Two-stage time minimizing assignment problem

This paper deals with the optimal selection of m out of n facilities to first perform m   given primary jobs in Stage-I followed by the remaining (n-m)$(n-m)$ facilities performing optimally the (n-m)$(n-m)$ secondary jobs in Stage-II. It is assumed that in both the stages facilities perform in parallel. The aim of the proposed study is to find that set of m   facilities performing the primary jobs in Stage-I for which the sum of the overall completion times of jobs in Stage-I and the corresponding optimal completion time of the secondary jobs in Stage-II by the remaining (n-m)$(n-m)$ facilities is the minimum. The developed solution methodology involves solving the standard time minimizing and cost minimizing assignment problems alternately after forbidding some facility-job pairings and suggests a polynomially bound algorithm. This proposed algorithm has been implemented and tested on a variety of test problems and its performance is found to be quite satisfactory.     

Improving routing and scheduling decisions at a distributor of industrial gasses

This paper investigates cyclical inventory replenishment for a company's regional distribution center that supplies, distributes, and manages inventory of carbon dioxide (_CO2)$({\mathrm{CO}}_2)$ at over 900 separate customer sites in Indiana. The company previously experienced high labor costs with excessive overtime and maintained a regular back-log of customers experiencing stockouts. To address these issues we implemented a three-phase heuristic for the cyclical inventory routing problem encountered at one of the company's distribution centers. This heuristic determines regular routes for each of three available delivery vehicles over a 12-day delivery horizon while improving four primary performance measures: delivery labor cost, stockouts, delivery regularity, and driver–customer familiarity. It does so by first determining three sets of cities (one for each delivery vehicle) that must be delivered to each day based on customer requirements. Second, the heuristic assigns the remaining customers in other cities to one of the three “backbone routes” determined in phase 1. And third, it balances customer deliveries on each daily route over the schedule horizon. Through our methodology, we were able to significantly reduce overtime, driving time, and labor costs while improving customer service.     

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.     

Probabilistic Modeling of Flood Hazard and its Risk Assessment for Eastern Region of India

This article models flood occurrence probabilistically and its risk assessment. It incorporates atmospheric parameters to forecast rainfall in an area. This measure of precipitation, together with river and ground parameters, serve as parameters in the model to predict runoff and subsequently inundation depth of an area. The inundation depth acts as a guide for predicting flood proneness and associated hazard. The vulnerability owing to flood has been analyzed as social vulnerability $(V_S)$, vulnerability to property $(V_P)$, and vulnerability to the location in terms of awareness $(V_A)$. The associated risk has been estimated for each area. The distribution of risk values can be used to classify every area into one of the six risk zones—namely, very low risk, low risk, moderately low risk, medium risk, high risk, and very high risk. The prioritization regarding preparedness, evacuation planning, or distribution of relief items should be guided by the range on the risk scale within which the area under study falls. The flood risk assessment model framework has been tested on a real‐life case study. The flood risk indices for each of the municipalities in the area under study have been calculated. The risk indices and hence the flood risk zone under which a municipality is expected to lie would alter every day. The appropriate authorities can then plan ahead in terms of preparedness to combat the impending flood situation in the most critical and vulnerable areas.     

Single cycle policies for the one-warehouse N-retailer inventory/distribution system

We address a multi-echelon inventory system with one-warehouse and N  -retailers. The demand at each retailer is assumed to be known and satisfied by the warehouse. Shortages are not allowed and lead times are negligible. Costs at each facility consist of a fixed charge per order and a holding cost. The goal is to determine single-cycle policies which minimize the average cost per unit time, that is, the sum of the average holding and setup costs per unit time at the retailers and at the warehouse. We propose a O(NlogN)$\mathrm{O}(N\log N)$ heuristic procedure to compute efficient single-cycle policies. This heuristic is compared with other approaches proposed by Schwarz, Graves and Schwarz and Muckstadt and Roundy. We carry out a computational study to test the effectiveness of the heuristic and to compare the performance of the different procedures. From the computational results, it is shown that the new heuristic provides, on average, better single-cycle policies than those given by the Muckstadt and Roundy method.     

A coordination mechanism for a scheduling game with parallel-batching machines

In this paper we consider the scheduling problem with parallel-batching machines from a game theoretic perspective. There are m parallel-batching machines each of which can handle up to b jobs simultaneously as a batch. The processing time of a batch is the time required for processing the longest job in the batch, and all the jobs in a batch start and complete at the same time. There are n jobs. Each job is owned by a rational and selfish agent and its individual cost is the completion time of its job. The social cost is the largest completion time over all jobs, the makespan. We design a coordination mechanism for the scheduling game problem. We discuss the existence of pure Nash Equilibria and offer upper and lower bounds on the price of anarchy of the coordination mechanism. We show that the mechanism has a price of anarchy no more than \(2-\frac{2}{3b}-\frac{1}{3\max \{m,b\}}\).     

A Robust Approach for Mitigating Risks in Cyber Supply Chains

In recent years, there have been growing concerns regarding risks in federal information technology (IT) supply chains in the United States that protect cyber infrastructure. A critical need faced by decisionmakers is to prioritize investment in security mitigations to maximally reduce risks in IT supply chains. We extend existing stochastic expected budgeted maximum multiple coverage models that identify “good” solutions on average that may be unacceptable in certain circumstances. We propose three alternative models that consider different robustness methods that hedge against worst‐case risks, including models that maximize the worst‐case coverage, minimize the worst‐case regret, and maximize the average coverage in the $(1?\alpha )$ worst cases (conditional value at risk). We illustrate the solutions to the robust methods with a case study and discuss the insights their solutions provide into mitigation selection compared to an expected‐value maximizer. Our study provides valuable tools and insights for decisionmakers with different risk attitudes to manage cybersecurity risks under uncertainty.     

Optimization models for the tool change scheduling problem

Traditional machine scheduling literature generally assumes that a machine is available at all times. Yet this assumption may not be accurate in real manufacturing systems. In many cases, a machine's tool must be changed after it has continuously worked for a period of time. This paper deals with a single machine scheduling problem subject to tool wear, given the allowed maximum continuous working time of the machine is _TL$T_{\mathrm{L}}$ (tool life) and the tool change time is _TC$T_{\mathrm{C}}$. Job processing and tool changes are scheduled simultaneously. In this paper, we examine this problem to minimize the total tardiness of jobs. Two mixed binary integer programming models are developed to optimally solve this problem. Computational experiments are performed to evaluate the models’ efficiency.     

Precision parameter in the variable precision rough sets model: an application

Despite their diverse applications in many domains, the variable precision rough sets (VPRS) model lacks a feasible method to determine a precision parameter (β)$(\beta )$ value to control the choice of β$\beta$-reducts. In this study we propose an effective method to find the β$\beta$-reducts. First, we calculate a precision parameter value to find the subsets of information system that are based on the least upper bound of the data misclassification error. Next, we measure the quality of classification and remove redundant attributes from each subset. We use a simple example to explain this method and even a real-world example is analyzed. Comparing the implementation results from the proposed method with the neural network approach, our proposed method demonstrates a better performance.