A joint replenishment policy with individual control and constant size orders

We consider inventory systems with multiple items under stochastic demand and jointly incurred order setup costs. The problem is to determine the replenishment policy that minimises the total expected ordering, inventory holding, and backordering costs–the so-called stochastic joint replenishment problem. In particular, we study the settings in which order setup costs reflect the transportation costs and have a step-wise cost structure, each step corresponding to an additional transportation vehicle. For this setting, we propose a new policy that we call the (s, 𝒬) policy, under which a replenishment order of constant size 𝒬 is triggered whenever the inventory position of one of the items drops to its reorder point s. The replenishment order is allocated to multiple items so that the inventory positions are equalised as much as possible. The policy is designed for settings in which backorder and setup costs are high, as it allows the items to independently trigger replenishment orders and fully exploits the economies of scale by consistently ordering the same quantity. A numerical study is conducted to show that the proposed (s, 𝒬) policy outperforms the well-known (𝒬, S) policy when backorder costs are high and lead times are small.     

Multi-echelon inventory control: an adjusted normal demand model for implementation in practice

This paper presents an approximation model for coordinated control of one-warehouse multiple-retailer inventory systems, where all locations use continuous review (R, nQ) policies. The motivation stems from close collaboration with a supply chain management software company, Syncron International, and one of their customers. A core objective has been to develop an accurate method for determining near-optimal reorder points that can be directly applied to real-life systems. The approach is based on decomposing the complex multi-echelon problem into N?+?1 single-echelon problems, using a near-optimal-induced backorder cost at the central warehouse. Important extensions made compared to earlier work include the addition of procedures to adjust for lead-time variability, and for undershooting the reorder point when customers’ order sizes vary. The result is a flexible model that is computationally and conceptually simple enough to be implemented in practice. A numerical study, including real data from the case company, illustrates that the new model outperforms existing methods in the literature. Compared to the current methods used by the case company, it offers significant improvements in both service-level fulfilment and system-wide inventory holding costs. Implementations of the model into the Syncron software are in progress.     

Integrating an EMQ model and product quality

Abstract

In this paper we further extend Chen and Wang's study concerning a CSP‐1 plan applied to the economic manufacturing quantity (EMQ) model with imperfect quality. Adopting the backorder assumption for shortages, the modified total inventory cost includes the setup cost, the holding cost, the backordering cost, the inspection cost, and the internal and external failure cost. By solving the modified EMQ model, we not only obtain the required level of product quality but also determine the minimum of the total inventory cost.     

An exploratory study of risk aversion in supply chain dynamics via human experiment and agent-based simulation

The literature on the impact of risk aversion on supply chains (SCs) is relatively limited and, in particular, there is a dearth of theory and a lack of empirical evidence concerning: (1) the impact of individual risk aversion on the generation and dynamics of the order policy (e.g. order patterns and inventory holding costs); (2) the impact of several combinations of risk-averse members in each stage of a multi-echelon SC. We explore these gaps through a multi-method approach (i.e. human experiments and agent-based simulation), thus using both empirical and simulated data. Specifically, based on results from a human experiment, we develop the conjecture that risk aversion is positively correlated to the desired stock level and consequently to the safety stock factor of inventory order policies. Building on this finding, we perform a simulation study to infer the impact of individual risk aversion in a multi-echelon SC. Results show that alternative compositions of the SC in terms of risk aversion levels of the echelons significantly influence inventory holdings and SC dynamics. The study implies that a company facing problems of high inventory days-on-hand should favour low-risk aversion managers, as instrumental to lowering stock and improving net working capital.     

Integrated optimisation of scheduling and ordering based on semi-finished goods delayed differentiation

The implementation of dynamic ordering policies is becoming increasingly important for the competitiveness of modern manufacturing systems. However, existing models on dynamic ordering pay little attention to production scheduling, which greatly affects the fulfilment of dynamic ordering, especially in complex manufacturing systems. Therefore, it is imperative to establish a new model which integrates both dynamic ordering and production scheduling. Accordingly, a quantitative measurement method for integration is needed. To this end, this paper proposes a semi-finished goods delayed differentiation (SFGDD) model by taking into account integration of the scheduling inventory control and dynamic ordering simultaneously. The objective of this model is to study the relationship between the shop floor inventory and the ordering control based on the semi-finished goods dynamic dispatching mechanism. In addition, the days of inventory (DOI) and a backorder penalty exponential function are developed to quantitatively measure such a relationship. To obtain the optimal results, this paper employs a heuristic genetic algorithm (HGA) with a heuristic encoding scheme to synchronise the generation and selection of inventory variables coherently. A case study on a semiconductor assembly and test manufacturing (ATM) is presented, and a significant revenue enhancement and inventory reduction are achieved accordingly.     

Minimizing the bullwhip effect in a supply chain using genetic algorithms

This paper presents a computational intelligence approach, which addresses the bullwhip effect in supply chains (SCs). A genetic algorithm (GA) is employed to reduce the bullwhip effect and cost in the MIT beer distribution game. The GA is used to determine the optimal ordering policy for members of the SC. The paper shows that the GA can reduce the bullwhip effect when facing deterministic and random customer demand combined with deterministic and random lead times. The paper then examines the effect of sales promotion on the ordering policies and shows that the bullwhip effect can be reduced, even when sales promotions occur in the SC.     

Optimization and optimality of a joint pricing and inventory control policy in periodic-review systems with lost sales

This paper studies a periodic review dynamic pricing and inventory control problem with fixed ordering cost included. Demand is uncertain and price-sensitive in a general form. At the end of each period, all unmet demand is lost. We focus on the optimization and optimality of an (s, S, p)-type policy, which operates as follows: whenever the inventory level is less than or equal to s, an order is placed to order-up-to level S; when the inventory level is larger than s, no order is issued; the price p is specified by the inventory level. We further numerically investigate the optimal solutions and their sensitivity to cost parameters and demand uncertainty.     

A capacity constrained production-inventory system with stochastic demand and production times

This paper considers a simple model of a capacity constrained production-inventory system with Poisson demand. The system is controlled by an S policy. The production time for a unit is modelled as a gamma distributed stochastic variable. Using M/G/1 queuing theory it is very easy to evaluate holding and backorder costs and optimise the ordering policy. The suggested model may be useful when evaluating investments in production.     

The use of rush deliveries in periodic review assemble-to-order systems

We calculate optimal safety stock in a periodic review (T,S) assemble-to-order system having multiple components and multiple finished goods (FGs). Customer orders for FGs arrive according to independent Poisson processes, and cannot be neither backlogged nor lost. In case of potential component stock-out, the studied system uses rush deliveries from suppliers. For this setting, approximate expressions of the optimal safety stock that minimise the sum of inventory holding and rush ordering costs are developed. Exact optimal safety stocks are calculated using Discrete Event Simulation, and compared numerically to the approximate expressions. The model is applied to a first-tier automotive supplier and yields to a significant reduction in terms of inventory holding and rush ordering costs. A sensitivity analysis on relevant system parameters such as components demand, assembly coefficients and unit rush ordering cost is conducted.     

A new algorithm for computing optimal (s, S) policies in a stochastic single item/location inventory system

It has been shown that a class of (s, S) policies is optimal to the single item/location inventory system. However, the computational complexity of finding the optimal (s, S) policy has restricted applications of this inventory system. This paper proposes a new algorithm to search for the optimal pair of s and S. We introduce a dummy cost factor and an auxiliary function into our algorithm. The algorithm searches for the optimal dummy cost through continuously evaluating the auxiliary function. It differs from the approach of Zheng and Federgruen (1991) in several aspects and has certain advantages. First, as it revises the dummy cost based on the sign of the auxiliary function, the primary goal of the search is not to compute the optimal s and S during each iteration. Second, by identifying the non-prospective sets of S, the algorithm further reduces the search effort. Numerical tests show that on the average, the proposed algorithm saves more than 30% of evaluation effort compared with Zheng and Federgruen's method.     

Economic production quantity model for deteriorating inventory with random machine unavailability and shortage

Both random machine unavailability and shortage are common occurrences in manufacturing industries. In this paper, machine unavailability is considered in deriving an economic production quantity (EPQ) model for deteriorating items. We develop four EPQ models for deteriorating inventory with random machine unavailability and shortage. The study considers lost sales, backorder and two kinds of machine unavailability distributions. Numerical examples are provided to illustrate the theory. Key parameter changes that affect costs are shown in the sensitivity analysis. From the results of the sensitivity analysis, it is shown that the random machine unavailability parameter and holding cost have significant effects on the optimal total cost and production down-time.     

Optimal reordering policies for the AHM inventory model with two supply modes

Summary We characterize the optimal reordering policies for the stationary periodic review AHM inventory model when there is a quick and a — generally cheaper — slow supplier, whose delivery lags differ by one period and whose fixed and unit ordering costs are arbitrary, as generalized (s,S) policies described by four parameters (s ₁,S ₁,s ₂,S ₂). Computational results using Howard's policy iteration algorithm yield four possible types of such policies depending on the model parameters.     

Decentralized inventory control in a two-stage capacitated supply chain

This paper investigates a two-stage supply chain consisting of a capacitated supplier and a retailer that faces a stationary random demand. Both the supplier and the retailer employ base stock policies for inventory replenishment. All unsatisfied demand is backlogged and the customer backorder cost is shared between the supplier and the retailer. We investigate the determination of decentralized inventory decisions when the two parties optimize their individual inventory-related costs in a noncooperative manner. We explicitly characterize the Nash equilibrium inventory strategies and identify the causes of inefficiency in the decentralized operation. We then study a set of simple linear contracts to see whether these inefficiencies can be overcome. Finally, we investigate Stackelberg games where one of the parties is assumed to be dominating.     

The trans-shipment problem in a two-echelon,multi-location inventory system with lost sales

In this paper, we address a two-echelon, multi-location pooling inventory system that consists of an outside supplier, a warehouse and two retailers. To control their inventories, both warehouse and retailers use (R,?s,?S) policy. The retailers face stochastic customer demands for a single product and the warehouse receives only the replenishment orders of retailers. In case of stock-out at retailers, emergency trans-shipments are used to satisfy the unmet demand at one retailer with the surplus from the other retailer. When the stock is insufficient at the warehouse, we propose two rationing policies to allocate on-hand stock between retailers. The demand that cannot be satisfied neither by stock on-hand nor by trans-shipment from retailers is considered lost. Our work has two objectives. First, we propose an inventory model based on three components: the optimisation inventory model, the trans-shipment policy and the rationing policies for determining the best values of (s,?S) at each location that minimise total system cost. Second, we validate this model via an empirical simulation study that allows us to identify the influential parameters on trans-shipment benefits.     

考虑产品租赁与缺货损失的制造商最优营销策略

SS〗（北京航空航天大学 经济管理学院,北京 100191）〖HT〗〖JZ）〗〖HJ2.1mm〗〖HT5〗〖GK2〗〖HT5”H〗 摘要： 〖HTSS〗针对制造型企业在产品服务化进程中所开展的产品租赁业务模式进行研究,以确定制造商的最优的销售周期及各类产品的最佳数量。考虑到产品的库存持有成本、缺货随时成本及产品折旧费用等因素,建立了基于总利润最大化的函数模型。在模型的求解过程中首先证明了解析解的重要性质：对于任意给定的销售周期,用于出租的产品与用于销售的产品之间存在最优的数量比例使得总利润最大,反之亦然。后续的算例与参数敏感性分析,给出了一些重要的管理洞察：制造商最优的营销策略受到出租产品需求率以及销售产品售价的影响;制造商选择开展产品出租业务时,就必须使得用于出租的产品数量处于合理的范围内。     

An Economic Lot Size Model for Perishable Products with Age-Dependent Inventory and Backorder Costs

This paper presents an Economic Lot Size (ELS) model for perishable products where the costs of holding inventory stocks (having backorders) in each period depend on the age of inventories (backorders). We propose a polynomial-time dynamic programming algorithm to solve two structured problems, one with non-decreasing demands and the other with non-decreasing marginal backorder cost with respect to the age of the backorder. Our results generalize a recent study on an ELS model for perishable product but without backorders.     

Simulation of an integrated age replacement and spare provisioning policy using SLAM

This paper presents a SLAM simulation model for determining a jointly optimal age replacement and spare part provisioning policy. The policy, referred to as a stocking policy, is formulated by combining age replacement policy with a continuous review (s, S) type inventory policy, where s is the stock reorder level and S is the maximum stock level. The optimal values of the decision variables are obtained by minimizing the total cost of replacement and inventory. The simulation procedure outlined in the paper can be used to model any operating situation having either a single item or a number of identical items. Results from a number of case problems specifically constructed by 5-factor second order rotatory design have been presented and the effects of different cost elements, item failure characteristics and lead time characteristics have been highlighted. For all case problems, optimal (s, S) policies to support the Barlow-Proschan age policy have also been determined. Simulation results clearly indicate the separate optimizations of replacement and spare provisioning policies do not ensure global optimality when total system cost has to be minimized.     

产能不确定环境下多供应商横向协同问题研究

为了减轻零部件产能不确定性所造成的制造商过高库存成本的影响,采用信息共享或者加班赶工及资源外包的方式,建立了多个供应商之间的两种横向协同模型,减量模型和增量模型.通过数据仿真的结果显示,相比于非协同模型,这两种协同模型能够明显地降低制造商的缺货成本和购买成本,同时消除了多余未齐套零部件的库存持有成本,最终有效地降低了制...     

Investigating replenishment policies for centralised and decentralised supply chains using stochastic programming approach

In this paper, a multiple period replenishment problem based on (s, S) policy is investigated for a supply chain (SC) comprising one retailer and one manufacturer with uncertain demand. Novel mixed-integer linear programming (MILP) models are developed for centralised and decentralised decision-making modes using two-stage stochastic programming. To compare these decision-making modes, a Monte Carlo simulation is applied to the optimization models’ policies. To deal with demand uncertainty, scenarios are generated using Latin Hypercube Sampling method and their number is reduced by a scenario reduction technique. In large test problems, where CPLEX solver is not able to reach an optimal solution in the centralised model, evolutionary strategies (ES) and imperialist competitive algorithm (ICA) are applied to find near optimal solutions. Sensitivity analysis is conducted to show the performance of the proposed mathematical models. Moreover, it is demonstrated that both ES and ICA provide acceptable solutions compared to the exact solutions of the MILP model. Finally, the main parameters affecting difference between profits of centralised and decentralised SCs are investigated using the simulation method.     

Just-in-time purchasing: an integrated inventory model involving deterministic variable lead time and quality improvement investment

Nowadays supply chain management is a popular practice in manufacturing systems, and just-in-time (JIT) production plays a crucial role in supply chain environments. Companies are using JIT production to gain and maintain a competitive advantage. The characteristics of JIT systems are consistent high quality, small lot sizes, frequent delivery, short lead time, and close supplier ties. This paper presents an integrated inventory model to minimize the sum of the ordering/setup cost, holding cost, quality improvement investment and crashing cost by simultaneously optimizing the order quantity, lead time, process quality and number of deliveries while the probability distribution of the lead time demand is normal. This integrated inventory model is useful particularly for JIT inventory systems where the vendor and the purchaser form a strategic alliance for profit sharing.