On online bin packing with LIB constraints

In many applications of packing, the location of small items below large items, inside the packed boxes, is forbidden. We consider a variant of the classic online one‐dimensional bin packing, in which items allocated to each bin are packed there in the order of arrival, satisfying the condition above. This variant is called online bin packing problem with LIB (larger item in the bottom) constraints. We give an improved analysis of First Fit showing that its competitive ratio is at most , and design a lower bound of 2 on the competitive ratio of any online algorithm. In addition, we study the competitive ratio of First Fit as a function of an upper bound (where d is a positive integer) on the item sizes. Our upper bound on the competitive ratio of First Fit tends to 2 as d grows, whereas the lower bound of two holds for any value of d. Finally, we consider several natural and well known algorithms, namely, Best Fit, Worst Fit, Almost Worst Fit, and Harmonic, and show that none of them has a finite competitive ratio for the problem. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Inventory policies for a make‐to‐order system with a perishable component and fixed ordering cost

We consider a make‐to‐order production system where two major components, one nonperishable (referred to as part 1) and one perishable (part 2), are needed to fulfill a customer order. In each period, replenishment decisions for both parts need to be made jointly before demand is realized and a fixed ordering cost is incurred for the nonperishable part. We show that a simple (s_n,S,S) policy is optimal. Under this policy, S along with the number of backorders at the beginning of a period if any and the availability of the nonperishable part (part 1) determines the optimal order quantity of the perishable part (part 2), while (s_n,S) guide when and how much of part 1 to order at each state. Numerical study demonstrates that the benefits of using the joint replenishment policy can be substantial, especially when the unit costs are high and/or the profit margin is low. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Transporting jobs through a two‐machine open shop

We consider the two‐machine open shop scheduling problem in which the jobs are brought to the system by a single transporter and moved between the processing machines by the same transporter. The purpose is to split the jobs into batches and to find the sequence of moves of the transporter so that the time by which the completed jobs are collected together on board the transporter is minimal. We present a ‐approximation algorithm. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Scheduling parallel machines with inclusive processing set restrictions and job rejection

In this article, we study a parallel machine scheduling problem with inclusive processing set restrictions and the option of job rejection. In the problem, each job is compatible to a subset of machines, and machines are linearly ordered such that a higher‐indexed machine can process all those jobs that a lower‐indexed machine can process (but not conversely). To achieve a tight production due date, some of the jobs might be rejected at certain penalty. We first study the problem of minimizing the makespan of all accepted jobs plus the total penalty cost of all rejected jobs, where we develop a ‐approximation algorithm with a time complexity of . We then study two bicriteria variants of the problem. For the variant problem of minimizing the makespan subject to a given bound on the total rejection cost, we develop a ‐approximation algorithm with a time complexity of . For the variant problem of maximizing the total rejection cost of the accepted jobs subject to a given bound on the makespan, we present a 0.5‐approximation algorithm with a time complexity of . © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 667–681, 2017     

Scheduling parallel machines with inclusive processing set restrictions

We consider the problem of assigning a set of jobs to different parallel machines of the same processing speed, where each job is compatible to only a subset of those machines. The machines can be linearly ordered such that a higher‐indexed machine can process all those jobs that a lower‐indexed machine can process. The objective is to minimize the makespan of the schedule. This problem is motivated by industrial applications such as cargo handling by cranes with nonidentical weight capacities, computer processor scheduling with memory constraints, and grades of service provision by parallel servers. We develop an efficient algorithm for this problem with a worst‐case performance ratio of + ε, where ε is a positive constant which may be set arbitrarily close to zero. We also present a polynomial time approximation scheme for this problem, which answers an open question in the literature. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Analysis of practical policies for a single link distribution system

In this paper we consider a transportation problem where several products have to be shipped from an origin to a destination by means of vehicles with given capacity. Each product is made available at the origin and consumed at the destination at the same constant rate. The time between consecutive shipments must be greater than a given minimum time. All demand needs to be satisfied on time and backlogging is not allowed. The problem is to decide when to make the shipments and how to load the vehicles with the objective of minimizing the long run average of the transportation and the inventory costs at the origin and at the destination over an infinite horizon. We consider two classes of practical shipping policies, the zero inventory ordering (ZIO) policies and the frequency‐based periodic shipping (FBPS) policies. We show that, in the worst‐case, the Best ZIO policy has a performance ratio of . A better performance guarantee of is shown for the best possible FBPS policy. The performance guarantees are tight. Finally, combining the Best ZIO and the Best FBPS policies, a policy that guarantees a performance is obtained. Computational results show that this policy gives an average percent optimality gap on all the tested instances of <1%. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Approximation algorithms for sequential batch‐testing of series systems

We introduce and study a generalization of the classic sequential testing problem, asking to identify the correct state of a given series system that consists of independent stochastic components. In this setting, costly tests are required to examine the state of individual components, which are sequentially tested until the correct system state can be uniquely identified. The goal is to propose a policy that minimizes the expected testing cost, given a‐priori probabilistic information on the stochastic nature of each individual component. Unlike the classic setting, where variables are tested one after the other, we allow multiple tests to be conducted simultaneously, at the expense of incurring an additional set‐up cost. The main contribution of this article consists in showing that the batch testing problem can be approximated in polynomial time within factor , for any fixed . In addition, we explain how, in spite of its highly nonlinear objective function, the batch testing problem can be formulated as an approximate integer program of polynomial size, while blowing up its expected cost by a factor of at most . Finally, we conduct extensive computational experiments, to demonstrate the practical effectiveness of these algorithms as well as to evaluate their limitations. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 275–286, 2016     

Level workforce planning for multistage transfer lines

In this article, we define two different workforce leveling objectives for serial transfer lines. Each job is to be processed on each transfer station for c time periods (e.g., hours). We assume that the number of workers needed to complete each operation of a job in precisely c periods is given. Jobs transfer forward synchronously after every production cycle (i.e., c periods). We study two leveling objectives: maximin workforce size () and min range (R). Leveling objectives produce schedules where the cumulative number of workers needed in all stations of a transfer line does not experience dramatic changes from one production cycle to the next. For and a two‐station system, we develop a fast polynomial algorithm. The range problem is known to be NP‐complete. For the two‐station system, we develop a very fast optimal algorithm that uses a tight lower bound and an efficient procedure for finding complementary Hamiltonian cycles in bipartite graphs. Via a computational experiment, we demonstrate that range schedules are superior because not only do they limit the workforce fluctuations from one production cycle to the next, but they also do so with a minor increase in the total workforce size. We extend our results to the m‐station system and develop heuristic algorithms. We find that these heuristics work poorly for min range (R), which indicates that special structural properties of the m‐station problem need to be identified before we can develop efficient algorithms. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 577–590, 2016     

Single batch machine scheduling with deliveries

We consider the problem of scheduling a set of n jobs on a single batch machine, where several jobs can be processed simultaneously. Each job j has a processing time p_j and a size s_j. All jobs are available for processing at time 0. The batch machine has a capacity D. Several jobs can be batched together and processed simultaneously, provided that the total size of the jobs in the batch does not exceed D. The processing time of a batch is the largest processing time among all jobs in the batch. There is a single vehicle available for delivery of the finished products to the customer, and the vehicle has capacity K. We assume that K = rD, where and r is an integer. The travel time of the vehicle is T; that is, T is the time from the manufacturer to the customer. Our goal is to find a schedule of the jobs and a delivery plan so that the service span is minimized, where the service span is the time that the last job is delivered to the customer. We show that if the jobs have identical sizes, then we can find a schedule and delivery plan in time such that the service span is minimum. If the jobs have identical processing times, then we can find a schedule and delivery plan in time such that the service span is asymptotically at most 11/9 times the optimal service span. When the jobs have arbitrary processing times and arbitrary sizes, then we can find a schedule and delivery plan in time such that the service span is asymptotically at most twice the optimal service span. We also derive upper bounds of the absolute worst‐case ratios in both cases. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 470–482, 2015     

Improved bounds for batch scheduling with nonidentical job sizes

Here, we revisit the bounded batch scheduling problem with nonidentical job sizes on single and parallel identical machines, with the objective of minimizing the makespan. For the single machine case, we present an algorithm which calls an online algorithm (chosen arbitrarily) for the one‐dimensional bin‐packing problem as a sub‐procedure, and prove that its worst‐case ratio is the same as the absolute performance ratio of . Hence, there exists an algorithm with worst‐case ratio , which is better than any known upper bound on this problem. For the parallel machines case, we prove that there does not exist any polynomial‐time algorithm with worst‐case ratio smaller than 2 unless P = NP, even if all jobs have unit processing time. Then we present an algorithm with worst‐case ratio arbitrarily close to 2. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 351–358, 2014     

Scheduling multiple products on parallel machines with setup costs

We consider a class of production scheduling models with m identical machines in parallel and k different product types. It takes a time p_i to produce one unit of product type i on any one of the machines. There is a demand stream for product type i consisting of n_i units with each unit having a given due date. Before a machine starts with the production of a batch of products of type i a setup cost c is incurred. We consider several different objective functions. Each one of the objective functions has three components, namely a total setup cost, a total earliness cost, and a total tardiness cost. In our class of problems we find a relatively large number of problems that can be solved either in polynomial time or in pseudo‐polynomial time. The polynomiality or pseudo‐polynomiality is achieved under certain special conditions that may be of practical interest; for example, a regularity pattern in the string of due dates combined with earliness and tardiness costs that are similar for different types of products. The class of models we consider includes as special cases discrete counterparts of a number of inventory models that have been considered in the literature before, e.g., Wagner and Whitin (Manage Sci 5 (1958), 89–96) and Zangwill (Oper Res 14 (1966), 486–507; Manage Sci 15 (1969), 506–527). © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

A stochastic assignment problem

There are n boxes with box i having a quota value Balls arrive sequentially, with each ball having a binary vector attached to it, with the interpretation being that if X_i = 1 then that ball is eligible to be put in box i. A ball's vector is revealed when it arrives and the ball can be put in any alive box for which it is eligible, where a box is said to be alive if it has not yet met its quota. Assuming that the components of a vector are independent, we are interested in the policy that minimizes, either stochastically or in expectation, the number of balls that need arrive until all boxes have met their quotas. © 2014 Wiley Periodicals, Inc. 62:23–31, 2015     

Minimal LST representations of MAP(n)s: Moment fittings and queueing approximations

A Markovian arrival process of order n, MAP(n), is typically described by two n × n transition rate matrices in terms of rate parameters. While it is straightforward and intuitive, the Markovian representation is redundant since the minimal number of parameters is n² for non‐redundant MAP(n). It is well known that the redundancy complicates exact moment fittings. In this article, we present a minimal and unique Laplace‐Stieltjes transform (LST) representations for MAP(n)s. Even though the LST coefficients vector itself is not a minimal representation, we show that the joint LST of stationary intervals can be represented with the minimum number of parameters. We also propose another minimal representation for MAP(3)s based on coefficients of the characteristic polynomial equations of the two transition rate matrices. An exact moment fitting procedure is presented for MAP(3)s based on two proposed minimal representations. We also discuss how MAP(3)/G/1 departure process can be approximated as a MAP(3). A simple tandem queueing network example is presented to show that the MAP(3) performs better than the MAP(2) in queueing approximations especially under moderate traffic intensities. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 549–561, 2016     

A finiteness proof for modified dantzig cuts in integer programming

Let be a basic solution to the linear programming problem subject to: where R is the index set associated with the nonbasic variables. If all of the variables are constrained to be nonnegative integers and x_u is not an integer in the basic solution, the linear constraint is implied. We prove that including these “cuts” in a specified way yields a finite dual simplex algorithm for the pure integer programming problem. The relation of these modified Dantzig cuts to Gomory cuts is discussed.     

Parallel machine scheduling with job assignment restrictions

In the classical multiprocessor scheduling problem independent jobs must be assigned to parallel, identical machines with the objective of minimizing the makespan. This article explores the effect of assignment restrictions on the jobs for multiprocessor scheduling problems. This means that each job can only be processed on a specific subset of the machines. Particular attention is given to the case of processing times restricted to one of two values, 1 and λ, differing by at most 2. A matching based polynomial time ε‐approximation algorithm is developed that has a performance ratio tending to . This algorithm is shown to have the best possible performance, tending to 3/2, for processing times 1 and 2. For the special case of nested processing sets, i.e., when the sets of machines upon which individual jobs may be assigned are non‐overlapping, the behavior of list scheduling algorithms is explored. Finally, for assignment restrictions determined by just one characteristic of the machines, such as disc storage or memory constraint in the case of high performance computing, we contribute an algorithm that provides a 3/2 worst case bound and runs in time linear in the number of jobs. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Optimizing the defensive characteristics of mild steel via the electrodeposition of ZnSi3N4 reinforcing particles

The effect of ZnSi₃N₄ deposition prepared via direct electrolytic co-deposition on mild steel was studied as a result its inherent vulnerability to corrosion in an aggressive environment and failure on the application of load. The experiment was conducted varying the mass concentration of silicon nitride (Si₃N₄) between 7 and 13 g at cell voltage of 0.3 and 0.5 V, at constant temperature of 45 °C. The morphologies of the coated surfaces were characterized using high resolution Nikon Optical Microscope and Scanning Electron Microscope (SEM) revealing that the particles of the ZnSi₃N₄ were homogeneously dispersed. The corrosion behaviour was studied using potentiodynamic polarization technique in 3.65% NaCl solution and the microhardness was examined using Brinell hardness testing technique. The result of the corrosion experiment confirmed an improved corrosion resistance with a reduction in corrosion rate from 9.7425 mm/year to 0.10847 mm/year, maximum coating efficiency of 98.9%, maximum polarization resistance of 1555.3 Ω and a very low current density of 9.33 × 10⁻⁶ A/cm². The negative shift in the E_corr revealed the cathodic protective nature of the coating. The microhardness was also found to have increased from 137.9 HBN for the unmodified steel to a maximum value of 263.3 HBN for the 0.5Zn13Si₃N₄ coated steel representing 90.9% increment in hardness as a result of the matrix grain refining and dispersion-strengthening ability of the incorporated Si₃N₄ particles.     

Asymptotic analysis of periodic policies for the inventory routing problem

In this article, a distribution system is studied where the sum of transportation and inventory costs is to be minimized. The inventory holding cost is assumed to be the same for all retailers. A fixed partition (FP) periodic policy is proposed with tight asymptotic worst‐case performance of 3/2 with respect to the best possible policy. This bound cannot be improved in the class of FP periodic policies. In partition‐based PB policies, the retailers are first partitioned into sets and then the sets are grouped in such a way that sets of retailers within a group are served together at selected times. A PB periodic, policy is presented with tight worst‐case asymptotic performance of with respect to the best possible policy. This latter performance improves the worst‐case asymptotic performance of of the previously best known policy for this problem. We also show that the proposed PB periodic policy has the best worst‐case asymptotic performance within the class of PB policies. Finally, practical heuristics inspired by the analyzed policies are designed and tested. The asymptotic worst–case performances of the heuristics are shown to be the same of those of the analyzed policies. Computational results show that the heuristics suggested are less than 6.4% on average from a lower bound on the optimal cost when 50 or more retailers are involved. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2013     

Skewness correction X̄ and R charts for skewed distributions

This paper proposes a skewness correction (SC) method for constructing the and R control charts for skewed process distributions. Their asymmetric control limits (about the central line) are based on the degree of skewness estimated from the subgroups, and no parameter assumptions are made on the form of process distribution. These charts are simply adjustments of the conventional Shewhart control charts. Moreover, the chart is almost the same as the Shewhart chart if the process distribution is known to be symmetrical. The new charts are compared with the Shewhart charts and weighted variance (WV) control charts. When the process distribution is in some neighborhood of Weibull, lognormal, Burr or binomial family, simulation shows that the SC control charts have Type I risk (i.e., probability of a false alarm) closer to 0.27% of the normal case. Even in the case where the process distribution is exponential with known mean, not only the control limits and Type I risk, but also the Type II risk of the SC charts are closer to those of the exact and R charts than those of the WV and Shewhart charts. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 555–573, 2003     

Vehicle routing problems with regular objective functions on a path

We investigate the problem of scheduling a fleet of vehicles to visit the customers located on a path to minimize some regular function of the visiting times of the customers. For the single‐vehicle problem, we prove that it is pseudopolynomially solvable for any minsum objective and polynomially solvable for any minmax objective. Also, we establish the NP‐hardness of minimizing the weighted number of tardy customers and the total weighted tardiness, and present polynomial algorithms for their special cases with a common due date. For the multivehicle problem involving n customers, we show that an optimal solution can be found by solving or O(n) single‐vehicle problems. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 34–43, 2014     

Investigating the surface integrity of aluminium based composites machined by EDM

In the present work, the surface characteristics of Electrical Discharge Machined (EDM) Al (6351)SiC and Al (6351)SiCB₄C composites are investigated. The composites are prepared by employing the conventional stir casting technique, as it can produce better particle dispersion in the matrix. The detailed experimental study is performed on the composites by varying current (I), duty factor (τ), pulse on time (T_on), and the gap voltage (V) in order to analyze the Heat Affected Zone (HAZ) formed in the sub surface and the average crater diameter formed on the machined surface of the composites as an output function. The formation of recast layers, presence of bubbles and the surface texture of the composites at various machining conditions are observed. The results show that the increased Metal Removal Rate (MRR) increases the depth of HAZ and the average crater diameter on the machined area. Further, the addition of B₄C particles to the composite produces more surface defect than the AlSiC composite.