Base-stock Level Research Articles

Inventory policies and safety stock optimization for supply chain planning

In this article, traditional supply chain planning models are extended to simultaneously optimize inventory policies. The inventory policies considered are the (r,Q) and (s,S) policies. In the (r,Q) inventory policy an order for Q units is placed every time the inventory level reaches level r, while in the s,S policy the inventory is reviewed in predefined intervals. If the inventory is found to be below level s, an order is placed to bring the level back to level S. Additionally, to address demand uncertainty four safety stock formulations are presented: (1) proportional to throughput, (2) proportional to throughput with risk‐pooling effect, (3) explicit risk‐pooling, and (4) guaranteed service time. The models proposed allow simultaneous optimization of safety stock, reserve, and base stock levels in tandem with material flows in supply chain planning. The formulations are evaluated using simulation. © 2018 American Institute of Chemical Engineers AIChE J, 65: 99–112, 2019

Modelling and analysis of the impact of correlated inter-event data on production control using Markovian arrival processes

Empirical studies show that the inter-event times of a production system are correlated. However, most of the analytical studies for the analysis and control of production systems ignore correlation. In this study, we show that real-time data collected from a manufacturing system can be used to build a Markovian arrival processes (MAP) model that captures correlation in inter-event times. The obtained MAP model can then be used to control production in an effective way. We first present a comprehensive review on MAP modeling and MAP fitting methods applicable to manufacturing systems. Then we present results on the effectiveness of these fitting methods and discuss how the collected inter-event data can be used to represent the flow dynamics of a production system accurately. In order to study the impact of capturing the flow dynamics accurately on the performance of a production control system, we analyze a manufacturing system that is controlled by using a base-stock policy. We study the impact of correlation in inter-event times on the optimal base-stock level of the system numerically by employing the structural properties of the MAP. We show that ignoring correlated arrival or service process can lead to overestimation of the optimal base-stock level for negatively correlated processes, and underestimation for the positively correlated processes. We conclude that MAPs can be used to develop data-driven models and control manufacturing systems more effectively by using shop-floor inter-event data.

Computing base-stock levels for a two-stage supply chain with uncertain supply

We consider independent decision makers in a two-stage supply chain subject to uncertainty in upstream supply, and we use a recently published computational algorithm to generate independent, single-stage (ISS) base-stock inventory solutions for each stage in the system. These solutions are computed by employing straightforward, linear functions to estimate the parameters that must be set to seed the single-stage computational algorithm. Those linear functions are derived from the system-optimal solutions, which are found by solving a Markov chain model of the two-stage system. We demonstrate that the ISS solutions are often quite close to the system-optimal solution, and moreover, we develop a fast, descent-based search to quickly find the system-optimal solutions starting from the ISS solutions. We use our solution algorithm to generate optimal solutions to 1100 randomly-generated problem instances, allowing us to explore the behavior of the two-stage inventory system under various cost, demand uncertainty, and supply uncertainty conditions. We find that the downstream stocking levels are strongly influenced by the properties of the downstream demand, while the upstream stocking level is very strongly influenced by the holding costs and supply uncertainty, and only marginally by the retailer penalty cost. Moreover, the system responds to changes in the cost and uncertainty environment mostly by shifting the burden of holding cost either upstream or downstream, leaving the downstream penalty cost relative stable across the large set of problem instances we study.

Technical Note—Perishable Inventory Systems: Convexity Results for Base-Stock Policies and Learning Algorithms Under Censored Demand

We develop the first nonparametric learning algorithm for periodic-review perishable inventory systems. In contrast to the classical perishable inventory literature, we assume that the firm does not know the demand distribution a priori and makes replenishment decisions in each period based only on the past sales (censored demand) data. It is well known that even with complete information about the demand distribution a priori, the optimal policy for this problem does not possess a simple structure. Motivated by the studies in the literature showing that base-stock policies perform near optimal in these systems, we focus on finding the best base-stock policy. We first establish a convexity result, showing that the total holding, lost sales and outdating cost is convex in the base-stock level. Then, we develop a nonparametric learning algorithm that generates a sequence of order-up-to levels whose running average cost converges to the cost of the optimal base-stock policy. We establish a square-root convergence rate of the proposed algorithm, which is the best possible. Our algorithm and analyses require a novel method for computing a valid cycle subgradient and the construction of a bridging problem, which significantly departs from previous studies. The e-companion is available at https://doi.org/10.1287/opre.2018.1724

Assortment Optimization with Product Level Demand and Substitution Information

This article presents a mathematical model for jointly optimizing base stock levels for the multiple items subject to service level goals. The proposed model uses the expected demand and substitution probabilities between products as inputs and has been used to analyze the effects of demand variability on profitability under service level constraint. The results of the analysis demonstrate that neglecting customer-driven substitution or excluding the impacts of variability and correlations in demand leads to significantly inefficient assortments.

Control of a continuous production inventory system with production quantity restrictions

Motivated by a real-world application in the chemical industry, we consider the problem of controlling a production asset that has to run continuously around the clock. This requirement causes minimum and maximum production quantities per period, resulting from the minimally and maximally feasible production rates. Our goal in this paper is to find a good control rule for this production inventory setting. To this end, we first show that the setting is analytically equivalent to a periodic-review inventory system with an order band, for which a modified base-stock policy is optimal. We then develop an iterative solution algorithm to approximate the optimal base-stock level under a predefined service-level target. This algorithm is easily implementable in a spreadsheet software tool with additional Visual Basic for Applications coding. In a numerical study, we find that the approximation works very well for a broad set of parameters. In contrast, simple rules-of-thumb such as the usage of a “standard” base-stock level that does not consider the order band may result in severe errors. Either the chosen base-stock level is too low, causing the service-level target to be undershot (by up to 40% in our analyzed settings), or it is too high, resulting in an overshoot of the service-level target and thus in excessive inventory. In the real-world application example, the new solution approach identifies an inventory saving potential of about 17%.

Development and evaluation of a Basestock-CONWIP pull production control strategy in balanced assembly systems

In this study, a new pull production control strategy called Basestock-Constant Work-in-Process (B-CONWIP) is proposed. It is used to control the flow of materials and information in balanced assembly production systems. This proposed control strategy uses one type of authorization cards called CONWIP card that limits the work-in-process (WIP) in the whole system. It has been applied in a single-product and a mixed-product assembly system balanced by two efficient Genetic algorithms introduced in literature. The performance of this control strategy is compared with another pull production control strategy called Basestock Kanban CONWIP (BK-CONWIP), which is a very promising production control strategy found in literature. The proposed strategy has two control parameters, CONWIP authorization cards and basestock levels while BK-CONWIP has three control parameters Kanban authorization cards, CONWIP authorization cards and basestock levels. The comparison is based on three performance measures average system WIP, percentage of satisfied customer demand (service level) and WIP variation between workstations. The performance of the proposed strategy B-CONWIP and BK-CONWIP is mainly similar in both types of assembly systems when mean demand rates are low with respect to mean service rates with the proposed strategy being easier to control and optimize. On the other hand, when mean demand rates are high with respect to mean service rates; B-CONWIP is preferable if service level is more important, while BK-CONWIP is preferable if WIP level is more important. Regarding WIP variation, it mainly depends on the efficiency of the balancing approach. The more efficient the balancing approach, the less WIP variation. Treating demand as lost instead of backordered results in decreased average system WIP and does not affect service levels in both PCSs. It is also shown that S-KDP is more flexible in dealing with situations of variable product mixes than d-KDP because control parameters can be used by any product which minimizes the effect of the unbalanced systems.

Solution procedures for lost sales base-stock inventory systems with compound Poisson demand

The continuous review base-stock policy under the lost sales assumption has been extensively studied in the inventory literature. However, most of the research that deals with the optimal policy parameter determination under compound Poisson demand focuses on the stuttering Poisson case. In this paper, we extend earlier research by providing a method that calculates the best cost-driven base-stock policy under more general compound Poisson demand processes and for both the complete and the partial rejection case. This is done by developing a simple recursive formula that computes the steady-state probabilities of the number of outstanding orders for general demand and lead-time distributions. Based on this, we are able to obtain the optimal base-stock level under the complete rejection case and an approximate base-stock level under the partial rejection policy. Through a numerical investigation, we show that our approach outperforms existing methods with regard to computational requirements.

Postponed two-pricing and ordering opportunity for selling a single season inventoried product

Postponement strategies are becoming increasingly important in light of a global trend in which products’ life-cycles are decreasing, such that even products that are not traditionally considered seasonal become “obsolete” within a short period of time (e.g., electronic devices, new cars). Our work addresses postponed-pricing and ordering decisions for a retailer who sells a newsvendor-type inventoried product, in a selling season that is divided into two sub-periods. The division of the selling season enables the retailer to on-line adjust her decisions when faced with a scenario (one that is highly prevalent in reality) in which potential demand changes (increases or decreases) following consumers’ experiences of the product in early stages of the selling season. We assume that the retailer has two opportunities for receiving shipments: prior to the first sub-period and prior to the second one. The retailer determines each order quantity (base-stock level) on the basis of the demand distribution for the corresponding sub-period. In each sub-period, after observing additional market signals, the retailer determines the price of the product for that sub-period. With the aid of a stochastic programming approach, we develop optimization problems and solution methods in order to obtain pricing and ordering decisions that maximize the expected profit of the retailer. We present an extensive numerical example that compares the suggested strategy to three alternative strategies, and conclude that price postponement and responsiveness to demand changes can each reduce leftovers and lost sales as well as substantially increase expected profit.

Inventory parameters for a serial supply chain with lost sales through genetic algorithm approach

Supply chain is a network of facilities with varying conflicting objectives and decision making is a complex process. The uncertainty in demand increases complexity in inventory control mechanism. Backordering, partial backordering and lost-sales are considered in the inventory management to characterise the excess demand. In the present competitive scenario, mostly consumers have no patience to wait and show urgency to buy their goods failing which the management has to meet a huge loss of supply chain members and hence the profit. There are very few research works regarding lost-sales parameter in the area of multi-echelon inventory systems. It is felt that the proposed modified gene-wise genetic algorithm (MGGA) supply chain model which so far not applied in this process may help to determine best base stock levels and review periods with lost sales particularly at retailer end which minimised total supply chain cost.

Inventory parameters for a serial supply chain with lost sales through genetic algorithm approach

Supply chain is a network of facilities with varying conflicting objectives and decision making is a complex process. The uncertainty in demand increases complexity in inventory control mechanism. Backordering, partial backordering and lost-sales are considered in the inventory management to characterise the excess demand. In the present competitive scenario, mostly consumers have no patience to wait and show urgency to buy their goods failing which the management has to meet a huge loss of supply chain members and hence the profit. There are very few research works regarding lost-sales parameter in the area of multi-echelon inventory systems. It is felt that the proposed modified gene-wise genetic algorithm (MGGA) supply chain model which so far not applied in this process may help to determine best base stock levels and review periods with lost sales particularly at retailer end which minimised total supply chain cost.

Spare Parts Inventory Control under a Fixed-Term Contract with a Long-Down Constraint

We are interested in service contracts for spare parts. We introduce a new performance measure, XLD (extreme long down), that limits the number of deliveries that are later than an agreed threshold during the contract period. We consider a single item, single location stockpoint serving multiple systems where demand is satisfied in an alternative way if the stockpoint is out of stock. Using a finite horizon Markov decision process, we derive the optimal spare parts inventory policy for meeting the contract at minimum costs. We prove that a state-dependent and time-dependent base stock policy is optimal. We also prove that the optimal base stock level is non-increasing in the number of allowed extreme long downs in the remaining contract period and that the optimal base stock level decreases at most by one unit per step. We formulate three heuristics for our finite horizon problem. These heuristics are a translation of heuristics commonly used for other service measures than the XLD measure. We assess their performance in comparison to the optimal policy. The results of our numerical study show that Heuristic 3, a myopic heuristic, is the best performing with an average optimality gap of 4.5% and an optimality gap lower than 5% in 81% of the instances. The maximum optimality gap is very high for all three heuristics, showing that important savings can be made by taking into account the actual contract performance and the remaining contract duration in stocking decisions.

Stochastyczny model do szacowania intensywności napraw dla systemu działającego w warunkach logistyki wydajnościowej

Performance Based Logistics (PBL) concept has an aim to improve the system availability and it has been extensively researched in the recent years. These researches showed that inventory level does not impact system availability as much as component reliability and repair time in repairable system operating under PBL contract. Based on that, in this paper, we propose a new stochastic model for determination of annual repair rate for critical aircraft components in such system in order to achieve desired availability. The result obtained could be used for planning of base stock level and capacity of repair facilities.

Accelerated Benders’ Decomposition for Integrated Forward/Reverse Logistics Network Design under Uncertainty

In this paper, a two-stage stochastic programming modelling is proposed, to design a multi-period, multistage, and single-commodity integrated forward/reverse logistics network design problem under uncertainty. The problem involved both strategic and tactical decision levels. The first stage dealt with strategic decisions, which are the number, capacity, and location of forward and reverse facilities. In the second stage, tactical decisions, such as base stock level as an inventory policy, were determined. The generic introduced model consisted of suppliers, manufactures, and distribution centers in forward logistic and collection centers, remanufactures, redistribution, and disposal centers in reverse logistic. The strength of the proposed model is its applicability to various industries. The problem was formulated as a mixed-integer linear programming model and was solved by using Benders’ Decomposition (BD) approach. In order to accelerate the Benders’ decomposition, a number of valid inequalities were added to the master problem. The proposed accelerated BD was evaluated through small-, medium-, and large-sized test problems. Numerical results confirmed that the proposed solution algorithm improved the convergence of BD lower bound and the upper bound, enabling to reach an acceptable optimality gap in a convenient time.

Service level agreements: ready-rate analysis with lump-sum and linear penalty structures

In operations management, service level agreements (SLAs) are widely used to evaluate and manage supplier performance. In a typical SLA, a target ready rate is periodically measured and a financial penalty is incurred if this target is not met. The ready rate considered in this study is defined as the long-run fraction of periods in which all customer demand is filled immediately from on-hand stock. Previous studies of SLAs have been solely concerned with one supplier serving one-customer, whereas in practice a supplier usually deals with more than one-customer. In multiple-customer cases, the supplier has an SLA with each customer and a penalty is incurred whenever the agreement is violated. In this work, we examine the impacts of various factors such as the base-stock level, the type of penalty and the review period duration on the supplier’s cost function when the supplier deals with multiple-customers. The results show that dealing with more customers is preferable for a supplier (assuming the overall demand is the same) and that a longer performance review phase is beneficial under a lump-sum penalty contract.

Optimal Dynamic Order Scheduling under Capacity Constraints Given Demand‐Forecast Evolution

We consider a manufacturer without any frozen periods in production schedules so that it can dynamically update the schedules as the demand forecast evolves over time until the realization of actual demand. The manufacturer has a fixed production capacity in each production period, which impacts the time to start production as well as the production schedules. We develop a dynamic optimization model to analyze the optimal production schedules under capacity constraint and demand‐forecast updating. To model the evolution of demand forecasts, we use both additive and multiplicative versions of the martingale model of forecast evolution. We first derive expressions for the optimal base stock levels for a single‐product model. We find that manufacturers located near their market bases can realize most of their potential profits (i.e., profit made when the capacity is unlimited) by building a very limited amount of capacity. For moderate demand uncertainty, we also show that it is almost impossible for manufacturers to compensate for the increase in supply–demand mismatches resulting from long delivery lead times by increasing capacity, making lead‐time reduction a better alternative than capacity expansion. We then extend the model to a multi‐product case and derive expressions for the optimal production quantities for each product given a shared capacity constraint. Using a two‐product model, we show that the manufacturer should utilize its capacity more in earlier periods when the demand for both products is more positively correlated.

Disposal versus rework – Inventory control in a production system with random yield

In a production environment where random yield plays a fairly significant role, a decision has to be made on how to handle products that do not satisfy given quality requirements. We consider a single-stage production system with a positive production time and random yield. To ensure that only high quality items are sold to the customer, a post-production quality control system has been put in place. We compare two different strategies for defective items: disposal or rework. Disposal is possible without any time delay whereas the rework process requires a positive rework time. While disposed-of items leave the production process, reworked products stay in the process and are assumed to be as good as products that are perfect when they are initially produced. The end products are stored in a warehouse to satisfy stochastic demand. We show how to determine the optimal base-stock level, which is very difficult because of unknown covariances between orders. Subsequently, an optimization model is proposed to support the planner’s decision on which strategy to choose when it comes to whether to dispose of or rework defective items. By means of a sensitivity analysis we show which parameters directly affect this decision and give managerial insights. The analysis indicates that significant cost reductions can be obtained by choosing the best strategy for defective products.

Optimal capacity allocation in a production–inventory system with base stock

We address the optimal allocation of a given capacity in a multi-product inventory–production system with base stock. In the system, the base stock level is equal to the sum of the finished goods and work-in-process inventory. Each exogenous demand releases production of a new unit and increases the level of work-in-process. Unsatisfied demand is backordered. Using an open single-server queueing network, we model the behavior of the work-in-process in the manufacturing system in order to determine the cost-optimal base stock level. We focus on the utilizations in the network and compare balanced and unbalanced systems regarding their base stock level. In particular, we analyze the effect of capacity reallocation and show that a manufacturing system consisting of production stations with constant utilization rates, results in the lowest base stock level. With the combined application of queueing network theory and majorization theory, we are able to provide analytical explanations of the network’s behavior.

Cash Conversion Systems in Corporate Subsidiaries

This paper models a cash conversion system in a subsidiary of a parent company where there is an active internal capital market, but otherwise the subsidiary has no access to additional external funds. The cash conversion system consists of a treasury, a single-product make-to-stock inventory, and a receivables pool. It implements a perpetual flow cycle, where funds convert to product and back to funds. The system is stationary, and revenues and costs flow directly to the parent company. The parent company aims to maximize equilibrium (long-run) financial metrics in terms of net profit rate and rate of return. To this end, we model this system as a discrete-state continuous-time Markov process and compute its equilibrium state distribution using analytic and numerical methods. These are then used to derive statistics of the equilibrium cash conversion cycle and define equilibrium financial rate metrics and cumulative counterparts that incorporate the time value of money. We further optimize the financial and operational designs of the system and, specifically, the internal capital allocation and inventory base stock level. Finally, noting the potential for friction in the parent–subsidiary relationship, we study numerically the impact of moral hazard and internal capital market inefficiency on optimal designs. The online appendix is available at https://doi.org/10.1287/msom.2017.0625 .

Joint optimisation of capacity and safety stock allocation

We study the joint optimisation of capacity and safety stock allocation in assembly systems. Particularly, we consider capacitated systems with base-stock policies and periodic review. Capacity allocation is restricted by budget constraints, which can connect multiple systems. Our objective is to minimise overall inventory holding costs while satisfying service level as well as budget constraints. We propose an algorithm to jointly approximate optimal capacity allocation and base-stock levels. To this end, we introduce a set of convex approximations for this non-convex optimisation problem. In order to solve the resulting convex programmes, we analytically compute sample path derivatives via infinitesimal perturbation analysis. By iteratively adapting the approximations, we achieve good capacity allocations and base-stock levels for the original problem. Furthermore, we introduce a heuristic to allocate capacity, which originates from link capacity allocation in communication networks and use it as a benchmark. The algorithm is applied to small illustrative examples as well as cases motivated by the semiconductor manufacturing process at IBM Systems. It turns out that particularly for high utilisation levels, our algorithm can achieve significant improvements compared to the capacity allocation heuristic.