chain with one supplier, one manufacturer, and multiple retailers, and then proposed a heuristic algorithm to obtain the integral values of four discrete variables in the JELP. In this paper, we first complement some shortcomings in Ben-Daya et al. (2010), and then propose a simpler improved alternative algorithm to obtain the four integral decision variables. The proposed algorithm provides not only less CPU time but also less total cost to operate than the algorithm by Ben-Daya et al. (2010). Furthermore, our proposed algorithm can solve certain problems, which cannot be solved by theirs. Finally, the solution obtained by the proposed algorithm is indeed a global optimal solution in each of all instances tested.     

Supply optimization for the production of raw sugar

Based on a case study from Venezuela, the production of raw sugar is investigated. Ideally, sugar mills operate at a constant production rate. However, safety stocks of the raw material cannot be maintained as sugar cane quality deteriorates very rapidly. Sugar cane is therefore continuously sourced in diverse quantities and qualities from hundreds of geographically dispersed haciendas and supplied to the milling process. Furthermore, due to weather conditions changing throughout the year, tight time windows must be observed for harvesting.The approach presented in this paper aims at preserving a constant supply while minimizing the associated costs. The entire planning problem is structured in a hierarchical fashion: (1) cultivation of the haciendas, (2) harvesting, and (3) dispatching of the harvesting crews and equipment. The corresponding optimization models and solution procedures are introduced and applied to the case study problem.     

Production planning of a hybrid manufacturing-remanufacturing system under uncertainty within a closed-loop supply chain

This paper deals with the production planning and control of a single product involving combined manufacturing and remanufacturing operations within a closed-loop reverse logistics network with machines subject to random failures and repairs. While consumers traditionally dispose of products at the end of their life cycle, recovery of the used products may be economically more attractive than disposal, while remanufacturing of the products also pursues sustainable development goals. Three types of inventories are involved in this network. The manufactured and remanufactured items are stored in the first and second inventories. The returned products are collected in the third inventory and then remanufactured or disposed of. The objective of this research is to propose a manufacturing/remanufacturing policy that would minimize the sum of the holding and backlog costs for manufacturing and remanufacturing products. The decision variables are the production rates of the manufacturing and the remanufacturing machines. The optimality conditions are developed using the optimal control theory based on stochastic dynamic programming. A computational algorithm, based on numerical methods, is used for solving the optimal control problem. Finally, a numerical example and a sensitivity analysis are presented to illustrate the usefulness of the proposed approach. The structure of the optimal control policy is discussed depending on the value of costs and parameters and extensions to more complex reverse logistics networks are discussed.     

Impact of RFID information-sharing strategies on a decentralized supply chain with reverse logistics operations

The integration of environmental practices in a supply chain has been study for the past few decades. However, most of the work relies on centralized decisions made by one player. Few papers address the complex dynamics of environmental decentralized supply chains and how these dynamics can affect environmental and economic outcomes. To study this problem, we consider a supply chain with a manufacturer and two different suppliers: a recycled-material and a raw-material supplier. The players make individual inventory decisions to satisfy demand and reduce cost. Further, this supply chain encompasses stochastic elements such as in demands, returns, and collection leadtimes. These decentralized decisions and random factors can cause underperforming results; therefore, new inventory models and technologies are needed to help companies increase coordination within these systems. We model the implementation of Radio Frequency Identification (RFID) in the supply chain to determine if real-time inventory monitoring and information sharing can help the system attain higher environmental benefits (more returns) and higher economic benefits (less cost). We study two scenarios through a simulation-based analysis: No RFID and RFID. Numerical studies show that environmental benefits are significantly increased with the attainment of more returns. However, although economic benefits are realized, they are less significant than the environmental benefits. Further regression and sensitivity analyses on the cost performance measures reveal that economic benefits depend on several drivers inside the system. We present managerial insights that illustrate what configurations within this complex system can lead to the achieving of environmental as well as economic benefits.     

The deterministic EOQ and EPQ with partial backordering at a rate that is linearly dependent on the time to delivery

Our original models for the EOQ and EPQ with partial backordering assumed that the backordering rate, β, is a constant. In this paper we extend those models to allow β to increase linearly as the time until delivery decreases. We show how those previous models can be adapted to find the optimal decision variable values for this new assumption and develop, for each model type, a condition that the initial value of β must meet for partial backordering to be optimal.