Optimal Stock Levels Research Articles

Capacity Scalability in Robust Design of Supply Flow Subject to Disruptions

Within the last decade, several cases of the supply chain vulnerability to major disruptions have been observed. The typical mitigation strategies such as safety inventory and excess capacity are inadequate to cover the major disruptions. Furthermore it is not economical to invest in such costly proactive strategies to recover from infrequent disruptions. The objective of this paper is to provide a decision making tool achieving robust supply flow by incorporating strategic stock and reconfigurable back-up supplier in mitigating disruptions. We consider a firm with two suppliers where the main supplier is cost-effective but prone to disruptions and the back-up supplier is reliable but expensive due to re-configurability characteristics. We present a multi-stage robust optimization model to determine optimal strategic stock levels and layout configuration of the back-up supplier for a supply chain subject to random realization of disruptions and available capacity during the ramp-up time. Furthermore, the partial available capacity of the backup supplier during the response time has been modelled using queuing theoretical models. The results show the optimality of highly scalable configuration as the decision maker becomes more risk averse.

Deterministic and stochastic optimal inventory control with logistic stock-dependent demand rate

It has been suggested by many supply chain practitioners that in certain cases inventory can have a stimulating effect on the demand. In mathematical terms this amounts to the demand being a function of the inventory level alone. In this work we propose a logistic growth model for the inventory dependent demand rate and solve first the continuous time deterministic optimal control problem of maximising the present value of the total net profit over an infinite horizon. It is shown that under a strict condition there is a unique optimal stock level which the inventory planner should maintain in order to satisfy demand. The stochastic version of the optimal control problem is considered next. A bang-bang type of optimal control problem is formulated and the associated Hamilton-Jacobi-Bellman equation is solved. The inventory level that signifies a switch in the ordering strategy is worked out in the stochastic case.

Design of supply networks with optimized safety stock levels

In this paper, we address two main issues. First, we determine, through a simulation model, the optimal size and distribution of the safety stocks in a supply network. The “optimal” size of safety stocks results from the minimization of the total logistics cost of the supply network, as a function of the safety stock coefficient (k). In particular, we define the “optimal” size of the safety stocks as the k value which minimizes the total logistics cost of the network. Second, the optimized values of k are used to run the same simulation model under different operating conditions of the network, which are obtained by introducing demand stochasticity, demand seasonality and lead time stochasticity. More precisely, once the optimal size of safety stocks has been set, we carry out further simulations, according to the design of experiments (DOE) procedure, and perform statistical analyses of the resulting outputs, to provide some insights about the design of the supply network under optimal safety stock level. The study is supported by a discrete-event simulation model, developed ad hoc and reproducing 4 different configurations of a fast moving consumer goods (FMCG) network. To run the model, real data related to the FMCG context were used. Results of this study can be useful to supply chain managers, to identify the optimal service level the network should deliver to customers, as well as to understand the behavior of supply networks under optimal safety stock level. Keywords : safety stock; supply network design; simulation model; design of experiments; optimization.

Lockout/tagout and optimal production control policies in failure-prone non-homogenous transfer lines with passive redundancy

This paper considers a production problem for a transfer line subject to random failures and repairs, and differs from other studies on transfer lines. It considers a manufacturing system consisting of three machines (two machines with passive redundancy, and one in series with the previous ones) producing one part type. The control problem is subject to non-negative constraints on work-in-process (WIP). The decision variables are the production rates of two main machines and a standby machine, and influence the WIP levels, the inventory levels and the system's capacity, which is assumed to be described by a finite-state Markov chain. The objective of this paper is to minimise WIP and finished goods inventory costs; it also aims to respect the essential space–time during intervention on machine down, in order to minimise the possibility of the circumvention of protection devices or of the retraction of lockout/tagout procedures through a passive redundancy system. This paper therefore verifies the effect of passive redundancy on optimal stock levels. Given that an analytical or even a numerical solution of the problem is very difficult to find, and that we want to have a more realistic model for industries, we present a combined approach, which is presented based on a combination of analytical formalism, simulation modelling, design of experiments, and response surface methodology to optimise a transfer line with passive redundancy, producing one part type. The usefulness of the proposed approach is illustrated through a numerical example and a sensitivity analysis.

Joint production and quality control of unreliable batch manufacturing systems with rectifying inspection

Production control policy and economic sampling plan design problems have been studied separately in previous research. This paper considers a joint production control policy and economic single sampling plan design for an unreliable batch manufacturing system. The production is controlled by a modified hedging point policy which consists of building and maintaining a safety stock of finished product to avoid shortages during corrective maintenance. The main objective of this paper is to determine simultaneously the economic production quantity, the optimal safety stock level and the economic sampling plan design which minimise the expected overall cost. A stochastic mathematical model is developed and solved using a simulation optimisation approach based on the response surface methodology. Simulation is used to imitate the complex dynamic and stochastic behaviour of processes as in the real-life industrial systems. The obtained results show clearly strong interactions between production quantity, inventory state and sampling plan design which confirm the necessity of jointly considering production and quality control parameters in an integrated model. Moreover, it is shown a significant impact of production system reliability on the economic sampling plan design and therefore on the quality of finished product delivered to consumers. Numerical example and sensitivity analyses are presented for illustrative purposes.

Optimization and Effectiveness of a Production Smoothing Policy in SCM

Kanban system has been known to be a superior tool to control complex production and inventory systems operating in the just-in-time (JIT) environment. The kanban system works more effectively at low inventory levels when the consumption rates of parts necessary to produce finished goods are leveled. The parts consumption leveling in JIT systems is called “Heijunka”. In this research, we investigate a multi-stage multi-product production and inventory system in which the production order quantity is exponentially smoothed. The paper presents an efficient algorithm based on simulation to determine the near optimal exponential smoothing factor and safety stock level at each workstation. We use numerical experiments to evaluate the performance of the exponentially smoothed ordering policy in a supply chain as compared to the original kanban system. And also the performance of the two types of optimization methods, global and local optimizations, in the supply chain are compared. We conclude that the locally optimized production smoothing is quite effective as a production and material replenishment ordering policy as an SCM.

Disruptions in One-Warehouse Multiple-Retailer Systems

We study two-echelon distribution systems (also known as one-warehouse, multiple-retailer (OWMR) systems) subject to supply disruptions. We propose algorithms to find the optimal or near-optimal stocking levels of all the locations in the system by assuming periodic review base-stock policies, deterministic demands at the retailers and non-overlapping disruptions at the supply processes of the warehouse and the retailer. This is the first paper to consider OWMR systems with all locations keeping inventory and all locations subject to supply disruptions. We show how supply disruptions at different parts of the network affect inventory decisions and we quantify the effects of ignoring the disruptions at different parts of the supply chain. Our results suggest that companies should work on reducing the duration of supply disruptions instead of trying to prevent them. In addition, if they choose to do nothing to prevent the consequences of some of the disruptions, these should not be the ones happening close to the customers.

BIOECONOMIC MODEL OF EASTERN BALTIC COD UNDER THE INFLUENCE OF NUTRIENT ENRICHMENT

Abstract The objective of this paper is to study the economic management of Eastern Baltic cod (Gadus morhua) under the influence of nutrient enrichment. Average nitrogen concentration in the spawning areas during the spawning season of cod stock is chosen to be an indicator of nutrient enrichment. The optimal cod stock is defined using a dynamic bioeconomic model for the cod fisheries. The results show that the current stock level is about half of the estimated optimal stock level and that the current total allowable catch (TAC) is about one‐fourth of the optimal equilibrium yield. The results also indicate that the benefit from a reduction in nitrogen very much depends on the harvest policies. If the TAC is set equal to the optimal equilibrium yield, the benefit of a nitrogen reduction from the 2009 level to the optimal nitrogen level would be about 604 million DKK over a 10‐year time horizon, given a discount rate of 4% per year. However, if a recovery management plan is chosen, the benefit would only be about 49 million DKK over a 10‐year time horizon.

Forest conservation versus conversion under uncertain market and environmental forest benefits in Ethiopia: The case of Sheka forest

Previous studies of costs and benefits of forest conservation haven't considered the irreversible nature of forest clearing and the uncertainty associated with forest preservation benefits. The present study adapted a dynamic optimization framework to analyze optimal land use decisions. Results show that ignoring negative climate change effects on tea production and forest carbon storage values leads to excessive deforestation and lower optimal forest stock levels. The analyses also suggest that optimal forest stock is inversely related with the discount rate and at discount rates higher than 5%, complete deforestation becomes the optimal land use choice. This points to the need to critically reassess discount rates currently applied to approval of projects in Ethiopia, which are generally higher than 5% and which do not distinguish projects with long-term environmental costs and benefits from others. It is therefore also necessary to introduce incentive mechanisms such as rewarding reductions in emissions from deforestation and forest degradation to prevent further clearing of forests.

Determining Optimal Stock Level in Multi-Echelon Supply Chains

Inventory control of Multi-echelon supply chains is a widely researched area. In most cases researchers choose analytic methods to analyze such logistics systems. Simulation is a very useful alternative for analyzing supply chain systems and a well-constructed model can provide a better approach and can give more realistic picture of the complex situation. In this article the authors introduce an interactive, configurable simulator to analyze stock levels in a complex supply chain. This new modeling approach (SIMWARE) is capable to simulate complex multi-echelon supply chains where the frequency of stock transfer between the individual levels of the supply chain can be optimized. The authors evaluate different optimization strategies and methods. The introduced SIMWARE method can be used to minimize the environmental impact of the supply chain by minimizing the transportation between the nodes of the supply chain hierarchy. The model provides an optimization methodology where the objective function is the total cost of the supply chain.

Possibility and necessity representations of fuzzy inequality and its application to two warehouse production-inventory problem

In this paper, possibility and necessity representations of fuzzy inequality constraints are presented and then crisp versions of the constraints are derived. Here analogous to chance constraints, real-life necessity and possibility constraints in the context of two warehouse multi-item dynamic production-inventory control system are defined and defuzzified following fuzzy relations. Hence, a realistic two warehouse multi-item production-inventory model with fuzzy constraints has been formulated for a finite period of time and solved for optimal production with the objective of having maximum profit. The rate of production is unknown, assumed to be a function of time and considered as a control variable. Also the present system produces some defective units alongwith the perfect ones and the rate of produced defective units is stochastic in nature. Demand of the good units is stock dependent and known and the defective units are sold at a reduced price. The space required per unit item and available storage space are assumed to be imprecise. The inequality of budget constraints is also imprecise. The space and budget constraints are expressed as necessity and/or possibility types. The model is reduced to an equivalent deterministic model using fuzzy relations and solved for optimum production function using Pontryagin’s optimal control policy, the Kuhn–Tucker conditions and generalized reduced gradient (GRG) technique. The model is illustrated numerically and values of demand, optimal production function and stock level are presented in both tabular and pictorial forms.

Resource Rents and Management Regimes: The Case of the Western Channel Sole Fishery

Understanding the economic and biological status of a fishery resource is critical to designing efficient management policies. In one such attempt, this article assesses current and potential rents in the sole fishery in the English Channel. The sole fishery is found to experience rent dissipation due to significant disinvestment in the stock and substantial fleet overcapacity. The analysis also investigates alternative paths of attaining the optimal stock level.

Dynamic pricing when consumers are strategic: Analysis of posted and contingent pricing schemes

We study dynamic pricing policies for a monopolist selling perishable products over a finite time horizon to strategic buyers. Buyers are strategic in the sense that they anticipate the firm’s price policies. It is expensive and administratively difficult for most brick and mortar retailers to change prices, placing limits on the number of price changes and the types of pricing policies they can adopt. The simplest policy is to commit to a set of price changes. A more complex alternative is to let the price depend on sales history. We investigate two pricing schemes that we call posted and contingent pricing. Using the posted pricing scheme, the firm announces a set of prices at the beginning of the horizon. In the contingent pricing scheme, price evolution depends upon demand realization. Our focus is on the posted pricing scheme because of its ease of implementation. Counter to intuition, we find that neither a posted pricing scheme nor a contingent pricing scheme is dominant and the difference in expected revenues of these two schemes is small. Limiting the number of price changes will result in a decrease in expected revenues. We show that a multi-unit auction with a reservation price provides an upper bound for expected revenues for both pricing schemes. Numerical examples suggest that a posted pricing scheme with two or three price changes is enough to achieve revenues that are close to the upper bound. Dynamic pricing is only useful when strategic buyers perceive scarcity. We study the impact of scarcity and derive the optimal stocking levels for large markets. Finally, we investigate whether or not it is optimal for the seller to conceal inventory or sales information from buyers. A firm benefits if it does not reveal the number of units it has available for sale at the beginning of the season, or subsequently withholds information about the number of units sold.

REDUCING COSTS OF SPARE PARTS SUPPLY SYSTEMS VIA STATIC PRIORITIES

We study static repair priorities in a system consisting of one repair shop and one stockpoint, where spare parts of multiple, critical repairables are kept on stock to serve an installed base of technical systems. Demands for ready-for-use parts occur according to Poisson processes, and are accompanied by returns of failed parts. The demands are met from stock if possible, and otherwise they are backordered and fulfilled as soon as a ready-for-use part becomes available. Returned failed parts are immediately sent into repair. The repairables are assigned to static priority classes. The repair shop is modeled as a single-server queue, where the failed parts are served according to these priority classes. We show that under a given assignment of repairables to priority classes, optimal spare parts stock levels follow from Newsvendor equations. Next, we develop fast and effective heuristics for the assignment of repairables to priority classes. Subsequently, we compare the performance of the system under these static priorities to the case with a First-Come First-Served (FCFS) service discipline. We show that in many cases static priorities reduce total inventory holding and backordering costs by more than 40%. Finally, we analyse the effect of the number of priority classes. We show that 2 priority classes suffice to obtain 90% of the maximal savings via static priorities.

Evaluation of forest management systems under risk of wildfire

We evaluate the economic efficiency of even- and uneven-aged management systems under risk of wildfire. The management problems are formulated for a mixed-conifer stand and approximations of the optimal solutions are obtained using simulation optimization. The Northern Idaho variant of the Forest Vegetation Simulator and its Fire and Fuels Extension is used to predict stand growth and fire effects. Interest rate and fire risk are found to be critical determinants of the superior stand management system and timber supply. Uneven-aged management is superior with higher interest rates with or without fire risk. Alterations in the interest rate affect optimal stocking levels of uneven-aged stands, but have only minor effects on the long-run timber supply. Higher interest rates reduce rotation length and regeneration investments of even-aged stands, which lead to markedly reduced timber supply. Increasing fire risk increases the relative efficiency of even-aged management because a single age cohort is less susceptible to fire damage over the course of the rotation than multiple cohorts in uneven-aged stands. Higher fire risk reduces optimal diameter limit under uneven-aged management and decreases optimal rotation length and planting density under even-aged management.

Optimizing Inventory Using Genetic Algorithm for Efficient Supply Chain Management

Problem statement: Today, inventory management is considered to be an important field in Supply chain management. Once the efficient and effective management of inventory is carried out throughout the supply chain, service provided to the customer ultimately gets enhanced. Hence, to ensure minimal cost for the supply chain, the determination of the level of inventory to be held at various levels in a supply chain is unavoidable. Minimizing the total supply chain cost refers to the reduction of holding and shortage cost in the entire supply chain. Efficient inventory management is a complex process which entails the management of the inventory in the whole supply chain and getting the final solution as an optimal one. In other words, during the process of supply chain management, the stock level at each member of the supply chain should account to minimum total supply chain cost. The dynamic nature of the excess stock level and shortage level over all the periods is a serious issue when implementation was considered. In addition, consideration of multiple products leads to very complex inventory management process. The complexity of the problem increases when more distribution centers and agents were involved. Approach: In present research, the issues of inventory management had been focused and a novel approach based on genetic algorithm had been proposed in which the most probable excess stock level and shortage level required for inventory optimization in the supply chain is distinctively determined so as to achieve minimum total supply chain cost. Results: The analysis provided us with an inventory level that made a remarkable contribution towards the increase of supply chain cost. We predicted the optimal inventory levels in all the supply chain members with the aid of these levels. Conclusion: We concluded that it is possible to minimize the supply chain cost by maintaining the optimal stock levels that we predicted from the inventory analysis. This will make the inventory management further effective and efficient thereby enhancing the customer servicing levels.

A Stochastic Inventory Model with Trade Credit

Suppliers routinely sell goods to retailers on credit. Common credit terms are tantamount to a schedule of declining discounts (escalating penalties) that depend on how long the retailer takes to pay off the supplier's loan. However, issues such as which stocking policies are optimal in the presence of supplier-provided credit have been investigated only when demand is assumed deterministic. Nearly all stochastic inventory models assume either time-invariant finance charges or charges that may vary with time but not with the age of the credit. In this article we present a discrete time model of the retailer's operations with random demand, which is used to prove that the structure of the optimal policy is not affected by credit terms, although the value of the optimal policy parameter is. This is followed by a continuous time model, which leads to an algorithm for finding the optimal stock level. We also model the supplier's problem and calculate the optimal credit parameters in numerical experiments.

Analysis of form postponement based on optimal positioning of the differentiation point and stocking decisions

In this paper we analyse the use of form postponement based on the positioning of the differentiation point and stocking policy. Six classes of manufacturing configurations are identified based on the choice of whether or not form postponement is employed and the decision regarding the stocking policy for the final product configurations as well as for the generic component. Analytical evaluation methods based on queuing models are used to assess operational measures for each class of configuration and solution algorithms are developed to determine the optimal positioning of the differentiation point and the optimal stocking levels. This allows us to compare the relative merits of all manufacturing configurations based on their respective best performances. The results of a numerical experiment show how different operational parameters may influence the choice of optimal configuration, the preference of early or late postponement, and the relative cost savings obtained from employing form postponement.

Inventory Service-Level Agreements as Coordination Mechanisms: The Effect of Review Periods

Asupplier stocking goods for delivery to a retailer may face a (finite-horizon) service-level agreement (SLA). In this context, the SLA is a commitment by a supplier to achieve a minimum fill rate over a specified time horizon. This kind of SLA is an important, but understudied coordination mechanism. We focus on the impact of two contract parameters: the length of the review period and the magnitude of the bonus for meeting or exceeding the service-level target. For a supplier following a base stock (order-up-to) inventory policy, increasing the bonus increases optimal supplier stocking levels, whereas lengthening the review period may increase or decrease optimal stocking levels. We investigate these mechanisms in a controlled laboratory setting and find that longer review periods are generally more effective than shorter review periods in inducing higher stocking levels. As in several earlier laboratory studies, the explanation lies in the improved feedback reliability that longer review periods provide. The primary managerial implication of our findings is that, in practice, longer review periods may be more effective than shorter ones at inducing service improvements.

Optimal inventory policy within hospital space constraints

The materials management group at any hospital is responsible for ensuring that their inventory policies provide a good service in delivering products. The group also needs to be aware of their own costs for distribution, in terms of the frequency of delivery. With future changes to the hospital's infrastructure, function and size, the group require that these policies are reviewed and prepared for the changes taking place. For this, inventory policy models need to be built and used to anticipate the effect of these changes. Due to the importance of many products, high service levels are essential, yet there are often space and delivery constraints, limiting the amount of stock which can be held and delivered at each location. We present in this paper a new constraint-based model for determining optimal stock levels for all products at a storage location, with restrictions on space, delivery and criticality of items taken into account. We validate this model on sterile and bulk items in a real-life setting of an intensive care unit within Cork University Hospital, Ireland.