Retailer policy, uncertainty reduction, and supply chain performance

We investigate how the retailer’s inventory policy affects the total cost of a serial supply chain. When the retailer uses the locally optimal (s,S) policy, there is randomness in order time and order quantity to the supplier whereas the supplier sees randomness only in order quantity for the suboptimal (R,T) policy and only in order time for another suboptimal (Q,r) policy. Using an extensive computational study, we find that the suboptimal policies perform better from the total supply chain perspective. The benefit of policy changes is magnified when the retailer costs are low, when the supplier costs are high, and when there is information sharing.     

An investigation of setup instability in non-stationary stochastic inventory systems

In stochastic inventory systems unfolding uncertainties in demand lead to the revision of earlier replenishment plans which in turn results in an instability or so-called system nervousness. In this paper, we provide the grounds for measuring system nervousness in non-stationary demand environments, and gauge the stability and the cost performances of (R,S) and (s,S) inventory policies. Our results reveal that, both the stability and the cost performance of inventory policies are affected by the demand pattern as well as the cost parameters, and the (R,S) policy has the potential to replace the cost-optimal (s,S) policy for systems with limited flexibility.     

Near-optimal (r,Q) policies for a two-stage serial inventory system with Poisson demand

We consider a two-stage serial inventory system whose cost structure exhibits economies of scale in both stages. In the system, stage 1 faces Poisson demand and replenishes its inventory from stage 2, and the latter stage in turn orders from an outside supplier with unlimited stock. Each shipment, either to stage 2 or to stage 1, incurs a fixed setup cost. We derive important properties for a given echelon-stock (r, Q) policy for an approximation of the problem where all states are continuous. Based on these properties, we design a simple heuristic algorithm that can be used to find a near-optimal (r, Q) policy for the original problem. Numerical examples are given to demonstrate the effectiveness of the algorithm.     

Unimodality of price-setting newsvendor's objective function with multiplicative demand and its applications

We present a general solution framework for the price-setting newsvendor problem with a multiplicative stochastic demand. Under mild assumptions, such as increasing price elasticity on the mean demand function and increasing generalized failure rate on the distribution of the random factor, we first prove that both the profit function with respect to price and its derived function with respect to order quantity are quasi-concave. Three applications are then studied under our solution framework: (1) We consider a wholesale price only contract by which a manufacturer sets a wholesale price and a newsvendor determines an order quantity and the retail price, and show that the manufacturer's profit function is unimodal with respect to retailing price or stocking factor under certain conditions. (2) We consider a newsvendor problem in which the demand depends on both the retail price and the level of sales effort, and the cost exerting the sales effort is proportional to the order quantity; we prove that there exists a unique pair of price and sales-effort levels that maximize the total profit. This result is established under a set of mild assumptions on the demand and cost functions. (3) We identify a property in the single-period profit function that satisfies Condition 1 of Huh and Janakiraman (2008), which in turn guarantees the optimality of (s, S) policy for an infinite stationary dynamic inventory-price control system with lost sales and fixed order costs. Finally, the unimodality of the newsvendor problem with a general stochastic and price-sensitive demand is studied.     

Exact and approximated calculation of the cycle service level in a continuous review policy

The paper proposes a method to compute the exact cycle service level for (s, Q) continuous review policy in the presence of undershoots and discrete demand in the discrete time domain. Prior to this, it is necessary to review the definition of the cycle service level in order to avoid the problems that can be found when applied it to the periodic review policy. Therefore, the aim of this paper is: (a) to review the definitions of the cycle service level when applied to continuous review policies; (b) to develop an exact calculation method of the CSL for a continuous review policy when undershoots are allowed and demand is discrete; and (c) to examine some common believes about the cycle service properties. Finally, the bias obtained when the service cycle level is estimated applying the common assumption of neglecting undershoots at the order point is illustrated with some numerical examples which show that it may lead to significant deviations to be ignored.     

A stochastic inventory model of dual sourced supply chain with lead-time reduction

Recently, the amount of literature on analyzing the effects of investment strategies to control lead times has been increasing. Issues on investment to reduce lead times are important because variability in lead time between successive stages often has a great effect on the coordination of supply chain.This paper considers dual-sourcing models with stochastic lead times and constant unit demand in which lead times are reduced at a cost that can be viewed as an investment. In order to obtain an analytically tractable model, the distributions of lead times for two suppliers are assumed to be exponential. In our two-supplier model, we will concentrate on lead times as random variables, which are made endogenous in the stochastic lead-time model through “expediting factors”, the constants of proportionality between the expedited lead times and ordinary lead times, as was done by Bookbinder and Çakanyildirim (Eur. J. Oper. Res. 115 (1999) 300).Firstly, we determine the order quantity (Q), reorder point level (r), and order splitting proportion (k₁) in the case of no lead-time reduction. Using the (Q,r) found, we decide the expediting factors and new k₁ in the case of lead-time reduction. We compare the expected total cost per unit time for the two models and investigate savings. Additionally, sensitivity analyses are conducted with respect to the various cost parameter ranges, and remarks are made for further research.     

Optimal inventory control of empty containers in inland transportation system

In this paper, we deal with an inventory control problem of empty containers in an inland transportation system. In inland container transportation, freights (containers) are transported between terminal and the customer’s location by trucks, trains and barges. Empty containers are an important logistic resource and shipping companies try to operate and manage empty containers efficiently. Because of the trade imbalance between hub ports, empty containers should be periodically repositioned from surplus areas to shortage areas. However, it is not easy to exactly forecast the demand of empty containers, and we therefore need to build an efficient way to reposition the empty containers. In this paper, we consider a shortage area and propose an efficient inventory policy to control empty containers. We assume that demands per unit time are independent and identically distributed random variables. To satisfy the demand of empty containers, we reposition empty containers from other hubs based on the (s, S) inventory policy, and also consider the lease of empty containers with zero lead time. For the leased containers, we should return the number of empty containers leased to the leaser after the specified period. For a given policy, simulation is used to estimate the expected cost rate and we use the optimization tool, OptQuest^® in Arena to obtain the near optimal (s, S) policy in numerical examples.     

Base stock policies with degraded service to larger orders

We study an inventory system controlled by a base stock policy assuming a compound renewal demand process. We extend the base stock policy by incorporating rules for degrading the service of larger orders. Two specific rules are considered, denoted as Postpone(q,t) and Split(q), respectively. The parameter q distinguishes between regular orders (of size less than or equal to q) and larger orders. We develop mathematical expressions for the performance measures: order fill rate of the regular orders and average on-hand inventory level. We make numerical experiments where the postpone parameter t and the base stock levels of each rule are such that all customers (of both order types) are indifferent between the two rules. When comparing the difference in the average on-hand inventory levels, we can then make an assessment of the threshold value of the cost of splitting an order (which may otherwise be hard to quantify) in the rule Split(q). Our numerical results indicate that this threshold value is increasing in the variance of the order sizes. Based on the numerical experiment our conclusion is therefore that when the variance of the order sizes is low, then Postpone(q,t) seems to be a good option, while when the variance is high, then Split(q) is more competitive.     

A new lot-sizing heuristic for manufacturing systems with product recovery

We consider a deterministic model of the manufacturing system with product recovery. Two types of policies for the problem had been proposed in literature, namely the (1,R) policy, in which one manufacturing setup is followed by R remanufacturing setups and the (P,1) policy, which has P manufacturing setups, following every remanufacturing setup. Teunter (2004) developed heuristics to evaluate the cost for both policies and recommended choosing the better one among them. In this paper, we develop a new class of general (P,R) policies, where the long-run ratio of the number of manufacturing setups to the number of remanufacturing setups is P/R. Rather than have P manufacturing setups followed by R remanufacturing setups, we interleave (or intersperse) the setups of the manufacturing lots and the remanufacturing lots in such a way that the buildup of the recoverable inventory is minimized. We develop interleaving based (P,R) policy heuristics for the problem. Numerical results presented in the paper show that the proposed heuristic outperforms or performs as well as the best of the Teunter (2004) policies for all the problems tested.     

Inventory management with random supply and imperfect information: A hidden Markov model

In most of the papers on inventory models operating in a random environment, the state of the environment in each period is assumed to be fully observed with perfect information. However, this assumption is not realistic in most real-life situations and we provide a remedy in this paper by assuming that the environment is only partially observed with imperfect information. We accomplish this by analyzing two formulations of single-item models with periodic-review and random supply in a random environment. In the first one, supply is random due to random capacity of production and random availability of transportation. We show that state-dependent base-stock policy is optimal if the capacity and all costs are observed, while demand and availability are unobserved. In the second model, we consider a model with random availability only with fixed-ordering cost. We show that state-dependent (s,S) policy is optimal if the availability process is observable.     

Evaluating the robustness of lead time demand models

This paper examines the robustness of lead time demand models for the continuous review (r, Q) inventory policy. A number of classic distributions, (e.g. normal, lognormal, gamma, Poisson and negative binomial) as well as distribution selection rules are examined under a wide variety of demand conditions. First, the models are compared to each other by assuming a known demand process and evaluating the errors associated with using a different model. Then, the models are examined using a large sample of simulated demand conditions. Approximation results of inventory performance measures—ready rate, expected number of backorders and on-hand inventory levels are reported. Results indicate that distribution selection rules have great potential for modeling the lead time demand.     

Discount pricing for a family of items: The supplier's optimal decisions

Consider a family of SKUs for which the supplier will offer a quantity discount, according to the aggregate purchases of the product group. Management of those items is based on the modified periodic policy. From the supplier's point of view, what are the optimal parameters (breakpoint and discount percentage)? For deterministic demand, we discuss the cases in which demand is both constant and price-sensitive. First as a noncooperative Stackelberg game, and then when the two parties make the discount and replenishment decisions jointly, we illustrate the impact of price-sensitivity and joint decision making on the supplier's discount policy.     

A robustness study of a multi-echelon inventory model via simulation

This paper examines the robustness of a standard model of multi-echelon inventory systems, specifically the models discussed in Axsäter (Oper. Res. 48(5) (2000) 686). A simulation model was developed to explore the model's ability to predict system performance for a two-echelon one-warehouse, multiple retailer system using (R,Q) inventory policies under conditions that violate the model's fundamental modeling assumptions. In particular, the impact of non-stationary demand on this stationary demand inventory model was examined. The model performs well at the low demand and large retailer order batch size situations, but our testing of the model indicated that care must be taken when applying this model to situations that violate its fundamental assumption. These results should help practitioners to better understand the assumptions of these models and to determine when or when not to apply these models in practice.     

Joint pricing and procurement of fashion products in the existence of clearance markets

This paper focuses on the joint pricing and procurement of fashion products in the existence of clearance markets. It is assumed that the expected regular season demand is a linear decreasing function of the price and the end of period excess inventory is sold at a known discounted price in a clearance market where the demand is a random variable that follows a general distribution. It is shown that the expected profit function is unimodal and the optimal procurement quantity and price can be found from the first order conditions. Existence of a clearance market increases the profit, price, and the procurement quantity. In order to prove this, the optimal procurement and pricing policy of a price-setting retailer who does not have a clearance market is provided. As opposed to the literature, it is shown that the expected profit function of this problem is unimodal as well. A numerical study demonstrating the magnitude of the increase in profit, procurement quantity, and price is reported.     

Lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand

This paper studies alternative methods for reducing lead time and their impact on the safety stock and the expected total costs of a (Q,s) continuous review inventory control system. We focus on a single-vendor-single-buyer integrated inventory model with stochastic demand and variable, lot size-dependent lead time and assume that lead time consists of production and setup and transportation time. As a consequence, lead time may be reduced by crashing setup and transportation time, by increasing the production rate, or by reducing the lot size. We illustrate the benefits of reducing lead time in numerical examples and show that lead time reduction is especially beneficial in case of high demand uncertainty. Further, our studies indicate that a mixture of setup time and production time reduction is appropriate to lower expected total costs.     

A Simple Method for Calculating the imin Rate for an Investment Project

The i_min rate of an investment project is the smallest rate such that all the intermediate balances of the project have the same sign or ore null. This rate is mainly used to determine whether an investment project is a pure or a mixed investment project. In this technical note we point out that as i_min is the greatest internal rate of return among the ones of pure truncated projects and since no eventual mixed truncated project can have a root with a value greater or equal to i_min , we then can easily obtain i_min by appropriate use of standard internal rate of return computing routines.     

Disaggregation and consolidation of imperfect quality shipments in an extended EPQ model

We consider a standard economic production quantity (EPQ) model. Due to manufacturing variability, a fraction P of the produced inventory will have imperfect quality, where P is a random variable with a known distribution. We consider a 100% inspection policy and further assume that the inspection rate is larger than that of production. Thus, all imperfect quality items will be detected by the end of the production cycle. For such an augmented EPQ model, we first derive the new optimal production quantity assuming that the imperfect quality items are salvaged once at the end of every production cycle. Then, we extend this base model to allow for disaggregating the shipments of imperfect quality items during a single production run. Finally, we consider aggregating (or consolidating) the shipments of imperfect items over multiple production runs. Under both scenarios we derive closed-form expressions for both the economic production quantity and the batching policy, and show that our desegregation/consolidation schemes can lead to significant cost savings over the base model.     

Exact and approximate calculation of the cycle service level in periodic review inventory policies

The parameters of stock policies are usually determined to minimize costs while satisfying a target service level. In a periodic review policy the time between reviews can be selected to minimize costs while the order-up-to-level is based on the fulfilment of a target service level. Generally, the calculation of this service measurement is obtained using approximations based on an additional hypothesis related to the demand pattern. Previous research has shown that there is a substantial difference between exact and approximate calculations in some general circumstances, so in these cases the service level is not accomplished or the stock level is overestimated. Although an exact calculation of CSL was developed in previous work, the computational effort required to apply it in practical environments leads to the proposal of two approximate methods (PI and PII) that, with the classic approximation, are analysed and evaluated in this paper. This analysis points out the risks of using the classic approximation and leads one to suggest PII as the most suitable and accurate enough procedure to compute the CSL straightforwardly in practice. Additionally, a heuristic approach based on PII is proposed to accept or reject an inventory policy in terms of fulfilling a given target CSL. This paper focuses on uncorrelated, discrete and stationary demand with a known distribution pattern and without backlog.