Optimal stocking strategies for inventory mechanism with a stochastic short-term price discount and partial backordering

Price discount is an important research topic in the field of inventory management. The existing research on this topic mainly considers fixed price discount, but ignores the situation in which stochastic short-term price discount may be involved. In this paper, we study an inventory problem considering stochastic short-term price discount and partial backordering. To address this problem, we propose an optimal replenishment and stocking model to maximise the retailers' profit. After that, a cost–benefit analysis-based heuristic method for solving the developed model is presented by considering two scenarios depending on whether a replenishment point belongs to a discount period or not. Furthermore, an algorithm is provided to elicit an optimal ordering policy from multiple solutions derived from the given heuristic solution method. Finally, a real case is offered to demonstrate the application of the proposed model, followed by a sensitivity analysis. The results indicate that a retailer can identify the optimal replenishment policy with the aim of achieving maximal profit in situations where stochastic short-term price discount and partial backordering are considered for certain inventory problems at hand. In addition, sensitivity analysis illustrates a fact that different values of the introduced parameters may influence the optimal replenishment policy.     

Warehouse location and two-echelon inventory management with concave operating cost

In this paper, we study a location–inventory network design problem which jointly optimises the warehouse location, the warehouse–retailer assignments, the warehouse–retailer echelon inventory replenishment and the safety stock-level decisions over an infinite planning horizon. The consideration of the facility operating cost, the safety stock cost and the two-echelon inventory cost results in an MIP model with several nonlinear terms. Due to the complex trade-offs among the various costs and multiple nonlinear terms in the model, traditional solution approaches no longer work for this problem. We outline a polymatroid cutting-plane approach based on the submodular property of the cost terms to address this problem. Computational results demonstrate that the cutting-plane method based on polymatroid inequalities can efficiently solve randomly generated instances with moderate sizes.     

Design and performance analysis of a novel parallel servo press with redundant actuation

The large capacity servo press is traditionally realized by means of simultaneous actuation of multiple motors. But there exist the over-constraint problem and interference among actuators, which increases the control difficulty and product cost. This paper proposed a novel parallel servo press with redundant actuation, which can avoid the over-constraint and actuation interference. The kinematic and dynamic model of the present servo press are established and thus the kinematic and dynamic performances are obtained under three working modes, i.e. the same and opposite direction modes and non-synchronous mode. The prototype of the active mechanism with the redundant actuators has been manufactured. The kinematic experiments are carried out by using API laser tracking system and the theoretical calculation results agree with the measured data very well, which validates the theoretical model and the present press mechanism.     

An efficient method for dynamic-demand joint replenishment problem with multiple suppliers and multiple vehicles

How to improve competitive edges to meet rapidly changing market environment and dynamic customer needs is critical for the survival and success of firms these days. A good supply chain and inventory management is a necessity in the intensive competitive market. This paper considers a dynamic-demand joint replenishment problem with multiple vehicle routing. The problem is first formulated as a mixed integer programming model with an objective to minimise total costs, which include ordering cost, purchase cost, production cost, transportation cost and holding cost, under a prerequisite that inventory shortage is prohibited in the system. A particle swarm optimisation model is proposed next to solve large-scale problems which are computationally difficult. A case study of a touch panel manufacturer is presented to examine the practicality of the models.     

Data envelopment analysis with multiple modes of functioning. Application to reconfigurable manufacturing systems

In principle, data envelopment analysis (DEA) does not consider the possibility, which can occur in practice, of a production system being able to operate in different modes of functioning. In this paper, a new DEA modelling approach is proposed in which the different modes of functioning are taken into account and included in the analysis. The observed input consumption and output production in each mode of functioning is used to derive a mode-specific technology. The overall DEA technology aggregates these mode-specific technologies according to their respective time allocations. The proposed model computes a target operating point for each mode of functioning so that the operation of the overall system is efficient. The proposed approach is applied to assess the technical, cost and allocative efficiency of a reconfigurable manufacturing system. The inputs considered are modules/tools usage, labour and energy consumption. The outputs are the number of units produced of each part type. The production possibility set is determined by previous observations of the system functioning, from which the best practices can be identified. Technical, cost and allocative efficiency scores can be computed. The proposed approach not only generates input cost savings but also lead time reductions.     

A stochastic lot-sizing model with multi-supplier and quantity discounts

This research considers a stochastic lot-sizing problem with multi-supplier and quantity discounts. The objectives are to minimise total costs, where the costs include ordering cost, holding cost, purchase cost and shortage cost, and to maximise service level of the system. In this paper, we first formulate the stochastic lot-sizing problem as a multi-objective programming (MOP) model. We then transform the model into a mixed integer programming (MIP) model. Finally, an efficient heuristic dynamic programming (HDP) model is constructed for solving large-scale stochastic lot-sizing problems. An illustrative example with two cases for a touch panel manufacturer is used to illustrate the practicality of these models, and a sensitivity analysis is applied to understand the impact of the changes in parameters to the outcomes. The results demonstrate that the proposed two models are effective and accurate tools for determining the replenishment of touch panels from multiple suppliers for multi-periods.     

On the stability and bullwhip effect of a production and inventory control system

This paper focuses on the discrete-time automatic pipeline, inventory and order-based production control system (APIOBPCS), a well-established production and inventory control model. The feedback mechanism within the replenishment rule enables the model to mitigate the bullwhip effect, but introduces a stability problem. In this research, a comprehensive stability analysis is conducted for arbitrary lead times using difference equation theory. On the basis of stability, a state space approach is advocated to analyse the impact of replenishment parameters, demand processes, and lead times on the robustness of the bullwhip effect. The stability results demonstrate that the production control system can easily be destabilised without incorporating the work-in-progress (WIP) feedback loop. Furthermore, it reveals that the stability problem for long lead times can be simplified with the stability condition independent of the lead time. The results obtained in this study provide useful guidelines for the selection of replenishment parameters to guarantee stability and mitigate the bullwhip effect.     

Supply chain design to guarantee quoted lead time and inventory replenishment: model and insights

Do lead time constraints only lead to re-think and re-optimise the inventory positioning along the supply chain or can they impact on the design of the supply chain itself? To answer such a question, we integrate the lead time constraints in a multi-echelon supply chain design model and challenge the difficulty of combining in the same model the long-term decisions (facility location, supplier selection) with the midterm decisions (inventory placement and replenishment, delivery lead time). The model guarantees the respect of the quoted lead time associated with each customer order and the replenishment of the different stocks (raw materials, intermediate and final products) in the different stages of the supply chain between any pair of consecutive orders. We use the model to investigate the impact of the quoted lead time and customer’s order frequency on supply chain design decisions and costs. Some of our results indicate that the lead time constraints can lead to bringing the sites of manufacturing and distribution close to the demand zone and to select local suppliers in spite of their higher cost.     

The effectiveness of investment in lead time reduction for a make-to-stock product

This paper focuses on a firm selling a make-to-stock product with a constant customer demand rate. The firm follows an exact (Q, r) policy for raw material inventory control and faces a random replenishment lead time. Through this research, we wish to gain a better understanding of the impact of investing in reducing supply lead time when the investment costs have to be borne, partly or fully, by the firm. This work is motivated by the recognition that lead time reduction is now of strategic importance in the successful operation of a firm. We examine different types of investment schemes in replenishment lead time reduction and the different cost models they generate. We present analytical and numerical results and insights for each type of model, compute the optimal (Q, r) policy and the associated investment levels. The work presents new results, and sheds light on some apparently counter-intuitive observations.     

双渠道多级分销网络的预防性库存分拨机制与方法研究

企业通过增加库存量来应对不可延期交货带来的缺货损失的传统运作方式在电子商务催生了线上线下双渠道分销模式后变得捉襟见肘。在双渠道多级分销模式下，传统囤货式的运作模式因多层级、多渠道而产生高额库存成本，这恰恰削弱了双渠道销售的高利润优势。因此，拥有双渠道多级分销网络的企业如何平衡库存成本与缺货损失就成为了本文的研究重点。本文考虑了拥有线上线下双渠道销售的一个由中心仓、区域仓和门店节点构成的三级供应链库存系统，借鉴库存共享思想提出了“预防性库存分拨机制”，即节点内线上线下库存、同层级一对多双向预防性调拨、上下级间一对一单向预防性补货的运作机制，并利用目标级联法(analysis target cascading, ATC)依据预测时间窗内的需求预测结果构建预防性分拨模型。最后以国内某大型进口红酒贸易企业为基础对模型进行仿真和分析，结果表明所提出的预防性库存分拨机制能够有效降低库存成本，为双渠道供应链系统低成本高效率的运作提供了实现的手段。     

基于供需一体化协同控制的供应链库存模型

根据供需一体化协同库存控制策略，构建了一个一体化库存模型。在模型里，假定提前期需求是随机的且服从正态分布，允许在提前期内发生缺货，并产生缺货成本；假定提前期是可控的，能够通过增加成本缩短提前期。该模型通过同时计算最优订货量、再订货点、提前期以及运送批次．使供需一体化库存总成本最小。实例分析证明该模型能够达到节约成本的目的。     

Efficient formulation and heuristics for multi-item single source ordering problem with transportation cost

Integrated inventory and transportation decisions are critical in the supply chain, providing significant gains for all parties. In this paper, we present a mathematical formulation for the dynamic demand multi-item single source replenishment problem with a piecewise linear transportation cost. Through an extensive experimental study, we find that the new formulation provides a tighter LP relaxation of the problem, while requiring fewer computational resources to optimally solve the problem when compared with existing model in the literature. We also present a new metaheuristic for this general class of coordinated capacitated replenishment problems. On average, the solutions from heuristics are within 1.23% of the optimal solution for the comprehensive set of test problems.     

An integrated inventory model involving manufacturing setup cost reduction in compound Poisson process

The collaboration of vendor and buyer is one of the key factors for successful supply chain management. The most common strategy for a cooperative system is to propose an integrated replenishment plan. Almost all inventory models assume that setup cost is deterministic and is not subject to control. However, in many practical situations, setup cost can be reduced at an added investment. The paper assumes that setup cost can be reduced at an added investment and shortage is permitted during the lead time. This article relaxes the assumption that the demand of lead time is deterministic and is assumed to be a compound Poisson process. A model is derived to determine an optimal integrated inventory policy with controllable setup cost. The expected annual integrated total cost function is derived and a solution procedure is established to find out the optimal solution. Finally, a numerical example is provided to illustrate the solution procedure.     

Applying machine learning to the dynamic selection of replenishment policies in fast-changing supply chain environments

Firms currently operate in highly competitive scenarios, where the environmental conditions evolve over time. Many factors intervene simultaneously and their hard-to-interpret interactions throughout the supply chain greatly complicate decision-making. The complexity clearly manifests itself in the field of inventory management, in which determining the optimal replenishment rule often becomes an intractable problem. This paper applies machine learning to help managers understand these complex scenarios and better manage the inventory flow. Building on a dynamic framework, we employ an inductive learning algorithm for setting the most appropriate replenishment policy over time by reacting to the environmental changes. This approach proves to be effective in a three-echelon supply chain where the scenario is defined by seven variables (cost structure, demand variability, three lead times, and two partners’ inventory policy). Considering four alternatives, the algorithm determines the best replenishment rule around 88% of the time. This leads to a noticeable reduction of operating costs against static alternatives. Interestingly, we observe that the nodes are much more sensitive to inventory decisions in the lower echelons than in the upper echelons of the supply chain.     

The Joint Replenishment Problem with a Powers-of-Two Restriction

In this paper we consider the joint replenishment problem in the light of recent work by the second and third authors concerning the selection of realistic and consistent reorder intervals in production/ distribution systems. After stating a general dynamic programming formulation of the joint replenishment problem, we present its usual statement which assumes constant reorder intervals. We then restrict the problem further by assuming the constant reorder intervals are powers-of-two multiples of some base planning interval. We present an algorithm based on concepts we developed that solves the joint replenishment problem with the powers-of-two restriction. Like other algorithms proposed for this problem, it is a simple sorting algorithm. Finally, we establish that the algorithm yields a solution whose average annual cost is within 6% of the general problem's long-run minimum average annual cost.     

Inventory and lead time planning with lead-time-sensitive demand

Supply and order lead times can have substantial effects on operations performance and perceived customer service, particularly under uncertain customer demand. Certain customers place a high premium on shorter order lead times, while others may be willing to trade a longer lead time for a lower price. This paper studies a problem in which a supplier wishes to determine the best positioning of a product with respect to order lead time and price. We consider a continuous review inventory replenishment system, where the difference between the procurement lead time and promised sales order lead time influences both cycle stock and safety stock costs, and procurement costs may increase as a result of investment in procurement lead time reduction. We provide models and methods for determining the best combination of price and sales lead time for systems with high economies of scale when demand depends on both sales lead time and price. Our results indicate that for a broad range of practical settings, such systems employ a pure make-to-stock policy or a policy that sets sales lead time equal to the procurement lead time at optimality.     

Inventory control of an item with a probabilistic replenishment lead time and a known supplier shutdown period

In this paper, we address an important practical situation, namely where the usual replenishment lead time (when the supplier's production facility is operating) is a random variable and the supplier shuts down for an interval of known duration (for maintenance, vacation, etc.) each year. The demand rate is constant and any demand when out of stock is assumed to be lost. Under such circumstances we develop a heuristic procedure to decide when to initiate replenishment as well as the associated order-up-to-levels. Through the use of simulation (which accurately estimates the average costs per unit time), the heuristic is shown to perform excellently in a selection of small size problems when one can find the optimal solution. For a large number of problems of more realistic size, the use of simulation reveals that the heuristic achieves substantial cost savings when compared with a simpler, baseline approach. The heuristic itself does not require the use of simulation. The sensitivity of total expected costs to various parameters (such as the length of the shutdown interval and characteristics of the lead time distribution) is discussed.     

产品全成本集成优化和生产模式的选择

主要对机械产品的材料成本和制造成本进行了集成优化,对面向大批量定制的产品全成本集成优化数学模型进行了研究,为企业选择合适的生产模式提供了一种新的方法.     

A dynamic programming approach to integrated assembly planning and supplier assignment with lead time constraints

As manufacturers face fierce competition in the global market, responsiveness has become an important competitiveness factor in addition to quality and cost. One essential responsiveness strategy is to reduce product development and lead times by integrating assembly planning with supplier assignment. This paper addresses the problem of integrated assembly and supply chain design under lead-time constraints by formulating and solving an optimisation problem with minimal total supply chain costs. This new time-constrained joint optimisation problem belongs to an NP-hard resource-constrained scheduling problem. To model this problem effectively, we develop a novel Hyper AND/OR graph and apply it for integrating assembly and supply chain decisions. We also develop a dynamic programming model and associated algorithm in order to solve the integrated optimisation problem with pseudo-polynomial time complexity in practice. Numerical case studies validate that the methods developed can solve the integrated decision-making problem optimally and efficiently. This paper overcomes the limitations of previous studies on concurrent assembly decomposition and supplier selection, which optimises cost without time constraints. The models and results of this research can be applied to a variety of areas including assembly design, maintenance module planning and supply chain restructuring.     

可靠的不完全轴辐网络设计模型

不完全轴辐网络的枢纽被毁坏将导致网络运输成本大量增加，研究可靠的不完全轴辐网络设计模型有利于减少枢纽毁坏带来的不利影响。在不完全轴辐网络设计模型基础上，针对枢纽毁坏后需求分配的两种模式 (single backup/multiple backup，SB/MB) ，构建可靠的不完全轴辐网络设计问题 (reliable incomplete hub-and-spoke network design problem，RIHNDP) 模型并线性化，通过算例验证了模型的有效性。结果表明，需求最多的节点总被选为枢纽。不同模式下的后补枢纽、分配方案可能不同：从管理者角度，为了降低管理难度，可采用SB模式；从出行者角度，为了更低的运输成本，宜采用MB模式。因为正常情况下可靠的不完全网络运输成本比不考虑枢纽毁坏的不完全网络高 (不超过5%，网络越密相差越小) ，有必要考虑枢纽毁坏设计可靠的网络，但当枢纽毁坏发生后RIHNDP能避免枢纽毁坏后网络不连通的情况，其运输成本比不考虑枢纽毁坏的不完全网络低。