Inventory of differential items selling from two shops under a single management with periodically increasing demand over a finite time-horizon

Inventories of differential items including the defective ones purchased/produced in a lot and sold from two shops (primary and secondary shops) under a single management are considered here over a finite time-horizon. A primary shop receives the differential units in a lot but sells only the non-defective ones whose demand periodically increases with time and decreases during the shortage period in such a way that it comes back to the initial value at the beginning of the next cycle. Hence in this shop, shortages are allowed and fully backlogged. Moreover, at the beginning of the next cycle, the retailer purchases purely non-defective units at a higher price to meet up the shortage amount along with the usual lot of differential units for regular sale. The defective units identified at the time of selling at the primary shop are continuously transferred to the adjacent secondary shop from which the defective ones are sold at a reduced price after some rework. Normally, the price of a defective item is fixed depending upon the quantum of its defect and people go for these items if they are cheap. Hence, demand for these units is dependent on the selling price, which is again inversely proportional to the rate of defectiveness. There may be five scenarios for dealing with defective units depending upon the coincidence of the time periods at two shops. For all scenarios, problems have been mathematically formulated and solved by the use of both parametric study and a gradient-based non-linear optimisation method. The models are illustrated with the help of numerical examples.     

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.     

The linear dynamic lot size problem with minimum order quantity

This paper continues the analysis of a special uncapacitated single item lot sizing problem where a minimum order quantity restriction, instead of the setup cost, guarantees a certain level of production lots. A detailed analysis of the model and an investigation of the particularities of the cumulative demand structure allow us to develop a solution algorithm based on the concept of atomic sub-problems. We present an optimal solution to an atomic sub-problem in an explicit form and prove that it serves as a construction block for the optimal solution of the original problem. Computational tests and a comparison with a published algorithm confirm the efficiency of the solution algorithm developed here.     

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.     

Myopic optimal policy for a multi-period, two-delivery-lead-times, stochastic inventory problem with minimum cumulative commitment and capacity

This paper studies a single-product, multi-period, stochastic inventory problem that imposes the lower and upper bounds on the cumulative order quantity during a planning horizon and allows two delivery lead times. This model includes three features. The first one is that a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer’s total cumulative order quantity during the planning horizon is constrained with the capacity. The second one is that the buyer agrees to purchase the product at least a certain percentage of the purchased capacity during the planning horizon. The third one is that the supplier allows the buyer to order the product with two-delivery-lead-times. We identify conditions under which a myopic ordering policy is optimal. We also develop an algorithm to calculate the optimal capacity when the minimum cumulative order quantity commitment is a certain percentage of the capacity. We then use the algorithm to evaluate the effect of the various parameters on the buyer’s minimum expected total cost during the planning horizon. Our computation shows that the buyer would benefit from the commitments and two-delivery-lead-times.     

Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand

In this paper, a joint pricing and inventory control for non-instantaneous deteriorating items is developed. We adopt a price and time dependent demand function. Shortages is allowed and partially backlogged. The major objective is to determine the optimal selling price, the optimal replenishment schedule and the optimal order quantity simultaneously such that, the total profit is maximized. We first show that for any given selling price, optimal replenishment schedule exists and unique. Then, we show that the total profit is a concave function of price. Next, we present a simple algorithm to find the optimal solution. Finally, we solve a numerical example to illustrate the solution procedure and the algorithm.     

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.     

Inventory management with random supply and imperfect information: A hidden Markov model

In most of the papers on inventory models operating in a random environment, the state of the environment in each period is assumed to be fully observed with perfect information. However, this assumption is not realistic in most real-life situations and we provide a remedy in this paper by assuming that the environment is only partially observed with imperfect information. We accomplish this by analyzing two formulations of single-item models with periodic-review and random supply in a random environment. In the first one, supply is random due to random capacity of production and random availability of transportation. We show that state-dependent base-stock policy is optimal if the capacity and all costs are observed, while demand and availability are unobserved. In the second model, we consider a model with random availability only with fixed-ordering cost. We show that state-dependent (s,S) policy is optimal if the availability process is observable.     

Near-optimal (r,Q) policies for a two-stage serial inventory system with Poisson demand

We consider a two-stage serial inventory system whose cost structure exhibits economies of scale in both stages. In the system, stage 1 faces Poisson demand and replenishes its inventory from stage 2, and the latter stage in turn orders from an outside supplier with unlimited stock. Each shipment, either to stage 2 or to stage 1, incurs a fixed setup cost. We derive important properties for a given echelon-stock (r, Q) policy for an approximation of the problem where all states are continuous. Based on these properties, we design a simple heuristic algorithm that can be used to find a near-optimal (r, Q) policy for the original problem. Numerical examples are given to demonstrate the effectiveness of the algorithm.     

A network approach to modeling the multi-echelon spare-part inventory system with backorders and interval-valued demand

A multi-echelon inventory system implies the existence of a hierarchy of stocking locations, and the dependence and interaction between them. We consider a multi-echelon, spare-part inventory management problem with outsourcing and backordering. The problem is characterized by deterministic repair time/cost, and supply and demand that lie within prescribed intervals and that vary over time. The objective is to minimize the total inventory and transportation costs. We develop a network model for problem analysis and present a network flow algorithm for solving the problem. We prove that the Wagner-Whitin property, known for the lot-sizing problem, can be extended to the spare-part inventory management problem under study.     

Lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand

This paper studies alternative methods for reducing lead time and their impact on the safety stock and the expected total costs of a (Q,s) continuous review inventory control system. We focus on a single-vendor-single-buyer integrated inventory model with stochastic demand and variable, lot size-dependent lead time and assume that lead time consists of production and setup and transportation time. As a consequence, lead time may be reduced by crashing setup and transportation time, by increasing the production rate, or by reducing the lot size. We illustrate the benefits of reducing lead time in numerical examples and show that lead time reduction is especially beneficial in case of high demand uncertainty. Further, our studies indicate that a mixture of setup time and production time reduction is appropriate to lower expected total costs.     

基于总成本费用模型的经济电流密度计算方法研究

传统的计算方法未考虑线路检修费用、线路退役费用、电价、导线价格等重要参变量的时间价值,导致电流密度取值较大,为此,提出基于总成本费用综合评价模型的经济电流密度计算方法。将线路的总成本费用分为初次投入成本、运行人工及维护成本等成本模块,每个模块分别表示为与线路截面、时间等因素相关联的表达式,从而推导出输电线路总成本费用的经济电流密度表达式。通过总成本费用模型对一条已建成的线路进行了验证,证明了方法的合理性和可行性。改进的计算方法对实际工程选型方案的确定有一定的参考价值。     

基于人流量视角下的公共建筑碳排放模型与实证研究

为了解决公共建筑碳排放核算类别繁多、结果粗放的难题,通过调研与程式化扎根理论得出影响公共建筑碳排放的关键因素,并依托实地传感测算试验,研究人流量对环境变化的具体作用机理,整合人时变量,构建了适用于公共建筑的动态碳排放核算模型。结果表明：1)编码处理和调研数据的相关性分析结果均显示人流量对公共建筑的能源消耗起到关键作用;2)人流量间接作用于用能系统以及人的自身排放共同组成温室气体的排放增量;3)经验证,研究构建的动态核算模型原始误差为5.36%,修正后误差降至4.807%（小于5%）,与实际运行工况有良好的交互性。研究成果完善了已有公共建筑的碳排放核算边界,构建了动态工况下的核算模型,实现了基于动态人流量变化下的公共建筑碳排放定量描述,为绿色建筑评价体系提供了理论依据与模型基础。