Using aggregate fill rate for dynamic scheduling of multi-class systems

For dynamic scheduling of multi-class systems where backorder cost is incurred per unit backordered regardless of the time needed to satisfy backordered demand, the following models are considered: the cost model to minimize the sum of expected average inventory holding and backorder costs and the service model to minimize expected average inventory holding cost under an aggregate fill rate constraint. Use of aggregate fill rate constraint in the service model instead of an individual fill rate constraint for each class is justified by deriving equivalence relations between the considered cost and service models. Based on the numerical investigation that the optimal policy for the cost model is a base-stock policy with switching curves and fixed base-stock levels, an alternative service model is considered over the class of base-stock controlled dynamic scheduling policies to minimize the total inventory (base-stock) investment under an aggregate fill rate constraint. The policy that solves this alternative model is proposed as an approximation of the optimal policy of the original cost and the equivalent service models. Very accurate heuristics are devised to approximate the proposed policy for given base-stock levels. Comparison with base-stock controlled First Come First Served (FCFS) and Longest Queue (LQ) policies and an extension of LQ policy (Δ policy) shows that the proposed policy performs much better to solve the service models under consideration, especially when the traffic intensity is high.     

Modeling and mitigating supply chain disruptions as a bilevel network flow problem

Years of globalization, outsourcing and cost cutting have increased supply chain vulnerability calling for more effective risk mitigation strategies. In our research, we analyze supply chain disruptions in a production setting. Using a bilevel optimization framework, we minimize the total production cost for a manufacturer interested in finding optimal disruption mitigation strategies. The problem constitutes a convex network flow program under a chance constraint bounding the manufacturer’s regrets in disrupted scenarios. Thus, in contrast to standard bilevel optimization schemes with two decision-makers, a leader and a follower, our model searches for the optimal production plan of a manufacturer in view of a reduction in the sequence of his own scenario-specific regrets. Defined as the difference in costs of a reactive plan, which considers the disruption as unknown until it occurs, and a benchmark anticipative plan, which predicts the disruption in the beginning of the planning horizon, the regrets allow measurement of the impact of scenario-specific production strategies on the manufacturer’s total cost. For an efficient solution of the problem, we employ generalized Benders decomposition and develop customized feasibility cuts. In the managerial section, we discuss the implications for the risk-adjusted production and observe that the regrets of long disruptions are reduced in our mitigation strategy at the cost of shorter disruptions, whose regrets typically stay far below the risk threshold. This allows a decrease of the production cost under rare but high-impact disruption scenarios.

     

Inventory control for point-of-use locations in hospitals

Most inventory management systems at hospital departments are characterised by lost sales, periodic reviews with short lead times, and limited storage capacity. We develop two types of exact models that deal with all these characteristics. In a capacity model, the service level is maximised subject to a capacity restriction, and in a service model the required capacity is minimised subject to a service level restriction. We also formulate approximation models applicable for any lost-sales inventory system (cost objective, no lead time restrictions etc). For the capacity model, we develop a simple inventory rule to set the reorder levels and order quantities. Numerical results for this inventory rule show an average deviation of 1% from the optimal service levels. We also embed the single-item models in a multi-item system. Furthermore, we compare the performance of fixed order size replenishment policies and (R,?s,?S) policies.     

Coordination mechanism for capacity reservation by considering production time,production rate and order quantity

In this paper we study the coordination of a dyadic supply chain producing a high-tech product by contracts. The product has a short life cycle and the buyer faces stochastic demands during the selling period. We consider the production time, which causes the inventory costs on supplier’s side. As the supplier builds production capacity in advance, the production rate is limited to the capacity created during the production time. In addition, we take into account the inventory cost and operational cost for the buyer. We examine the model under both full information and partial information updating situations, and propose a coordinating contract for each case. Our analysis includes the study of members’ decisions under both forced and voluntary compliance regimes. Numerical results are presented to provide more insights into the models developed and the mechanisms proposed.     

Inventory competition and allocation in a multi-channel distribution system

Consider a supply chain involving one manufacturer and one independent retailer. The manufacturer distributes her product to the end consumer through the independent retailer as well as through her direct channel. Each of the two channels faces a stochastic demand. If one channel is out of stock, a fraction of the unsatisfied customers visit the other channel, which induces inventory competition between the channels. Under the scenario described above, will the manufacturer ever undercut the retailer’s order when the capacity is infinite? What are the equilibria of the game? How does a capacity constraint affect the equilibrium outcome? What is the optimal inventory allocation strategy for the manufacturer? Using a game theoretic model we seek answers to the above questions. Both the capacitated and the infinite capacity games are considered. We establish the necessary condition for a manufacturer to undercut a retailer’s order and show that a manufacturer may deny the retailer of inventory even when the capacity is ample. We show that there can be an equilibrium in the capacitated game where a manufacturer might not use the entire capacity and still deny a retailer inventory. We also show that a mild capacity constraint may make both parties better off and thereby increase the total supply chain profit. We develop a simple yet practical contract called the reverse revenue sharing contract and show that along with a fixed franchise fee this contract can coordinates our decentralized supply chain.     

Sourcing from suppliers with random yield for price-dependent demand

We study a multi-period inventory planning problem. In each period, the firm under consideration can source from two possibly unreliable suppliers for a price-dependent demand. Our analysis suggests that the optimal procurement policy is neither a simple reorder-point policy nor a complex one without any structure, as previous studies suggest. Instead, we prove the existence of a reorder point for each supplier. No order is placed to that supplier for any inventory level above the reorder point and a positive order is issued to that supplier for almost every inventory level below the reorder point. We characterize conditions under which the optimal policy reveals monotone response to changes in the inventory level. Furthermore, two special cases of our model are examined in detail to demonstrate how our analysis generalizes a number of well-known results in the literature.     

JIT环境下工厂线边库存容量投资协调策略研究

在JIT环境下,制造商要求长期合作的供应商在其工厂周边租用仓库,而自己只维持较少的线边库存。本文以此为背景,假定制造商投资建设工厂线边库存的费用与其容量大小成正比,分别建立了供应链分散决策和集中决策模型,并提出了制造商工厂线边库存投资建设协调模型。研究结果表明,相比分散决策,供应链集中决策时制造商投资建设的最优工厂线边库存容量更大,从而有利于供应商和整个供应链,而不利于制造商。算例分析证明提出的基于不对称博弈的线边库存投资费用分担策略能够实现整个供应链利益的帕累托优化。     

Periodic review inventory systems with a service level criterion

Full-cost inventory models are mostly studied in the literature, whereas service level constraints are more common to be observed in practical settings. In this paper, we consider periodic review inventory systems with service level restrictions. The control of such inventory systems is limited to (s, S)-type policies in the literature. To the best of our knowledge, we are the first authors to compare such policies with optimal replenishment policies, and illustrate an average cost difference of 0.64%. This justifies the use of these popular (s, S) policies in practice. Furthermore, we propose a new one-dimensional search procedure that is bounded to set the reorder level s and order-up-to level S, whereas the solution space is unbounded and two dimensional. Our heuristic procedure is guaranteed to satisfy the service level constraint and numerical experiments illustrate that it results in an average cost deviation of 1–2% compared with the best (s, S) policy. Consequently, it significantly outperforms all existing procedures from literature, both in service and costs.     

Stochastic inventory problem with piecewise quadratic holding cost function containing a cost-free interval

In this paper, we consider a periodic-review stochastic inventory model with an asymmetric or piecewise-quadratic holding cost function and nonnegative production levels. It is assumed that the cost of deviating from an ideal production level or existing capacity is symmetric quadratic. It is shown that the optimal order policy is similar to the (s, S) policies found in the literature, except that the order-up-to quantity is a nonlinear function of the entering inventory level. Dynamic programming is used to derive the optimal policy. We provide numerical examples and a sensitivity analysis on the problem parameters.This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. A5872. The authors wish to thank an anonymous referee for very helpful comments on an earlier version of this paper.     

A Stochastic Petri Net Approach for Inventory Rationing in Multi-Echelon Supply Chains

Manufacturing supply chains are considered as discrete event dynamical systems (DEDS) where coordination of material and information flows is essential to satisfy customer orders and to improve the bottomline of the constituent organizations. A critical problem that is often faced by distribution centres that hold finished good inventory is that of inventory rationing. Inventory rationing is a useful strategy to tackle the problem of conflicting objectives i.e., minimizing inventory costs (holding and backorder) on the one hand and achieving the desired customer service levels (CSLs) on the other. The focus of this paper is to formulate Generalized Stochastic Petri net models to address the inventory rationing problem in the context of multi-echelon make-to-stock distribution chains, where the goods flow through multiple echelons, typically from product manufacturers all the way up-to the retail outlets. The statistical inventory control (SIC) policies modeled by the GSPN are (R, s, S) and a variant that we propose, (R^∗, s, S). We compare the performance of the model under two rationing settings. The first setting considers a case without cooperation, where the individual local stockpoints maximize their own performance. The second setting considers a case with cooperation, where the local stockpoints cooperate with each other to maximize the overall system performance. We provide a methodology to approximately determine the optimal rational fractions with different weights assigned to expected backorder and holding cost components (b/h). We present some interesting results obtained after rigorous numerical experimentation on the model.     

Coordinating inventory control and pricing strategies: The continuous review model

We analyze an infinite horizon, single product, continuous review model in which pricing and inventory decisions are made simultaneously and ordering cost includes a fixed cost. We show that there exists a stationary (s,S) inventory policy maximizing the expected discounted or expected average profit under general conditions.     

A periodic-review inventory system with a capacitated backup supplier for mitigating supply disruptions

We consider a periodic-review inventory system with two suppliers: an unreliable regular supplier that may be disrupted for a random duration, and a reliable backup supplier that can be used during a disruption. The backup supplier charges higher unit purchasing cost and fixed order cost when compared to the regular supplier. Because the backup supplier is used at unplanned moments, its capacity to replenish inventory is considered limited. Analytical results partially characterize the structure of the optimal order policy: a state-dependent (X(i), Y(i)) band structure (with corresponding bounds of X(i) and Y(i) to be given), where i represents the status of the regular supplier. Numerical studies illustrate the structure of the optimal policy and investigate the impacts of major parameters on optimal order decisions and system costs.     

Contracting with an urgent supplier under cost information asymmetry

We investigate a contract setting problem faced by a manufacturer who can procure major modules from an overseas supplier, as well as a local supplier. The overseas supplier is prime and offers quality products, whereas the local supplier is viewed only as a backup, and its products are inferior in quality. As the local supplier needs to put in additional effort to fulfill the urgent orders, it is difficult for the manufacturer to estimate this urgent supplier’s production cost. This asymmetric cost information becomes an obstacle for the manufacturer in managing the urgent supplier. In this paper, we study two types of contingent contracts. One is the common price-only contract, and the other is a contract menu consisting of a transfer payment and a lead time quotation. We construct a Stackelberg game model and evaluate how the involvement of an urgent supplier with private cost information affects performances of the prime supplier and the manufacturer in different scenarios (with or without the urgent supplier, under different contingent contracts). We also conduct numerical experiments to show how the parameters of the contracts affect profits of the manufacturer.     

Supply chain scheduling: Sequence coordination

A critical issue in supply chain management is coordinating the decisions made by decision makers at different stages, for example a supplier and one or several manufacturers. We model this issue by assuming that both the supplier and each manufacturer have an ideal schedule, determined by their own costs and constraints. An interchange cost is incurred by the supplier or a manufacturer whenever the relative order of two jobs in its actual schedule is different from that in its ideal schedule. An intermediate storage buffer is available to resequence the jobs between the two stages. We consider the problems of finding an optimal supplier's schedule, an optimal manufacturer's schedule, and optimal schedules for both. The objective functions we consider are the minimization of total interchange cost, and of total interchange plus buffer storage cost. We describe efficient algorithms for all the supplier's and manufacturers’ problems, as well as for a special case of the joint scheduling problem. The running time of these algorithms is polynomial in both the number of jobs and the number of manufacturers. Finally, we identify conditions under which cooperation between the supplier and a manufacturer reduces their total cost.     

Supplier–manufacturer coordination in capacitated two-stage supply chains

Manufacture-to-order is an increasingly popular strategy in commodity electronics and other similar markets where many different product configurations can be produced from common components. To succeed in this environment, manufacturers need to keep both cost and order fulfillment time low. In this article, we compare three different mechanisms that a manufacturer, whose revenues depend on order delays, may use to affect its component supplier’s inventory decisions. These mechanisms are specifying components inventory level, offering a share of the earned revenues to the supplier (called simple revenue sharing), and offering a two-part revenue-sharing scheme. We show that whereas the first two approaches do not lead to supply chain coordination, the two-part scheme does. We demonstrate with numerical experiments that up to a point, the component supplier benefits from having a high utilization of its production facility, whereas the manufacturer benefits from having excess production capacity.     

Newsvendor with multiple options of expediting

We consider a manufacturer facing single period inventory planning problem with uncertain demand and multiple options of expediting. The demand comes at a certain time in the future. The manufacturer may order the product in advance with a relatively low cost. She can order additional amount by expediting after the demand is realized. There are a number of expediting options, each of which corresponds to a certain delivery lead time and a unit procurement price. The unit procurement price is decreasing over delivery lead time. The selling price is also decreasing over time. In this paper, we assume that the manufacturer must deliver all products to the customer in a single shipment. The problem can be formulated as a profit maximization problem. We develop structural properties and show how the optimal solution can be identified efficiently. In addition, we compare our model with the classical newsvendor model and obtain a number of managerial insights.     

Managing an integrated production inventory system with information on the production and demand status and multiple non-unitary demand classes

In this paper, we study a system consisting of a manufacturer or supplier serving several retailers or clients. The manufacturer produces a standard product in a make-to-stock fashion in anticipation of orders emanating from n retailers with different contractual agreements hence ranked/prioritized according to their importance. Orders from the retailers are non-unitary and have sizes that follow a discrete distribution. The total production time is assumed to follow a k₀-Erlang distribution. Order inter-arrival time for class l demand is assumed to follow a k_l-Erlang distribution. Work-in-process as well as the finished product incur a, per unit per unit of time, carrying cost. Unsatisfied units from an order from a particular demand class are assumed lost and incur a class specific lost sale cost. The objective is to determine the optimal production and inventory allocation policies so as to minimize the expected total (discounted or average) cost. We formulate the problem as a Markov decision process and show that the optimal production policy is of the base-stock type with base-stock levels non-decreasing in the demand stages. We also show that the optimal inventory allocation policy is a rationing policy with rationing levels non-decreasing in the demand stages. We also study several important special cases and provide, through numerical experiments, managerial insights including the effect of the different sources of variability on the operating cost and the benefits of such contracts as Vendor Managed Inventory or Collaborative Planning, Forecasting, and Replenishment. Also, we show that a heuristic that ignores the dependence of the base-stock and rationing levels on the demands stages can perform very poorly compared to the optimal policy.     

Modeling and analysis for determining optimal suppliers under stochastic lead times

The policy of simultaneously splitting replenishment orders among several suppliers has received considerable attention in the last few years and continues to attract the attention of researchers. In this paper, we develop a mathematical model which considers multiple-supplier single-item inventory systems. The item acquisition lead times of suppliers are random variables. Backorder is allowed and shortage cost is charged based on not only per unit in shortage but also per time unit. Continuous review (s,Q)$(s\text{,}Q)$ policy has been assumed. When the inventory level depletes to a reorder level, the total order is split among n suppliers. Since the suppliers have different characteristics, the quantity ordered to different suppliers may be different. The problem is to determine the reorder level and quantity ordered to each supplier so that the expected total cost per time unit, including ordering cost, procurement cost, inventory holding cost, and shortage cost, is minimized. We also conduct extensive numerical experiments to show the advantages of our model compared with the models in the literature. According to our extensive experiments, the model developed in this paper is the best model in the literature which considers order splitting for n-supplier inventory systems since it is the nearest model to the real inventory system.