Modified Base-stock Policy Research Articles

Minimizing conditional value‐at‐risk under a modified basestock policy

Consider a single‐product, make‐to‐stock, risk‐averse company that manages its finished goods inventory by a basestock policy. Item demand is modeled as a Poisson process, and unit production time is modeled as an exponential random variable. Annual cost is equal to the sum over one year of the inventory‐holding and back‐ordering costs. The company wants to minimize the annual cost conditional value‐at‐risk by an appropriate basestock selection called the optimal basestock. After offering evidence that the optimal basestock is analytically intractable, we derive a closed‐form approximation of the optimal basestock. In two independent simulation experiments, we found that the average penalty for using the approximation is less than 1%; we believe this accuracy would be acceptable for practical applications. Leveraging the approximation's accuracy and simplicity, we establish several results that may serve as predictors of the company's appropriate basestock adjustments to changes in operational, economic, and risk aversion parameters. We illustrate how our research results were successfully applied in a Fortune 10 energy company. We extend the problem setting in two different directions to widen the applicability of our research results.

Volume Flexibility at Responsive Suppliers in Reshoring Decisions

We investigate how volume flexibility, defined by a sourcing cost premium beyond a base capacity, at a local responsive supplier impacts the decision to reshore supply. The buyer also has access to a remote supplier that is cheaper with no restrictions to volume flexibility. We show that with unit lead time difference between both suppliers, the optimal dual sourcing policy is a modified dual base-stock policy with three base-stock levels. Fast orders follow a modified base-stock policy with two base-stock levels: the inventory position is raised to the higher base-stock level by using the base capacity; no overtime is used if this order increases the inventory position above the lower base-stock level. Else, the base capacity and overtime are used to raise the inventory position up to the low base-stock level. After ordering from the fast supplier, an order to the slow supplier is placed to raise the inventory position to a third base-stock level. Surprisingly, in contrast to single sourcing with limited volume flexibility, a more complex dual sourcing model results in a “simpler policy that replaces demand in each period. The latter allows analytical insights into the sourcing split between the responsive and the remote supplier. Our analysis shows how increased volume flexibility at responsive suppliers promotes the decision to reshore operations and effectively serves as a (cost) benefit. It also shows how investing in base capacity or additional volume flexibility act as strategic substitutes.

Managing Perishable Inventory Systems with Product Returns and Remanufacturing

Motivated by emerging practice in the cut flower industry, we consider a periodic‐review inventory system for a perishable product with a lifetime of two periods. There are two separate customer demands for the new product with two‐period remaining lifetime and the old product with one‐period remaining lifetime, and a fixed proportion of the unsatisfied demand for one product will purchase the other product as a substitute. One distinctive feature of our system is that a random portion of the sold new product is returned and can be remanufactured and remarketed as the old product for sale. The objective is to maximize the expected total discounted profit over a finite planning horizon. We show that the optimal remanufacturing policy is a modified base–stock policy, and that the optimal manufacturing quantity of the new product decreases in the inventory level of the old product after remanufacturing. Furthermore, when the inventory level of the old product is large, the optimal manufacturing quantity asymptotically approaches a constant, which is lower and upper bounded by two newsvendor fractile solutions. We also conduct a numerical study to derive insights into the effects of remanufacturing and demand substitution. In particular, we show that remanufacturing can be a powerful way of mitigating negative environmental impacts in the cut flower industry. Finally, we discuss two model extensions that allow a joint production capacity and a multi‐period lifetime.

Heuristic methods for the capacitated stochastic lot-sizing problem under the static-dynamic uncertainty strategy

We consider a lot-sizing problem in a single-item single-stage production system facing non-stationary stochastic demand in a finite planning horizon. Motivated by common practice, the set-up times need to be determined and frozen once and for all at the beginning of the horizon while decisions on the exact lot sizes can be deferred until the setup epochs. This operating scheme is referred to as the static-dynamic uncertainty strategy in the literature. It has been shown that a modified base stock policy is optimal for a capacitated system with minimum lot size restrictions under the static-dynamic uncertainty strategy. However, the optimal policy parameters require an exhaustive search, for which the computational time grows exponentially in the number of periods in the planning horizon. In order to alleviate the computational burden for real-life size problems, we developed and tested seven different heuristics for computational efficiency and solution quality. Our extensive numerical experiments showed that average optimality gaps less than 0.1% and maximum optimality gaps below 4% can be attained in reasonable running times by using a combination of these heuristics.

Managing Perishable Inventory Systems with Product Returns and Remanufacturing

Motivated by emerging practice in the cut flower industry, we consider a periodic-review inventory system for a perishable product with a lifetime of two periods. There are two separate customer demands for the new product with two-period remaining lifetime and the old product with one-period remaining lifetime, and a fixed proportion of the unsatisfied demand for one product will purchase the other product as a substitute. One distinctive feature of our system is that a random portion of the sold new product is returned and can be remanufactured and re-marketed as the old product for sale. The objective is to maximize the expected total discounted profit over a finite planning horizon. We show that the optimal remanufacturing policy is a modified base-stock policy, and that the optimal manufacturing quantity of the new product decreases in the inventory level of the old product after remanufacturing. Furthermore, when the inventory level of the old product is large, the optimal manufacturing quantity asymptotically approaches a constant, which is lower and upper bounded by two newsvendor fractile solutions. We also conduct a numerical study to derive insights into the effects of remanufacturing and demand substitution. In particular, we show that remanufacturing can be a powerful way of mitigating negative environmental impacts in the cut flower industry. Finally, we discuss two model extensions that allow a joint production capacity and a multi-period lifetime.

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%.

Simulation–optimization approach for a continuous-review, base-stock inventory model with general compound demands, random lead times, and lost sales

A continuous-review, base-stock inventory model considering lost sales is proposed for general compound demands and random lead times. This model is a generalized form of the ( S, d) policy, which has already been shown to be the best modified base-stock policy (MBSP) for Poisson demand and fixed lead times. In this paper, customers’ inter-arrival times, demand sizes, and lead times are extended in a probabilistic situation with free distributions. Then, a hybrid simulation–optimization approach is developed to handle these generalized conditions. This approach uses design of experiments, a simulation model, and regression analysis to obtain the long-run cost function of the system under this extended MBSP. The optimal settings of this policy are achieved using a mathematical optimization model. Employing a simulation model, a cost function, and mathematical models makes this approach applicable for finding the optimal settings even in the presence of realistic restrictions and uncertainties. Moreover, a simulation-based procedure is introduced to find the optimal stock level for the traditional base-stock policy. The applicability of the proposed approach is illustrated through a real-world case study. Finally, a sensitivity analysis is applied using a series of benchmark instances, and some robustness properties are shown.

Cost minimising order schedules for a capacitated inventory system

In this paper, we study an inventory system with multiple retailers under periodic review and stochastic demand. The demand is modelled as a discrete random variable. Linear holding and backorder costs as well as fixed order costs are assumed. Orders to replenish inventories can be placed at a manufacturer with a limited capacity according to a cyclic order schedule. A fixed portion of the total available capacity in a period is allocated to each retailer, who follows a modified base-stock policy to determine the order quantities. Thus, the order policy consists of four policy parameters for each retailer: the length of the review period, the first order point within a planning horizon, the individual capacity limit, and the modified base-stock level. We present an algorithm to compute the exact optimal policy parameters and two heuristics. In a numerical study, we compare the results of these approaches and derive insights into the performance of the heuristics. In addition, we introduce three different schedule types and identify the situations, in which they perform best.

Evaluation of the Impact of Uncertain Advance Demand Information on Production/Inventory Systems

In this paper, we conduct a simulation study to evaluate the impact of using imperfect advance demand information (ADI) in a single stage production/inventory system. We mean by ADI the fact that the production system receives customer orders in advance of their due-dates. We consider four types of ADI: 1) Perfect ADI, 2) ADI with imperfect due-dates, 3) ADI with imperfect demand quantities and 4) ADI with updates. The production system is controlled by a modified base-stock policy which has two parameters that are S, the base-stock level, and L, the production release lead time. We intend to shed light on the impact of imperfect ADI (ADI types 2, 3, 4) on the performance of production/inventory systems. The aim of the simulation study is twofold. Firstly, the objective is to find the optimal parameters of the modified base-stock policy and secondly, to evaluate the benefits of imperfect ADI in a production/inventory system.

A modified (S − 1, S) inventory system for deteriorating items with Poisson demand and non-zero lead time

An inventory system is considered for continuous decaying items with non-zero lead time and stochastic demand when shortages are allowed and all unsatisfied demands are backlogged. In this research we consider orders as separate packages where replenishment is one-for-one and a modified base stock policy is applied. In this paper, a penalty cost is introduced for stochastic inventory models with decaying items when less than one unit of the product is delivered to the customers. The objective of the warehouse is to maximize his average profit. Since the concavity analysis of the model is extremely complicated, an upper bound is introduced and an algorithm is presented for finding the optimal solution. Finally, a numerical example is presented and sensitivity analysis is carried out for a number of important parameters.

STOCHASTIC MULTI-ITEM INVENTORY SYSTEMS WITH MARKOV-MODULATED DEMANDS AND PRODUCTION QUANTITY REQUIREMENTS

We study a multi-item two-stage production system subject to Markov-modulated demands and production quantity requirements. The demand distribution for each item in each period is governed by a discrete Markov chain. The products are manufactured in two stages. In the first stage, a common intermediate product is manufactured, followed by product differentiation in the second stage. Lower and upper production limits, also known as production smoothing constraints, are imposed on both stages for all items. We propose a close-to-optimal heuristic to manage this system. To do so, we develop a lower bound problem and show that a state-dependent, modified base-stock policy is optimal. We also show when and why the heuristic works well. In our numerical study, the average optimality gap was 4.34%. We also establish some monotonicity results for policy parameters with respect to the production environment. Using these results and our numerical observations, we investigate the joint effect of (i) the two-stage production process, (ii) the production flexibility, and (iii) the fluctuating demand environment on the system's performance. For example, we quantify the value of flexible production as well as the effect of smoothing constraints on the benefits of postponement. We show that a redesign of the production process to allow for delayed product differentiation is more effective and valuable when it is accompanied by an investment in production flexibility.

Modified base-stock policies for continuous-review, lost-sales inventory models with Poisson demand and a fixed lead time

Abstract This paper reconsiders the lost-sales inventory system studied by Hill (2007) . The commonly assumed policy to apply to the system is a pure base-stock policy (PBSP) for which the best base stock is easily found. Hill shows that his simple delay policy (SDP) and full delay policy (FDP) perform better. The SDP is a (s,d) policy where s is the base stock of the best PBSP and d is a common lower bound on the delay between the placement of successive replenishment orders. We show by simulation that the d value suggested by Johansen (2001) outperforms Hill's suggestion and that the performance often can be further improved by optimizing d. For the test bed investigated by Hill, we show that, for some parameter settings, an additional improvement is achieved when s and d are optimized simultaneously. The policy suggested by Johansen performs better than the FDP in all settings where the former policy reduces the average cost of the best PBSP by at least 1%.

Joint pricing and inventory replenishment decisions with returns and expediting

We study a single-item periodic-review model for the joint pricing and inventory replenishment problem with returns and expediting. Demand in consecutive periods are independent random variables and their distributions are price sensitive. At the end of each period, after the demand is realized, a buyer can return excess stocks to a supplier. Or, if there are stockouts, the buyer can place an expediting order at the supplier to reduce the amount of shortage. Unfilled demands are fully backlogged. We characterize the optimal dynamic policy that determines the pricing, inventory replenishment, and adjustment decisions in each period so that the total expected discounted profit is maximized. For a very general stochastic demand function, we can show that the optimal replenishment policy is a modified base-stock policy, the optimal pricing policy is a modified base-stock-list-price policy, and the optimal policy for inventory adjustment follows a dual-threshold policy. We further study the operational effect of returns and expediting. Analytical and numerical results demonstrate that returns and expediting lead to a significant profit increase in a number of situations, including limited supply capacity, sufficient flexibility of the expediting order, high demand uncertainty, and a price-sensitive market.

Energy-Efficient Transmission Scheduling With Strict Underflow Constraints

This paper considers a single source transmitting data to one or more receivers/users over a shared wireless channel. Due to random fading, the wireless channel conditions vary with time and from user to user. Each user has a buffer to store received packets before they are drained. At each time step, the source determines how much power to use for transmission to each user. The source's objective is to dynamically allocate power in a manner that minimizes total power consumption and packet holding costs, while satisfying strict buffer underflow constraints and a joint power constraint in each slot. The primary application motivating this problem is wireless media streaming. For this application, the buffer underflow constraints prevent the user buffers from emptying, so as to maintain playout quality. In the case of a single user, a state-dependent modified base-stock policy is shown to be optimal with linear power-rate curves, and a state-dependent finite generalized base-stock policy is shown to be optimal with piecewise-linear convex power-rate curves. When certain technical conditions are satisfied, efficient methods to compute the critical numbers that complete the characterizations of the optimal control laws in each of these cases are presented. The structure of the optimal policy for the case of two users is then analyzed.

Optimal control of a capacitated inventory system with multiple demand classes

AbstractThis article studies the optimal control of a periodic‐review make‐to‐stock system with limited production capacity and multiple demand classes. In this system, a single product is produced to fulfill several classes of demands. The manager has to make the production and inventory allocation decisions. His objective is to minimize the expected total discounted cost. The production decision is made at the beginning of each period and determines the amount of products to be produced. The inventory allocation decision is made after receiving the random demands and determines the amount of demands to be satisfied. A modified base stock policy is shown to be optimal for production, and a multi‐level rationing policy is shown to be optimal for inventory allocation. Then a heuristic algorithm is proposed to approximate the optimal policy. The numerical studies show that the heuristic algorithm is very effective. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 43–58, 2011

Modified base-stock policies for semiconductor production system with dependent yield rates

We consider a two-stage production system faced by semiconductor manufacturing which produces a hierarchy of multiple grades of outputs. In the first stage, a single type of input (wafer) is used to produce multiple types of semi-finished parts with dependent yield rates, and in the second stage, each type of semi-finished parts can be transformed into a corresponding type of final products, or downgraded to a type of lower grade final products. Random customer demands are faced on the final products, and demands of different types of final products are not allowed to be substituted. The advantage of this production system is that it can prevent unhealthy ordering from customers who intentionally send out false demand signals for high grade products and revise the orders to lower grade products when the delivery time is close, which was observed in semiconductor manufacturing. The objective of the study is to plan the quantity of the input at the first stage and the respective downgrade quantities at the second stage so as to meet the required service level at the minimum cost. With some common assumptions, we propose a modified base-stock policy for this two-stage production system and show that the occurrence of nil excess inventory above the base-stock level follows a renewal process. We further extend the modified base-stock policy to a better policy that invokes risk pooling over multiple grade products. The performance of these two polices are evaluated via simulation to provide managerial insights.

Dual-supply inventory problem with capacity limits on order sizes and unrestricted ordering costs

This paper considers a single-product dual-supply problem under a periodically reviewed, finite planning horizon. The downstream party, the manufacturer, is supplied by two upstream parties, local and global suppliers, with consecutive leadtimes. Both suppliers place per period minimum and maximum capacity limits on the manufacturer's orders. It is shown that a two-level modified base stock policy is optimal without any restrictions on the ordering costs. Using various analytical results, it is illustrated how the optimal policy parameters change as a function of the problem parameters. To prove the analytical results, a new functional property—bounded increasing [decreasing] differences—which is a subset of the increasing [decreasing] differences property commonly used in the literature is introduced. Numerical analyses are used to explain the trade-offs between complementary services in terms of prices, leadtimes and order capacity limits. For example, it is shown that the manufacturer follows different strategies for different product types: for inventory-cost-driven products, she relies on the local supplier to keep her supply chain responsive. Furthermore, the manufacturer procures from the local supplier as part of a balanced supply portfolio, i.e., orders from the local supplier are not limited to emergency situations. This role of the local supplier diminishes, however, as the leadtime increases. It is also found that increases in minimum capacity limits are generally more favorable to the local supplier. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resources: Appendix with additional proofs and further details of numerical analysis.]

Inventory Sharing Under Decentralized Preventive Transshipments

We consider preventive transshipments between two stores in a decentralized system with two demand subperiods. Replenishment orders are made before the first subperiod, and the stores may make transshipments to one another between the subperiods. We prove that the transshipment decision has a dominant strategy, called a control-band conserving transfer policy, under which each store chooses a quantity to transship in or out that will keep its second-subperiod starting inventory level within a range called a control band. We prove that the optimal replenishment policy is a modified base-stock policy in which the order-up-to level depends on the initial inventory and capacity level at the other store. Finally, we prove that there does not exist a transfer price that coordinates the decentralized supply chain. Our research also explains many of the differences between preventive and lateral transshipments, including differences in the optimal transfer policies and the existence or nonexistence of transfer prices that coordinate the system.

Capacitated Production Control with Virtual Lateral Transshipments

We study the optimal control of a firm with two capacitated manufacturing plants situated in two distinct geographical regions. Demands from each region are mostly satisfied by the local plant. However, if necessary, some of the newly arrived demands can be designated to be served by the other, more remote, plant. The sources of the above virtual lateral transshipments, unlike the ones involved in the real lateral transshipments, do not need to have nonnegative inventory levels throughout the transshipment processes. We develop results about the simultaneous preservation of supermodularity and diagonal dominances of the cost functions and then use these results to derive structural results for the optimal policies. Specifically, to perform optimally, we find that each plant should adopt a modified base-stock policy in observance of its own capacity, while the base level should mildly decrease in the other plant's starting inventory level. Our computational results illustrate the benefits realizable by using transshipment.

Decentralized inventory control in a two-component assembly system

We investigate a two-component assembly system facing stationary stochastic demand with constant component replenishment lead times. Holding cost are charged for each component inventory, which are managed by component suppliers; final product demand is backordered when cannot be fulfilled in time and a penalty cost is charged. We assume the long lead-time component supplier takes normal base-stock policy while the short lead-time component supplier takes a modified base-stock policy. Static game and Stackelberg games are considered. Equilibria are analyzed and the cost in equilibria are compared with the system optimal solution, difference shows the deterioration of system performance caused by decentralized inventory control. We try to design a mechanism to coordinate the decentralized system, that is to make decentralized system perform as well as system optimal solution though the decisions separated. We show that a liner transfer based on the backorder between the component suppliers qualifies this task.