The effects of the warranty cost on the imperfect EMQ model with general discrete shift distribution

In this paper, we investigate the effect of the warranty cost on optimization of the economic manufacturing quality (EMQ). This is done for a deteriorating process where the production process shifts from the in-control state to the out-of-control state following a general discrete probability distribution. Once the production process goes out of control, the production process produces some defective items. The defective item cost includes reworking and warranty costs. Thus, in order to economically operate a production-inventory system with products sold under warranty, the tradeoffs among the production setup, inventory, and defective item cost, including the reworked cost before sale and the warranty cost after sale, needed to be analysed. This objective in this paper is to determine the production lot size while minimizing the total cost per unit of time per unit of time. Various special cases are presented. Two of them are extensions of results obtained previously in the literature. Finally, a numerical example is given which uses a discrete Weibull probability distribution. Sensitivity analysis of the model with respect to cost and time parameters is also performed.     

Lot sizing in case of defective items with investments to increase the speed of quality control

In many cases the quality of each item in a lot is checked. Speeding up the quality checking process increases the responsiveness of the system and saves cost. The percentage of defective items is a random variable and two models are proposed. In one of the models the system remains always at the same state, while in the other one after each order cycle, the state of the system may change, thus the percentage of defective items may be different in consecutive periods. In both cases the speed of the quality checking is a variable, and procedures are provided to find the optimal lot sizes and screening speed for general and specific investment cost functions. The characteristics of the two model settings will largely be different when the percentage of defective items is high. Among the important managerial insights gained is that a high unit backlogging cost, especially spurs the system to invest more intensively into improving the quality checking process.     

A new EPQ model: integrating lower pricing,rework and reject situations

The economic production quantity (EPQ) is a well-known and commonly used inventory control technique. It has been used for well over 50 years to optimize lot sizes in transportation/production. The standard results are easy to apply but are based on a number of assumptions. A common assumption in the EPQ model is that all units produced are of perfect quality, this will underestimate the actual required quantity. Many researchers have studied the effects after relaxing this assumption on the EPQ model. The previous studies had considered that imperfect quality and defective items are either to be reworked instantaneously and kept in stock or rejected at a cost. The objective of this paper is to provide a framework to integrate lower pricing, rework and reject situations into a single EPQ model. A 100% inspection is performed in order to identify the amount of good quality items, imperfect quality items and defective items in each lot. This model assumes that items of imperfect quality, not necessarily defective, could be used in another production situation or sold to a particular purchaser at a lower price. The electronic and clothing industries give good examples for such situations. A mathematical model is developed and a numerical example is presented to illustrate the solution procedures. It is found that the time factor of when to sell the imperfect items is critical, as this decision will affect the inventory cost and the batch quantities.     

Critical acceptance values and sample sizes of a variables sampling plan for very low fraction of defectives

Acceptance sampling plans are practical tools for quality control applications, which involve quality contracting on product orders between the vendor and the buyer. Those sampling plans provide the vendor and the buyer rules for lot sentencing while meeting their preset requirements on product quality. In this paper, we introduce a variables sampling plan for unilateral processes based on the one-sided process capability indices _CPU$C_{\mathrm{PU}}$ (or _CPL)$C_{\mathrm{PL}})$, to deal with lot sentencing problem with very low fraction of defectives. The proposed new sampling plan is developed based on the exact sampling distribution rather than approximation. Practitioners can use the proposed sampling plan to determine accurate number of product items to be inspected and the corresponding critical acceptance value, to make reliable decisions. We also tabulate the required sample size n$n$ and the corresponding critical acceptance value _C0$C_0$ for various α$\alpha$-risks, β$\beta$-risks, and the levels of lot or process fraction of defectives that correspond to acceptable and rejecting quality levels.     

The Effect of Distribution Processes on Replenishment Lead Time and Inventory

We investigate the interrelationship of distribution center picking policies and supply chain inventory performance. In particular, we show how the picking sequence in the upstream supply chain link affects the inventory levels of items being replenished to a downstream link for a common “ship‐when‐full” trailer dispatching policy. Perturbing the picking sequence affects items’ inventory levels asymmetrically which causes the aggregate system inventory to vary. We separate the items in replenishment into those units in transit and those awaiting shipment from the upstream distribution step: we call the latter the residual replenishment. We show that the process governing aggregate residual replenishment is Markov and has a stationary distribution that is discrete uniform. Computing the item‐level residual distribution is intractable and so we develop analytical models from which we derive hypotheses for the effectiveness of stable vs. random picking sequences, how item residual replenishment varies with stable picking sequences, and how the aggregate inventory level changes with picking sequence. These suggest a heuristic sequencing algorithm for minimizing inventory, which performs well in simulation tests over a large testbed of parameter sets.     

Class‐Based Storage with a Finite Number of Items: Using More Classes is not Always Better

Class‐based storage is widely studied in the literature and applied in practice. It divides all stored items into a number of classes according to their turnover. A class of items with higher turnover is allocated to a region closer to the warehouse depot. In the literature, it has been shown that the use of more storage classes leads to a shorter travel time for storing and retrieving items. A basic assumption in this literature is that the required storage space for all items equals their average inventory level, which is valid only if an infinite number of items can be stored in each storage region. This study revisits class‐based storage by considering each storage space to contain only a finite number of items. We develop a travel time model and an algorithm that can be used for determining the optimal number and boundaries of storage classes in warehouses. Different from the conventional research, our findings illustrate that commonly a small number of classes is optimal. In addition, we find the travel time is fairly insensitive to the number of storage classes in a wide range around the optimum. This suggests that a manager can select a near‐optimal number of storage classes in an easy way and need not be worried about the impact of storage‐class reconfigurations. We validate our findings for various cases, including different ABC‐demand curves, space‐sharing factors, number of items, storage rack shapes, discrete storage locations, and stochastic item demand.     

Simplest strategies method for manufacturing workcell restoration

We consider the production process of a manufacturing workcell. Production items obtained from an outside supplier are not processed adequately as far as their quality is concerned. Production items meeting the required quality depend on the workcell state, which degrades according to the number of produced items. The workcell is completely restored by some restoring operations leading to its as-new condition. The method of deriving the restoration period, which leads to the maximum probability that produced items meet the required quality, is introduced. It is based on the nontraditional approach, i.e. on the simplest strategies method for the formulation of the problem presented here. The implementation of this optimization approach is illustrated with an example.     

A simple integrated production policy of an imperfect item for vendor and buyer

This article develops a simple approach for determining an optimal integrated vendor–buyer inventory policy for an item with imperfect quality. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. This model is assumed to produce a certain number of defective items during the production process. Items of poor quality detected in the screening process of a lot are sold at a discounted price. The expected annual integrated total cost function is derived and a solution procedure is proposed to determine the optimal policy. Finally, a numerical example is also given to illustrate the solution procedure presented in this article.     

A Model for Resource Constrained Production and Inventory Management

We present a general model for multi-item production and inventory management problems that include a resource restriction. The decision variables in the model can take on a variety of interpretations, but will typically represent cycle times, production batch sizes, number of production runs, or order quantities for each item. We consider environments where item demand rates are approximately constant and performing an activity such as producing a batch of a product or placing an order results in the consumption of a scarceresource that is shared among the items. Some examples of shared resources include limited machine capacity, a restriction on the amount of money that can be tied up in stock, orlimited storage capacity. We focus on the case where the decision variables must be integer valued or selected from a discrete set of choices, such as when an integer number of production runs is desired for each item, or in order quantity problems where the items come in pack sizes containing more than one unit and, therefore, the order quantities must be an integer multiple of the pack sizes. We develop a heuristic and a branch and bound algorithm for solving the problem. The branch and bound algorithm includes reoptimization procedures and the heuristic to improve its performance. Computational testing indicates that the algorithms are effective for solving the general model.     

PROCEDURES FOR DETERMINING RELATIVE FREQUENCIES OF PRODUCTION/ORDER IN MULTISTAGE ASSEMBLY SYSTEMS*

We show that the problems of determination lot sizes in a multistage assembly system for the case of instantaneous production and constant demand for the end item can be reduced to the problems of determining relative frequenceis of production/order for items at each production stage. We further show that such frequencies are independent of the demand levels. Optimal and near-optimal solution procedures for this reduced problem are provided. The near-optimal procedure successively treats each stage of production as a final production stage while simulatenously incorporating decisions made at lower stages into decisions made at higher stages. Experimental results show that the near-optimal procedure results in optimal solutions 75 percent of the time and performs considerably better than representative heuristics available in the literature. Further, its performance is relatively less susceptible to product/structural characteristics of the system.     

Optimal sampling techniques in off-line quality control

This paper addresses the problem of quality control for manufacturing environments. The quality control station is placed in an off-line position, i.e. external to the item flow. This layout is mandatory when the station is unable (because of costs and times) to inspect the whole set of items produced. The aim of the present study is to describe and evaluate how the limited capacity of the quality control station affects the efficiency of the connected production system and how the service time of the inspection station may be profitably managed as a further variable of the quality inspection process. Optimal policies for both random and deterministic sampling techniques are determined and compared.     

Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing

In this paper, we study 1-space bounded multi-dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes with unit length on each side. In d-dimensional space, any two dimensions i and j define a space P _ij . When an item arrives, we must pack it into an active bin immediately without any knowledge of the future items, and 90^°-rotation on any plane P _ij is allowed. The objective is to minimize the total number of bins used for packing all these items in the sequence. In the 1-space bounded variant, there is only one active bin for packing the current item. If the active bin does not have enough space to pack the item, it must be closed and a new active bin is opened. For d-dimensional bin packing, an online algorithm with competitive ratio 4 ^d is given. Moreover, we consider d-dimensional hypercube packing, and give a 2 ^d+1-competitive algorithm. These two results are the first study on 1-space bounded multi dimensional bin packing and hypercube packing.     

Machine learning for multi-criteria inventory classification applied to intermittent demand

Multi-criteria inventory classification groups inventory items into classes, each of which is managed by a specific re-order policy according to its priority. However, the tasks of inventory classification and control are not carried out jointly if the classification criteria and the classification approach are not robustly established from an inventory-cost perspective. Exhaustive simulations at the single item level of the inventory system would directly solve this issue by searching for the best re-order policy per item, thus achieving the subsequent optimal classification without resorting to any multi-criteria classification method. However, this would be very time-consuming in real settings, where a large number of items need to be managed simultaneously.

In this article, a reduction in simulation effort is achieved by extracting from the population of items a sample on which to perform an exhaustive search of best re-order policies per item; the lowest cost classification of in-sample items is, therefore, achieved. Then, in line with the increasing need for ICT tools in the production management of Industry 4.0 systems, supervised classifiers from the machine learning research field (i.e. support vector machines with a Gaussian kernel and deep neural networks) are trained on these in-sample items to learn to classify the out-of-sample items solely based on the values they show on the features (i.e. classification criteria). The inventory system adopted here is suitable for intermittent demands, but it may also suit non-intermittent demands, thus providing great flexibility. The experimental analysis of two large datasets showed an excellent accuracy, which suggests that machine learning classifiers could be implemented in advanced inventory classification systems.     

On revenue maximization with sharp multi-unit demands

We consider markets consisting of a set of indivisible items, and buyers that have sharp multi-unit demand. This means that each buyer \(i\) wants a specific number \(d_i\) of items; a bundle of size less than \(d_i\) has no value. We consider the objective of setting prices and allocations in order to maximize the total revenue of the market maker. The pricing problem with sharp multi-unit demand buyers has a number of properties that the unit-demand model does not possess, and is an important question in algorithmic pricing. We consider the problem of computing a revenue maximizing solution for two solution concepts: competitive equilibrium and envy-free pricing. For unrestricted valuations, these problems are NP-complete; we focus on a realistic special case of “correlated values” where each buyer \(i\) has a valuation \(v_iq_j\) for item \(j\), where \(v_i\) and \(q_j\) are positive quantities associated with buyer \(i\) and item \(j\) respectively. We present a polynomial time algorithm to solve the revenue-maximizing competitive equilibrium problem. For envy-free pricing, if the demand of each buyer is bounded by a constant, a revenue maximizing solution can be found efficiently; the general demand case is shown to be NP-hard.     

Hiring Behavior Analysts: Free Gifts at a Booth Increase Verbal Contacts with a Recruiter,but Not Serious Job Inquiries

ABSTRACT

The job market for certified behavior analysts currently is excellent, which poses a serious challenge for organizations looking to hire such individuals. We evaluated whether the provision of small giveaways at a recruitment booth set up at two behavior-analysis conferences and at a university career fair influenced the relative number of attendees who verbally contacted a recruiter for an organization looking to hire certified and prospective behavior analysts. We also examined whether the provision of gifts influenced the relative number of attendees who left an e-mail address requesting further contact about possible employment. An alternating-treatments design was used to compare the giveaways and no-giveaways conditions. The giveaways items significantly increased the number of attendees who spoke with the recruiter, but not the number who requested further contact. These findings provide support for the use of giveaways items to generally attract attention to a recruiter, but further research is needed to determine whether their use increases applications for employment.     

Setups and effective capacity: the impact of lot sizing techniques in an MRP environment

This study investigates how lot sizing techniques influence the profit performance, inventory level, and order lardiness of an assembly job shop controlled by MRP. Four single-level lot sizing techniques are compared by simulation analysis under two levels of master schedule instability and two levels of end item demand. A second analysis investigates the influence of a multilevel lot sizing technique, the generalized constrained-K (GCK) cost modification, on the four single-level techniques at low demand and low nervousness. The analyses reveal a previously unreported phenomenon. Given the same inventory costs, the single-level lot sizing techniques generate substantially different average batch sizes. The lot sizing techniques maintain the following order of increasing average batch size (and decreasing total setup time):

economic order quantity (EOQ)

period order quantity (POQ)

least total cost (LTC)

Silver-Meal heuristic (SML)

The causes for different average batch sizes among the lot sizing techniques are analysed and explained. Demand lumpiness, inherent in multilevel manufacturing systems controlled by MRP, is found to be a major factor. The number of setups each lot sizing technique generates is the primary determinant of profit performance, inventory level, and order tardiness. EOQ, a fixed order quantity technique, is less sensitive to nervousness than the discrete lot sizing techniques. EOQ_, however, generates the smallest average batch size, and, therefore, the most setups. Since setups consume capacity, EOQ, is more sensitive to higher demand. SML generates the largest average batch sizes, and is, therefore, less sensitive to increased demand. At low demand, the other lot sizing techniques perform better on all criteria. They generate smaller batches and, therefore, shorter actual lead times. The GCK cost modification increases the average batch size generated by each lot sizing technique. GCK improves the profit and customer service level of EOQ the lot sizing technique with the smallest batches. GCK causes the other lot sizing techniques to generate excessively large batches and, therefore, excessively long actual lead times.     

Bin packing with “Largest In Bottom” constraint: tighter bounds and generalizations

The (online) bin packing problem with LIB constraint is stated as follows: The items arrive one by one, and must be packed into unit capacity bins, but a bigger item cannot be packed into a bin which already contains a smaller item. The number of used bins has to be minimized as usually. We show that the absolute performance bound of algorithm First Fit is not worse than 2+1/6≈2.1666 for the problem, improving the previous best upper bound 2.5. Moreover, if the item sizes do not exceed 1/d, then we improve the previous best result 2+1/d to 2+1/d(d+2), for any d≥2. (Both previously best results are due to Epstein, Nav. Res. Logist. 56(8):780–786, 2009.) Furthermore, we define a problem with the generalized LIB constraint, where some incoming items cannot be packed into the bins of some already packed items. The (in)compatibility of the incoming item with the items already packed becomes known only at the arrival of the actual item, and is given by an undirected graph (and, as usual in case of online graph problems, we can see only that part of the graph what already arrived). We show that 3 is an upper bound for this general problem if some natural transitivity constraint is satisfied.     

A COMPARISON OF ALTERNATIVE FORECASTING STRATEGIES FOR MULTI-STAGE PRODUCTION-INVENTORY SYSTEMS

In multi-stage production-inventory systems, the demand for precursor items derives from the demand for successor items at the later stages in the system. This paper presents a method for evaluating the performance of two different strategies for forecasting the demand for precursor items. The dependent strategy relies on successor item forecasts to build a precursor item forecast, while the independent strategy relies on the extrapolation of past precursor demand. An expression indicating the conditions under which one strategy is preferred to the other is developed, and the effect of changing these conditions is illustrated with simulation results.     

Online bin packing of fragile objects with application in cellular networks

We study a specific bin packing problem which arises from the channel assignment problems in cellular networks. In cellular communications, frequency channels are some limited resource which may need to share by various users. However, in order to avoid signal interference among users, a user needs to specify to share the channel with at most how many other users, depending on the user’s application. Under this setting, the problem of minimizing the total channels used to support all users can be modeled as a specific bin packing problem as follows: Given a set of items, each with two attributes, weight and fragility. We need to pack the items into bins such that, for each bin, the sum of weight in the bin must be at most the smallest fragility of all the items packed into the bin. The goal is to minimize the total number of bins (i.e., the channels in the cellular network) used. We consider the on-line version of this problem, where items arrive one by one. The next item arrives only after the current item has been packed, and the decision cannot be changed. We show that the asymptotic competitive ratio is at least 2. We also consider the case where the ratio of maximum fragility and minimum fragility is bounded by a constant. In this case, we present a class of online algorithms with asymptotic competitive ratio at most of 1/4+3r/2, for any r>1. A preliminary version of this paper appeared in Proc. of Workshop on Internet and Network Economics (WINE’05, pp. 564–573). The research of W.-T.C. was supported in part by Hong Kong RGC grant HKU5172/03E. The research of F.Y.-L.C. was supported in part by Hong Kong RGC Grant HKU7142/03E. The research of D.Y. was supported by NSFC (10601048). The research of G.Z. was supported in part by NSFC (60573020).     

Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem

In the binary single constraint Knapsack Problem, denoted KP, we are given a knapsack of fixed capacity c and a set of n items. Each item j, j = 1,...,n, has an associated size or weight w_j and a profit p_j. The goal is to determine whether or not item j, j = 1,...,n, should be included in the knapsack. The objective is to maximize the total profit without exceeding the capacity c of the knapsack. In this paper, we study the sensitivity of the optimum of the KP to perturbations of either the profit or the weight of an item. We give approximate and exact interval limits for both cases (profit and weight) and propose several polynomial time algorithms able to reach these interval limits. The performance of the proposed algorithms are evaluated on a large number of problem instances.