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.     

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.     

Single item inventory control under periodic review and a minimum order quantity

In this paper we study a periodic review single item single stage inventory system with stochastic demand. In each time period the system must order none or at least as much as a minimum order quantity Q_min. Since the optimal structure of an ordering policy with a minimum order quantity is complicated, we propose an easy-to-use policy, which we call (R, S, Q_min) policy. Assuming linear holding and backorder costs we determine the optimal numerical value of the level S using a Markov Chain approach. In addition, we derive simple news-vendor-type inequalities for near-optimal policy parameters, which can easily be implemented within spreadsheet applications. In a numerical study we compare our policy with others and test the performance of the approximation for three different demand distributions: Poisson, negative binomial, and a discretized version of the gamma distribution. Given the simplicity of the policy and its cost performance as well as the excellent performance of the approximation we advocate the application of the (R, S, Q_min) policy in practice.     

Considering stochastic lead times in a manufacturing/remanufacturing system with deterministic demands and returns

In this paper we study a manufacturing/remanufacturing system with stochastic lead times and a constant demand. We base our approach on previous research in which we have developed models to describe an inventory system with stochastic lead times. In this paper, we first adopt this method to manufacturing/remanufacturing situations, where there are essentially two supply sources for replenishing serviceable inventory. We then provide a solution procedure when a cycle ordering policy is used. Secondly, we investigate the possibility to use a dual sourcing ordering policy in which each order is split between a manufacturing and a remanufacturing process. Finally, we compare the two ordering policies and illustrate how the lead-time patterns influence the economic consequences.     

Optimal policies in hybrid manufacturing/remanufacturing systems with product substitution

In hybrid control systems for simultaneous remanufacturing of used products and manufacturing of new ones, the two operations are not directly interconnected if remanufactured items are downgraded and have to be sold in markets different from those for new products. Sometimes a connection between these markets is given by a downward substitution property which allows the producer to offer a new item instead of a remanufactured one in case of a shortage of a remanufactured product. Thus, shortage costs can be avoided, but a loss in profit due to sale of a high-graded product at the price of a low-graded one has to be accepted. For a single-period problem with stochastic returns of used products and stochastic demands of serviceable ones, it is shown how the manufacturing and remanufacturing decisions have been coordinated in order to maximize the total expected profit. It turns out that under strictly proportional costs and revenues a medium-simple ‘order-up-to policy’ with two parameters and two parameter functions is optimal. However, optimal policies in situations where manufacturing leadtimes exceed leadtimes for remanufacturing turn out to be different from those in the opposite leadtime case. The research presented combines methods for policy analysis in stochastic manufacturing/remanufacturing problems and in stochastic inventory control problems with substitutable products.     

A new when-to-schedule policy in online scheduling based on cumulative task delays

This paper proposes a new when-to-schedule policy in online scheduling, which considers timing of rescheduling based on the concept of a control limit policy and rolling schedules. Under the proposed policy, rescheduling is carried out based on a cumulative delay which can be a measure to determine suitable timing of rescheduling. Some computational experiments demonstrate the effectiveness of the proposed policy by applying it to single-machine dynamic scheduling with sequence-dependent setup times and urgent jobs, where total setups are minimized as well as rescheduling frequency. It is also demonstrated that the proposed policy can outperform typical rescheduling policies.     

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.     

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.     

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.     

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 local search algorithm for the optimization of the stochastic economic lot scheduling problem

This paper describes a model for the stochastic economic lot scheduling problem (SELSP) and a Local Search heuristic to find close to optimal solutions to this model. The SELSP considers multiple products, which have to be scheduled on a single facility with limited capacity and significant setup times and costs. The demand is modeled as a stationary compound renewal process. The objective is to find a schedule that minimizes the long-run average costs for setups and inventories while satisfying a given fill rate. We use a cyclic scheduling approach in which the individual cycle time of each product is a multiple of some basic period (fundamental cycle).For the deterministic version of the SELSP, efficient heuristics have been developed which guarantee the feasibility of the solution by adding an additional constraint to the problem. In our case this is not sufficient, because for the calculation of the average inventory levels and fill rates we need to develop a schedule with detailed timing of the lots. We present an efficient heuristic for this scheduling problem, which can also be used to check the feasibility of the solution. Thereby, the most time-consuming step (the calculation of average inventory levels and fill rates) is only performed for a limited set of candidates.The algorithm was tested on deterministic benchmark problems from literature and on a large set of stochastic instances. We report on the performance of the heuristic in both cases and try to identify the main factors influencing the objective.     

The effects of a free-repair warranty on the discrete-time periodic replacement policy

This paper presents the effects of a free-repair warranty on a periodic replacement policy with a discrete time process. Considering a repairable product that should be operational at the time over an indefinitely long operation cycle n (n=1, 2, …), under the discrete-time periodic replacement policy, a product is preventively replaced at pre-specified operation cycles N, 2N, 3N, … (N=1, 2, …). When the product fails, a minimal repair is performed at the time of failure, and the failure rate is not disturbed by each repair. The cost models from the customers' perspectives are developed for both warranted and non-warranted products. The corresponding optimal replacement period N? is derived such that the long-run expected cost rate is minimized. Under the assumption of the discrete time increasing failure rate, the existence and uniqueness of the optimal replacement period are shown, and the impact of a free-repair warranty on the optimal periodic replacement policies is investigated analytically. The optimal N* for a warranted product should be adjusted toward the end of the warranty period. Finally, numerical examples are demonstrated for the optimal policy illustration and verification. The observations from the numerical results provide valuable information for a buyer (user) to adjust the optimal periodic replacement policy if a product is operating in discrete time under a free-repair warranty.     

Production planning of a hybrid manufacturing-remanufacturing system under uncertainty within a closed-loop supply chain

This paper deals with the production planning and control of a single product involving combined manufacturing and remanufacturing operations within a closed-loop reverse logistics network with machines subject to random failures and repairs. While consumers traditionally dispose of products at the end of their life cycle, recovery of the used products may be economically more attractive than disposal, while remanufacturing of the products also pursues sustainable development goals. Three types of inventories are involved in this network. The manufactured and remanufactured items are stored in the first and second inventories. The returned products are collected in the third inventory and then remanufactured or disposed of. The objective of this research is to propose a manufacturing/remanufacturing policy that would minimize the sum of the holding and backlog costs for manufacturing and remanufacturing products. The decision variables are the production rates of the manufacturing and the remanufacturing machines. The optimality conditions are developed using the optimal control theory based on stochastic dynamic programming. A computational algorithm, based on numerical methods, is used for solving the optimal control problem. Finally, a numerical example and a sensitivity analysis are presented to illustrate the usefulness of the proposed approach. The structure of the optimal control policy is discussed depending on the value of costs and parameters and extensions to more complex reverse logistics networks are discussed.     

Determination of an order-up-to policy in the stochastic economic lot scheduling model

We consider a production–inventory problem with compound renewal item demand. The model consists of stockpoints, one for each item, controlled according to (R,S)-policies and one machine which replenishes them. The replenishment orders are produced with a fixed rate on the machine with significant setup times and costs, which are stochastic and sequence dependent. The time between the release and the production of the replenishment order is called the waiting time. We develop analytical approximations for the first two moments of this waiting time, the order-up-to levels and the average physical inventory levels for all stockpoints, given the target fill rates. These analytical approximations allows for a quick evaluation of the waiting time which is important when optimization of the system is considered.     

Optimal production–inventory strategies for a HMMS-type reverse logistics system

The aim of the paper is to find optimal inventory policies in a reverse logistics system with special structure. It is assumed that demand is a known continuous function in a given planning horizon and return rate of used items is a given function. There is a constant delay between the using and return process. We investigate two stores. The demand is satisfied from the first store, where the manufactured and remanufactured items are stored. The returned products are collected in the second store and then remanufactured or disposed. The costs of this system consist of the quadratic holding costs for these two stores and the quadratic manufacturing, remanufacturing and disposal costs.The model is represented as an optimal control problem with two state variables (inventory status in the first and second store) and with three control variables (rate of manufacturing, remanufacturing and disposal). The objective is to minimize the sum of the quadratic deviation from described inventory levels in stores and from described manufacturing, remanufacturing and disposal rates. In this form, the model can be considered as a generalization of the well-known Holt et al. (Planning Production, Inventories, and Work Forces, Prentice-Hall, Englewood Cliffs, NJ, 1960) model with two warehouses. After solving the problem, we give some numerical examples to represent the optimal path in dependence of the demand rates.     

Scheduling multiple robots in a no-wait re-entrant robotic flowshop

No-wait re-entrant robotic flowshops are widely used in the electronic industry, such as PCB and semiconductor manufacturing. In such an industry, cyclic production policy is often used due to large lot size and simplicity of implementation. This paper addresses cyclic scheduling of a no-wait re-entrant robotic flowshop with multiple robots for material handling. We formulate the problem and propose a polynomial algorithm to find the minimum number of robots for all feasible cycle times. Consequently, the minimum cycle time for any given number of robots can be obtained with the proposed algorithm. The algorithm runs in O(N⁵) time in the worst case, where N is the number of machines in the robotic flowshop.     

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 production rate control policy for stochastic repair and remanufacturing systems

We consider the control of a manufacturing system responding to planned demand at the end of the expected life of each individual piece of equipment and unplanned demand triggered by a major equipment failure. The difficulty of controlling this type of production system resides in the variable nature of the remanufacturing process. In practice, remanufacturing operations for planned demand can be executed at different rates, referring to different component replacement and repair strategies. We formulate this problem as a multi-level control problem and propose a suboptimal control policy. The proposed control policy is described by inventory thresholds triggering the use of different execution modes. Determination of the control policy parameters is based on parameter optimization of analytical cost expressions. A numerical example based on a real case is presented. Our analysis demonstrates that the use of the proposed control approach can lead to a significant reduction in the total average cost, as compared to current practices.     

From the outside in: Consumer anti-choice and policy implications in the mobile gaming market

Significant growth in mobile media consumption has prompted a call to better understand the socio-cultural and policy dimensions of consumer choices. Contrary to industry and technology led analysis, this study argues that to guide consumer choice and innovation via regulatory policies requires an understanding of both ex-ante as well as in ex-post consumption conditions. This study examines mobile phone gaming to uncover how consumer anti-choice shapes decision-making as a framework for closely interrogating the ways in which policy concerns impact on consumers’ behavior. Through eleven focus groups (n=62), the study empirically identifies voluntary, intentional, and positive consumer anti-choice behaviors all of which impact policy initiatives when consumers, both gamers and non-gamers, self-regulate their behaviors. Findings point to four types of policy implication: regulating the self-regulated, understanding anti-choice, boundary-setting and including the self-excluded.