Exact and approximated calculation of the cycle service level in a continuous review policy

The paper proposes a method to compute the exact cycle service level for (s, Q) continuous review policy in the presence of undershoots and discrete demand in the discrete time domain. Prior to this, it is necessary to review the definition of the cycle service level in order to avoid the problems that can be found when applied it to the periodic review policy. Therefore, the aim of this paper is: (a) to review the definitions of the cycle service level when applied to continuous review policies; (b) to develop an exact calculation method of the CSL for a continuous review policy when undershoots are allowed and demand is discrete; and (c) to examine some common believes about the cycle service properties. Finally, the bias obtained when the service cycle level is estimated applying the common assumption of neglecting undershoots at the order point is illustrated with some numerical examples which show that it may lead to significant deviations to be ignored.     

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.     

Robust optimal policies of production and inventory with uncertain returns and demand

We consider an inventory and production planning problem with uncertain demand and returns, in which the product return process is integrated into the manufacturing process over a finite planning horizon. We first propose an inventory control model for the return and remanufacturing processes with consideration of the uncertainty of the demand and returns. Then a robust optimization approach is applied to deal with the uncertainty of the problem through formulating a robust linear programming model. Moreover, properties on the robust optimization model are studied, and an equivalent robust optimization model based on duality theory is obtained which allows the solutions to be derived more efficiently. Finally, we provide a set of numerical examples to verify the effectiveness of the approach and analyze the effects of the key parameters on the solutions.     

A state space augmentation algorithm for the replenishment cycle inventory policy

In this work we propose an efficient dynamic programming approach for computing replenishment cycle policy parameters under non-stationary stochastic demand and service level constraints. The replenishment cycle policy is a popular inventory control policy typically employed for dampening planning instability. The approach proposed in this work achieves a significant computational efficiency and it can solve any relevant size instance in trivial time. Our method exploits the well known concept of state space relaxation. A filtering procedure and an augmenting procedure for the state space graph are proposed. Starting from a relaxed state space graph our method tries to remove provably suboptimal arcs and states (filtering) and then it tries to efficiently build up (augmenting) a reduced state space graph representing the original problem. Our experimental results show that the filtering procedure and the augmenting procedure often generate a small filtered state space graph, which can be easily processed using dynamic programming in order to produce a solution for the original problem.     

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.     

A heuristic for balancing the inventory level of different locations through lateral shipments

Solving transshipment problems to optimality is difficult, unless several simplifying hypotheses are assumed (such as unit-sized customer demands and replenishments, negligible replenishment lead time, etc.). For this reason, some heuristics have been recently proposed in order to provide rules, which incorporate relevant factors of the problem, to find conditions under which it makes sense to transship a certain number of units from one retailer to another. Most of these studies concern emergency transshipment, which means that shipments between locations can occur only when a shortage happens, and shipments are assumed to be fast enough to satisfy the location in shortage. When this assumption is not feasible, as in many real cases, transshipments between locations have to be performed before a shortage happens. The paper addresses this case, which can be named ‘preventive’ transshipment, where the inventory level of different locations at the same echelon is balanced through lateral shipments, before a shortage happens. A heuristic for deciding on transshipment policy (when to transship and how much), trying to minimise overall expected costs, is presented. A simulation study considering different scenarios is performed and results confirm the effectiveness of the heuristic.     

Variance amplification and the golden ratio in production and inventory control

A discrete linear control theory model of a generic model of a replenishment rule is presented. The replenishment rule, which we term a “Deziel Eilon—automatic pipeline, inventory and order-based production control system”, is guaranteed to be stable. From a z-transform model of the policy, an analytical expression for bullwhip is derived that is directly equivalent to the common statistical measure often used in simulation, statistical and empirical studies to quantify the bullwhip effect. This analytical expression clearly shows that we can reduce bullwhip by taking a fraction of the error between the target and actual inventory and pipeline (or work in progress (WIP) or “orders placed but not yet received”) positions. This is in contrast to the common situation where ordering policies account for all of the error every time an order is placed. Furthermore, increasing the average age of the forecast reduces bullwhip, as does reducing the production/distribution lead-time. We then derive an analytical expression for inventory variance using the same procedure to identify the closed form bullwhip expression.We assume that a suitable objective function is linearly related to the bullwhip and inventory variance amplification ratios and then optimise the PIC system for different weightings of order rate and inventory level variance. We highlight two forms of the objective function, one where “the golden ratio” can be used to determine the optimal gain in the inventory and WIP feedback loop and another that allows the complete range of possible solutions to be visualised. It is interesting that the golden ratio, which commonly describes the optimum behaviour in the natural world, also describes the optimal feedback gain in a production and inventory control system.     

Business cycle stylized facts and inventory behaviour: New evidence for the Euro area

The purpose of this paper is for the first time to use Business Tendency Survey data, first, to identify new facts that are useful for the interpretation of the decline in the volatility of real activity in the Euro area, and, second, to test the inventory management hypothesis as an explanation for the Great Moderation in Europe. We present stylized facts from the Business Tendency data on series for inventories, current production, current orders, and expected production for the Euro area, emphasizing the decline in the volatility of the series. Further, we investigate whether the decline in inventory volatility can be attributed to an endogenous change in the persistence of shocks to the accumulation dynamics of inventories or to an exogenous change in the shocks hitting the inventory optimisation process. Our results at Euro level generally indicate that there is no evidence of a break in the inventory accumulation process. On the contrary, the impact of exogenous shocks on inventory volatility appears to be steadily declining over time, beginning from the mid-1980s.     

Inter-temporal inventory competition and the effects of capacity constraints

This paper addresses an intertemporal inventory competition between a supplier (a provider, manufacturer) and a retailer engaged in a supply chain. The paper's focus is on the effect of capacity constraints on both parties when demands are seasonal. The paper provides a comparative study of two solution approaches, one is based on supply chain competition and the other is based on system wide optimization. Our results demonstrate that with dynamic inventory competition, the retailer reduces inventory costs by reducing the response period to higher demands while increasing the supply requests compared to the system-wide optimal approach. As a result, the supplier's inventory costs increase. An example illustrating these particular facets of the problem and its application is presented and discussed in light of the supplier and the retailer coordinating policies.     

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.     

Comparison of a new bootstrapping method with parametric approaches for safety stock determination in service parts inventory systems

In this paper, we address the problem of forecasting and managing the inventory of service parts where the demand patterns are highly intermittent. Currently, there are two classes of methods for determining the safety stock for the intermittent item: the parametric and bootstrapping approaches. Viswanathan and Zhou (2008) developed an improved bootstrapping based method and showed through computational experiments that this is superior to the method by Willemain et al. (2004). In this paper, we compare this new bootstrapping method with the parametric methods of Babai and Syntetos (2007). Our computational results show that the bootstrapping method performs better with randomly generated data sets, where there is a large amount of (simulated) historical data to generate the distribution. On the other hand, with real industry data sets, the parametric method seems to perform better than the bootstrapping method.     

On the interaction between forecasting and stock control: The case of non-stationary demand

The effect of using estimated (forecast) demand parameters on the performance of an inventory control system is an intriguing and important subject. Recent research has been undertaken on this phenomenon assuming stationary demand data. In this paper we extend the research to non-stationary demands, by means of simulation. The case of a periodic order-up-to-level inventory system is considered and the experimental structure allows us to evaluate in a progressive manner the accumulated effect of using the optimal forecasting method, optimal forecast parameters and correct variance expression procedures. The results allow insights to be gained into operational issues and demonstrate the scope for improving stock control systems.     

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.     

Optimal inventory control of empty containers in inland transportation system

In this paper, we deal with an inventory control problem of empty containers in an inland transportation system. In inland container transportation, freights (containers) are transported between terminal and the customer’s location by trucks, trains and barges. Empty containers are an important logistic resource and shipping companies try to operate and manage empty containers efficiently. Because of the trade imbalance between hub ports, empty containers should be periodically repositioned from surplus areas to shortage areas. However, it is not easy to exactly forecast the demand of empty containers, and we therefore need to build an efficient way to reposition the empty containers. In this paper, we consider a shortage area and propose an efficient inventory policy to control empty containers. We assume that demands per unit time are independent and identically distributed random variables. To satisfy the demand of empty containers, we reposition empty containers from other hubs based on the (s, S) inventory policy, and also consider the lease of empty containers with zero lead time. For the leased containers, we should return the number of empty containers leased to the leaser after the specified period. For a given policy, simulation is used to estimate the expected cost rate and we use the optimization tool, OptQuest^® in Arena to obtain the near optimal (s, S) policy in numerical examples.     

基于可拓物元法的轨道交通换乘站服务水平综合评价

为了更好地帮助车站运营者对车站服务水平进行综合评价，以反映不同客流组织措施的效果进而进行方案抉择，从行人基本出行体验、走行体验及设备设施体验3方面入手，建立综合服务水平指标体系，并基于可拓理论提出换乘站服务水平综合评价方法。针对客流问题给出4种客流组织场景，利用Anylogic软件对苏州轨道交通石湖东路站进行仿真，得到不同组织场景下的各项指标，随后基于可拓物元法对各场景进行综合评价分析，结合关联度矩阵、具体指标与仿真效果，确定最佳的客流组织方式为场景1，可将综合服务水平由现状的“一般”提高至“良好”。可拓物元法建立的综合评价模型可为车站管理者进行组织措施提供参考，也可为车站运营组织提供技术支撑。     

Inventory control in a two-echelon dual-channel supply chain with setup of production and delivery

This paper considers a two-echelon dual-channel supply chain model with setup of production and delivery and develops a new inventory control policy for the supply chain. Previously, a two-echelon supply chain model without setup of production and delivery is considered and a one-for-one inventory control policy is applied to the supply chain. In the inventory control policy, production is stopped when the warehouse inventory reaches the upper limit and is started again immediately after the inventory drops below the limit. Moreover, delivery to the retailer is stopped when the store inventory reaches the upper limit and is started again immediately after the inventory drops below the limit. The total cost that consists of inventory holding costs and lost sales cost is considered, and setup costs are not considered in the total cost. Once setup costs are introduced, the one-for-one inventory control policy is no longer appropriate. Then, this paper develops a new control policy for the two-echelon dual-channel supply chain with setup of production and delivery. As performance measure, the total cost that consists of inventory holding costs, lost sales cost, and production and delivery setup costs is considered, and the total cost calculated on the basis of Markov analysis demonstrates the effectiveness of the proposed control policy.     

A simulation-based evaluation of the cost of cycle time reduction in Agere Systems wafer fabrication facility—a case study

With the vast amount of capital invested in the semiconductor industry and the high level of competitiveness, semiconductor manufacturers are continuously searching for new methods to gain more market share and increase their profits. New technologies are continuously in demand, and are pushing the semiconductor manufacturers to seek better market position through constant improvement in their processes and products.Agere Systems is one of the leading companies in the microelectronics industry. This paper presents a comprehensive framework for strategic capacity expansion of production equipment at Agere Systems wafer fabrication facility (fab). We integrate simulation modeling, design of experiments, statistical analysis, and economic justification tools to aid in this highly complex decision-making process. We compliment the framework with a particular implementation. The procedure involved studying the factors in the fab that significantly impact the cycle times of the four main technologies that are currently in process and will stay in demand for at least the next few years. Moreover, the goal was to quantify the economic impact of reducing cycle times.To accomplish the objectives of this research, a valid simulation model of the production line of the fab was built. The production equipment (tool sets) that significantly influence production cycle time were identified through factor screening experiments. Based on these factors, several scenarios involving the acquisition of additional tools, aimed at cutting down cycle times, were identified and the operating characteristics curves were constructed. These characteristics curves were used to relate cycle time to production volume capabilities. Finally, an economic analysis was conducted to evaluate the return on investment in additional tools.The outcome of the case study was the identification of bottleneck facilities in the fab that have a significant impact on the cycle time of the four technologies. In the economic analysis, the cost of adding machines to these facilities was compared with the benefits resulting from the increase in production capacities.     

Product price and performance level in one market or two separated markets under various cost structures and functions

Market characteristics, including intrinsic demand and customer sensitivity on price and product performance level, are distinct at different markets. Comparisons of various product development strategies in one market or two geographically separated markets are conducted for three classes of products: development intensive products (DIPs) with constant unit cost, marginal cost-intensive products (MIPs) with constant fixed cost, and marginal and development intensive products (MDIPs) with non-constant unit cost and fixed cost. Results show that larger demand size, less customer sensitivity on price and/or more sensitivity on performance level lead to more profit, a higher sale price and a not-lower product performance. The customer reservation or the saturation performance level should be generally adopted though the optimal performance level does exist occasionally. Unit cost and/or fixed cost must increase in performance at an increasing rate for the existence of one optimal performance level. Due to the impact of demand size, one high-end (low-end) MDIP or DIP could be introduced into one low-end (high-end) market at a different price if the demand size is significantly large in the low-end market. For DIPs, offering one niche high-end product is not worse than offering the low-end product into two markets. For MIPs with negligible fixed cost, the product line strategy is not worse than the standard product development strategy. Additionally, the product cost reduction approach adopted in one product line has significant effects on the best product development strategy and sequence.     

Joint pricing and procurement of fashion products in the existence of clearance markets

This paper focuses on the joint pricing and procurement of fashion products in the existence of clearance markets. It is assumed that the expected regular season demand is a linear decreasing function of the price and the end of period excess inventory is sold at a known discounted price in a clearance market where the demand is a random variable that follows a general distribution. It is shown that the expected profit function is unimodal and the optimal procurement quantity and price can be found from the first order conditions. Existence of a clearance market increases the profit, price, and the procurement quantity. In order to prove this, the optimal procurement and pricing policy of a price-setting retailer who does not have a clearance market is provided. As opposed to the literature, it is shown that the expected profit function of this problem is unimodal as well. A numerical study demonstrating the magnitude of the increase in profit, procurement quantity, and price is reported.