Stochastic integer programming models for reducing wastages and shortages of blood products at hospitals

Major challenges in the management of the blood supply chain are related to the shortage and wastage of the blood products. Given the perishable characteristics of this product, storing an excessive number of blood units on inventory could result on the wastage of this limited resource. On the other hand, having shortages may result in cancellations of critical health related activities and as a result a potential increase on fatality rates at hospitals.This paper presents integer programming models to minimize the total cost, shortage and wastage levels of blood products at a hospital within a planning horizon. The primary focus is on the red blood cells and the platelet components of the whole blood cells. The stochastic and deterministic models included consider uncertain demand rates, demand for two types of patients, and crossmatch-to-transfusion ratio. Results show wastage rates decreasing from 19.9% to 2.57% on average. In addition, the shortages and total cost are reduced 91.43% and 20.7% respectively for a given capacity increases. Computational results are included and discussed.     

The benefit of VMI strategies in a stochastic multi-product serial two echelon system

We consider a multi-product serial two echelon inventory system with stochastic demand. Inventories at the downstream location are replenished periodically using an automatic ordering system. Under vendor managed inventory strategies the upstream stage is allowed to adapt these orders in order to benefit from economies of scale. We propose three different VMI strategies, aiming to reduce the order picking cost at the upstream location and the transportation costs resulting in reduced total supply chain costs. In a detailed numerical study the VMI strategies are compared with a retailer managed inventory strategy for two different demand models suitable for slow moving products. It is shown that if inventory holding costs are low, compared to handling and transportation costs, efficiencies at the warehouse are improved and total supply chain costs are reduced.     

Random network models and sensitivity algorithms for the analysis of ordering time and inventory state in multi-stage supply chains

Supply chains in reality face a highly dynamic and uncertain environment, especially the uncertain end-customer demands and orders. Since the condition of product market changes frequently, the tasks of order management, product planning, and inventory management are complex and difficult. It is imperative for companies to develop new ways to manage the randomness and uncertainty in market demands. Based on the graphical evaluation and review technique, this paper provides a simple but integrated stochastic network mathematical model for supply chain ordering time distribution analysis. Then the ordering time analysis model is extended so that the analysis of inventory level distribution characteristics of supply chain members is allowed. Further, to investigate the effects of different end-customer demands on upstream orders and relative inventory levels, model-based sensitivity analysis algorithms for ordering fluctuations and inventory fluctuations are developed. A detailed numerical example is presented to illustrate the application of the proposed models to a multi-stage supply chain system, and the results of which shows the effectiveness and flexibility of the proposed stochastic network models and algorithms in order and inventory management.     

The impact of information sharing on ordering policies to improve supply chain performances

Bullwhip effect represents the amplification and distortion of demand variability as moving upstream in a supply chain, causing excessive inventories, insufficient capacities and high operational costs. A growing body of literature recognizes ordering policies and the lack of coordination as two main causes of the bullwhip effect, suggesting different techniques of intervention. This paper investigates the impact of information sharing on ordering policies through a comparison between a traditional (R, S) policy and a coordination mechanism based on ordering policy (a combination of (R, D) and (R, S) policies). This policy relies on a slow, easy to implement, information sharing to overcome drawbacks of the effect, in which replenishment orders are divided into two parts; the first is to inform the upstream echelons about the actual customer demand and the second is to inform about the adjustment of the inventory position, smoothing at the same time the orders of the different levels of the supply chain. A simulation model for a multi-echelon supply chain quantifies the supply chain dynamics under these different policies, identifying how information sharing succeeds to achieve an acceptable performance in terms of both bullwhip effect and inventory variance.     

Quantifying and mitigating the bullwhip effect in a benchmark supply chain system by an extended prediction self-adaptive control ordering policy

An undesired observation known as the bullwhip effect in supply chain management leads to excessive oscillations of the inventory and order levels. This paper presents how to quantify and mitigate the bullwhip effect by introducing model predictive control (MPC) strategy into the ordering policy for a benchmark supply chain system. Instead of quantifying the bullwhip effect with commonly used statistical measure, we derive equivalently the expression of bullwhip metric via control-theoretic approach by applying discrete Fourier transform and (inverse) z-transform when the demand signal is stationary stochastic. A four-echelon supply chain is formulated and its dynamical features are analyzed to give the discrete model. An extended prediction self-adaptive control (EPSAC) approach to the multi-step predictor is implemented in the development of MPC formulation. The closed-form solution to MPC problem is derived by minimizing a specified objective function. The transfer function for MPC ordering policy is then obtained graphically from an equivalent representation of this closed-form solution. A numerical simulation shows that MPC ordering policy outperforms the traditional ordering policies on reducing bullwhip effect.     

Fuzzy knowledge-based token-ordering policies for bullwhip effect management in supply chains

The “Bullwhip Effect” is a well-known example of supply chain inefficiencies and refers to demand amplification as moving up toward upstream echelons in a supply chain. This paper concentrates on representing a robust token-based ordering policy to facilitate information sharing in supply chains in order to manage the bullwhip effect. Takagi–Sugeno–Kang and hybrid multiple-input single-output fuzzy models are proposed to model the mechanism of token ordering in the token-based ordering policy. The main advantage of proposed fuzzy models is that they eliminate the exogenous and constant variables from the procedure of obtaining the optimal amount of tokens which should be ordered in every period. These fuzzy approaches model the mentioned mechanism through a push–pull policy. A four-echelon SC with fuzzy lead time and unlimited production capacity and inventory is considered to survey the outcomes. Numerical experiments confirm the effectiveness of proposed policies in alleviating BWE, inventory costs and variations.     

A study on inventory replenishment policies in a two-echelon supply chain system

Inventory control plays an important role in supply chain management. Properly controlled inventory can satisfy customers’ demands, smooth the production plans, and reduce the operation costs; yet failing to budget the inventory expenses may lead to serious consequences. The bullwhip effect, observed in many supply chain management cases, causes excessive inventory due to information distortion, i.e. the order amount is exaggerated while a minor demand variation occurs, and the information amplified dramatically as the supply chain moves to the upstream. In this paper, one of the main causes of bullwhip effect, order batching, is considered. A simplified two-echelon supply chain system, with one supplier and one retailer that can choose different replenishment policies, is used as a demonstration. Two types of inventory replenishment methods are considered: the traditional methods (the event-triggered and the time-triggered ordering policies), and the statistical process control (SPC) based replenishment method. The results show that the latter outperforms the traditional method in the categories of inventory variation, and in the number of backlog when the fill-rate of the prior model is set to be 99%. This research provides a different approach to inventory cost-down other than the common methods like: information sharing, order batch cutting, and lead time reduction. By choosing a suitable replenishment policy, the number of backorder and the cost of inventory can be reduced.     

Bi-objective reliable location-inventory-routing problem with partial backordering under disruption risks: A modified AMOSA approach

In this paper, we present a reliable model of multi-product and multi-period Location-Inventory-Routing Problem (LIRP) considering disruption risks. An inventory system with stochastic demand in which the supply of the product is randomly disrupted in distribution centers, is considered in this paper. Partial backordering is used in case stock out occurs by considering the probability of the confronting defects in distribution centers in time of disruption. We presented a bi-objective mixed-integer nonlinear programming (MINLP) model. The first objective minimizes the locating, routing and transportation costs and inventory components which consist of ordering, holding and partial backordering costs. The second objective is to minimize the total failure costs related to disrupted distribution centers that leads to reliability of the supply chain network. Because of NP-hardness of the proposed model, we modified Archived Multi-Objective Simulated Annealing (AMOSA) meta-heuristic algorithm to solve the bi-objective problem in large scales and compared the results with three other algorithms. To improve performance of the algorithms Taguchi method is used to tune parameters. Finally, several numerical examples are generated to evaluate solution methods and five multi-objective metrics are calculated to compare results of the algorithms.     

An integrated multi-stage supply chain inventory model under an infinite planning horizon and continuous price decrease

This paper studies an integrated inventory model in a supply chain that involves procurement, production and delivery activities. The model is studied in an environment where products experience continuous price decrease and planning is performed in an infinite time horizon. In this model, a manufacturing facility purchases a fixed-quantity of raw materials from an outside supplier, processes the materials, and delivers a fixed-quantity of finished products to a customer periodically. In order to take advantage of the decreasing price trend, customers demand frequent deliveries of small lots of finished products, and this inventory management strategy has been used by many successful companies in technology-related industries. Therefore, the ultimate intention of this research is to study and model the inventory system for high-tech companies whose products are experiencing continuous price decrease. This model is used to determine an optimal economic lot size model for raw material procurement, production setup and finished goods delivering under an infinite planning horizon. Two efficient algorithms are developed in this paper to solve this nonlinear model and the test results consistently indicate that ordering of raw materials and delivery of finished goods should be frequent in small lots for low ordering and shipment costs. Finally an operational schedule is provided to show the implementation procedure of the model.     

闭环供应链混合切换库存控制模型研究

针对一类具有回收、再制造、再分销的闭环供应链系统,以再制造产品的补货能力为切换信号设计了基于再制造优先的混合切换库存控制策略,使得市场需求优先由再制造产品满足,并应用切换控制理论研究混合切换库存控制策略的性能特征,分析系统参数对闭环供应链系统的关键性能指标的影响。仿真分析表明,合理的切换控制策略可以有效抑制闭环供应链运作过程的波动,保证系统具有良好的“牛鞭效应”特征、平稳的库存管理成本以及较高的顾客服务水平。     

Critical number ordering policy for LIFO perishable inventory systems

This paper considers a stochastic perishable product inventory system characterized by LIFO (Last-In-First-Out) issuing, critical number ordering and a two-period lifetime. Exact and approximate closed form expressions for expected outdates are derived. The approximation, which is straightforward to compute, is shown to be accurate over a wide range of model parameters. The paper concludes by comparing optimal policies and expected costs in the LIFO system with the corresponding policies and costs in a system controlled by FIFO (First-In-First-Out) issuing.     

Production and allocation policies in a two-class inventory system with time and quantity dependent waiting costs

This paper presents an integrated production and inventory allocation model in a two-echelon supply chain system. The higher echelon is a manufacturer, who produces a single commodity. The lower echelon consists of two types of major commodity distributors who might face stochastic or deterministic demands from multiple retailers. Our analytical model provides optimal decision policies that minimize total production and customer waiting costs from the manufacturer's perspective when there are time and quantity dependent customer waiting costs. We identify the value of the integrated policy and compare it with typical approximations such as aggregating the multiple demands or applying the single demand multiple times.     

3级网状随机性库存控制策略的仿真优化

研究了多制造商,多分销商和多零售商的3级网状随机性库存系统的(r,Q)库存控制策略问题.由于该系统具有顾客到达时间服从泊松分布,随机顾客需求量,随机顾客购买行为,随机订货时间和制造商生产容量有限制等特点,使得解析方法很难描述系统中的多种复杂随机因素并无法求解有效的库存控制策略.为此建立了以总成本最小为目标的数学模型,运用了基于仿真的优化方法,通过将仿真方法与粒子群优化算法相结合对问题进行求解.最后通过仿真实例与比较,验证了模型和基于仿真的粒子群优化方法的可行性和有效性.也表明了基于仿真的优化方法在供应链管理中的适用性.     

On ordering adjustment policy under rolling forecast in supply chain planning

Rolling forecast is a useful tool for lowering total cost with regard to practical inventory management. The details regarding a rolling forecast are obtained from a customer’s projected ordering data. The customer estimation of a rolling forecast may deviate from actual orders because of unstable conditions or customer’s deliberation. This study investigates what measures a customer might apply in responding to a situation where the rolling forecast deviates from the actual order. In addition, an appropriate ordering adjustment policy is proposed for better monitoring the supply chain performance with regard to a variant level of error concerning rolling forecast data. This study also considers the influence of lead time and inventory cost structure. We adopted a simulation approach, employing a model developed and examined in several different settings. The proposed ordering adjustment policies are determined by AVG, SD, and RMSE calculated from differences existing between historical forecasts and realized data. Levels of estimate error and estimate bias in a rolling forecast are included in the experimental procedure. Results reveal that the RMSE ordering adjustment policy is the most effective in situations of normal and downside estimation bias, whereas the AVG policy is more appropriate in the case of upside estimation bias. The level of estimation error is irrelevant to the selection of ordering adjustment policies, but it is positively associated with inventory costs. Stock-out costs and lead time are positively associated with inventory costs. Accuracy of the rolling forecast is therefore deemed to be essential in a situation involving a long lead time with high stock-out costs.     

The impact of product characteristics and innovativeness on the benefits of collaboration

Horizontal collaboration is a promising avenue to improve the efficiency of logistical operations. However, the benefits strongly depend on the degree of fit between partners. In this paper, we analyze the impact of the partners' product characteristics on those benefits, focusing on their innovativeness. Companies supplying functional versus innovative products have different requirements in supply chain efficiency and responsiveness, which impacts the benefits that can be reached with a given partner. To assess the collaborative benefits, we use a location–inventory model accounting for the partners' individual interests and the costs revealing the responsiveness level of the supply chain (facilities, transportation, cycle inventory, safety stocks and stock-outs). The model offers a set of Pareto-optimal solutions balancing the partners' costs to support the selection and negotiation process. Finally, we perform numerical experiments in which the partners supply products with identical or different levels of innovativeness and with various demand volumes, leading to valuable managerial insights on the impact of product characteristics on collaborative benefits.     

A production base-stock policy for recycling supply chain management in the presence of uncertainty

This study focuses on solving master planning problems for a recycling supply chain with uncertain supply and demand. A recycling supply chain network includes collectors, disassemblers, remanufacturers, and redistributors working from the collection of returned goods to the distribution of recovered products to the market. The objective of this study is to maximize the total profit of the entire recycling supply chain. Considering the stochastic property of the recycling supply chain, this study institutes stocking and processing policies for each member of the recycling supply chain to better respond to unknown future demand. We propose a heuristic algorithm called stochastic recycling process planning algorithm (SRPPA) to address master planning problems in the recycling supply chain and its supply and demand uncertainties. The main SRPPA process consists of three phases. In the leader determination phase, SRPPA identifies the most important node as the leader of the recycling supply chain. In the candidate policy set generation phase, SRPPA defines the search range for the inventory policy and forms the candidate policy sets based on the characteristics of the leader. In the best policy set selection phase, SRPPA constructs the simulation process for each inventory policy candidate to identify the best policy set. A scenario analysis is then presented to show the effectiveness and efficiency of SRPPA.     

Simulation-based optimization of process control policies for inventory management in supply chains

A simulation-based optimization framework involving simultaneous perturbation stochastic approximation (SPSA) is presented as a means for optimally specifying parameters of internal model control (IMC) and model predictive control (MPC)-based decision policies for inventory management in supply chains under conditions involving supply and demand uncertainty. The effective use of the SPSA technique serves to enhance the performance and functionality of this class of decision algorithms and is illustrated with case studies involving the simultaneous optimization of controller tuning parameters and safety stock levels for supply chain networks inspired from semiconductor manufacturing. The results of the case studies demonstrate that safety stock levels can be significantly reduced and financial benefits achieved while maintaining satisfactory operating performance in the supply chain.     

Single period stochastic inventory problems with ordering or returns policies

In recent years, there has been an increasing adoption of returns policies in the coordination of the supply chain, where market demand is always assumed to be satisfied by manufacturing or by ordering from suppliers. However, many industries face the important decision of how to balance their inventory level. This problem has long been studied in financial institutions such as banks. This study presents an optimal inventory policy under a given stochastic demand such as a uniformly distributed demand, single-item, and single period review inventory system. The optimal inventory control policy obtained in this study is called a four-point policy: that is, when the entity’s inventory level is below a reorder point, the entity must increase his stock level by ordering and order up-to a fixed level (second point); when the entity’s inventory level is over a return point (third point); the stock level must be decreased by returns and decreased to a fixed level (fourth point); otherwise, nothing should be done. We also analyze the (K, S)-convex properties of the inventory cost function.     

A decision rule for coordination of inventory and transportation in a two-stage supply chain with alternative supply sources

This paper deals with a two-stage supply chain that consists of two distribution centers and two retailers. Each member of the supply chain uses a (Q,R) inventory policy, and incurs standard inventory holding and backlog costs, as well as ordering and transportation costs. The distribution centers replenish their inventory from an outside supplier, and the retailers replenish inventory from one of the two distribution centers. When a retailer is ready to replenish its inventory that retailer must decide whether it should replenish from the first or second distribution center. We develop a decision rule that minimizes the total expected cost associated with all outstanding orders at the time of order placement; the retailers then repeatedly use this decision rule as a heuristic. A simulation study which compares the proposed policy to three traditional ordering policies illustrates how the proposed policy performs under different conditions. The numerical analysis shows that, over a large set of scenarios, the proposed policy outperforms the other three policies on average.     

基于混合需求的供应链多级库存协同订货模型

针对供应链多级库存系统存在混合需求的情况,建立了基于混合需求的多级库存协同订货模型。该模型假设在供应链中只有最下游节点面临的需求是独立需求,而其他上游节点面临的需求都是与之相关的相关需求。由于相关需求是一种块状需求,其库存成本构成与独立需求明显不同。因此,通过对多级库存系统的库存成本构成进行重新分析,分别给出了需求确定时不允许缺货和允许缺货的协同订货模型。另外,还通过对安全库存的分析给出了需求不确定时的协同订货模型。最后,给出了模型求解的遗传算法,并进行了实例仿真分析,展示了这种协同订货模型在混合需求的供应链中的实用性。