C Rajendran

In traditional supply chain inventory management, orders used to be the major information that firms exchanged. Information sharing among firms within a supply chain has been a cornerstone of recent innovations in supply chain management. Lee et al. (2000) considered a two-level supply chain, consisting of a manufacturer and a retailer, with non-stationary AR(1) end demand and showed that the manufacturer benefits significantly when the retailer shares its demand information. In our work, we extend the study to quantify the value (i.e., benefit) of information sharing (in terms of demand variance reduction and inventory reduction) to a multi-stage serial supply chain with the number of stages greater than two. The lead time at every stage is positive and deterministic. Base stock levels at each installation are calculated under two scenarios-no information sharing and complete information sharing. The dependency of the benefit of information sharing on parameters like demand correlation and lead times is presented. It is seen that as the number of stages in a serial supply chain increases, the demand variance and hence the bullwhip effect increases; so is the case with an increase in the demand correlation. In addition, a comparative study of a supply chain with stages having respective lead times in decreasing order and a supply chain with stages having respective lead times in increasing order has also been carried out in order to relatively analyze the benefits of information sharing at different stages across these two supply chain settings. It is possibly for the first time in the literature that the benefit of information sharing has been studied and quantified (in terms of the reduction in the total demand variation and the reduction in inventory) in a multi-stage serial supply chain with more than three stages with positive and deterministic lead times.

In this paper, we consider a serial supply chain (SC) operating with deterministic and known customer demands and costs of review or orders, holding, and backlog at every installation over a finite planning horizon. We present an evaluation of two order policies: Periodic-review order-up-to S policy (i.e., (T, S) policy), and (s, S) policy. We first present a mathematical programming model to determine optimal re-order point and base-stock for every member in the SC. By virtue of the computational complexity associated with the mathematical model, we present genetic algorithms (GAs) to determine the order policy parameters, s and S for every stage. We compare the performances of GAs (for obtaining installation s and S) with the mathematical model for the periodic-review order-up-to (T, S) policy that obtains in its class optimal review periods and order-up-to levels. It is observed that the (s, S) policy emerges to be mostly better than the (T, S) policy.

The shortest path problem is the problem of finding one-to-one path from the source to the destination. In real life, the problem involves conflicting and competing objectives, and many researchers solve the multiobjective shortest path optimization problem using a weighted linear combination of objectives. However, the solution of weighted sum is highly sensitive to the weights given, limiting the practicability of this method. Solving the problem by simultaneous optimization of the objective functions to generate a set of nondominated solutions can help to build a decision support system for travelers to choose their own path on the basis of their individual preferences. This chapter proposes a multiobjective mathematical model, solved using e-approach to obtain (heuristically) nondominated solutions of shortest paths with respect to time and distance. In this study, we consider minimizing both distance and time as the objective functions with real-life constraints such as time-dependent dynamic and deterministic travel times, time-dependent dynamic and deterministic waiting times, and time-dependent one-way traffic along the roads. We implement the proposed model by using the real-life planning data (1658 nodes and 4224 links) of Chennai city network (a metropolitan city in India with highly interconnected network of roads), and present the discussion on the multiobjective routing problem with real-life considerations.

88In this chapter, we consider the development of mixed integer linear programming (MILP)-based classifier and linear programming (LP)-based classifiers for solving a classification problem. The conventional MILP-based/LP-based classifiers generally provide good results in terms of accuracy when the data set is linearly separable. However the challenge is to develop computationally efficient classifiers that can handle data that are not linearly separable. In this chapter, we propose a novel LP-based classifier that can address the classification of such data sets with multiple objectives. The salient contributions of the proposed LP-based two-phase classifier are in terms of treating the decision variables as unrestricted in sign; accounting for the contribution of attributes from their interaction effects and the contribution of attributes from their higher order polynomial degrees; treating the classification threshold/cut-off as a decision variable; converting the bandwidth of boundary of threshold to a crisp boundary with the consideration of multiple objectives; and finally the ability to find a nondominated set of solutions with respect to multiple objectives. Consequently, the proposed LP-based classifier is able to handle data that are not inherently linearly separable, unlike the conventional MILP-based and LP-based classifiers. To evaluate the performance of the proposed classifiers, we consider two data sets that are already available in the literature. We also compare the accuracy of all the proposed LP-based classifiers with the artificial neural networks, and the results indicate that one of the proposed LP-based classifiers (LP-based two-phase classifier) is able to give good results even when the data set is not linearly separable.

Autoregressive integrated moving average (ARIMA) method is a widely used time series forecasting technique. Most of the time, we try different combinations of parameters (p, d, q) and (P, D, Q) and select the best model mostly based on the likelihood score. The best model’s performance with respect to the data is, however, measured in real-life applications usually using the mean absolute percentage error (MAPE) criterion. This chapter deals with ARIMA time series models. We present a multiobjective deterministic pseudo-evolutionary algorithm to generate offspring time series from a certain number of best performing parent models, based on criterion such as MAPE or maximum absolute percentage error, and using the relative fitness values of parents obtained deterministically. The best seasonal/nonseasonal ARIMA models become the parent models from which offspring time series are generated. We then obtain for the training data set a netfront containing the nondominated set of solutions derived from offspring and parent time series, and hence we obtain the nondominated set of forecasted time series for the user’s test data set, by using the nondominated set of solutions obtained earlier for the training data set.

In this paper, we study the problem of transforming a job-shop layout into a flow-shop layout by introducing additional machines, so that all job-related operations can be processed in a flow-shop layout. The objective is to find the shortest sequence of machines, so that the overhead of introducing additional machines can be reduced. This transformation of job-shop layout into flow-shop layout has the advantage of automating the flow-line, which is an important step in digital manufacturing. The study first focuses on a special case (which is studied generally in the literature) where all the jobs would have the same and equal number of operations to be performed in a job-shop, but each job has a different machine routing when compared to other jobs. We propose a Mixed Integer Liner Programming (MILP) model for solving this special case. Further, in order to evaluate the performance of the proposed MILP model, we compare the same with an existing model in literature. From the results, we confirm that the proposed model is superior in terms of the CPU time, in solving the problem instances considered for the study. The study also extends this special case, and considers the generalized case where jobs could have different number of operations, and the study proposes a comprehensive MILP model for solving the generalized case.

This book examines the Capacitated Lot Sizing Problem (CLSP) in process industries. In almost all process industries, there are situations where products have short/long setup times, and the setup of the product and its subsequent production are carried over, across consecutive periods. The setup of a product is carried over across more than one successive period in the case of products having long setup times. A product having short setup has its setup time less than the capacity of the period in which it is setup. The setup is immediately followed by its production of the product and it may also be carried over, across successive time period(s). Many process industries require production of a product to occur immediately after its setup (without the presence of idle time between the setup and production of the product), and they also require the product to be continuously produced without any interruption. This book considers a single-machine, single-level and multiple-item CLSP problem. This book introduces the Capacitated Lot Sizing Problem with Production Carryover and Setup Crossover across periods (CLSP-PCSC). Mathematical models are proposed which are all encompassing that they can handle continuous manufacturing (as in process industries), and also situations where the setup costs and holding costs are product dependent and time independent/time dependent, with possible backorders, and with other appropriate adaptations. Comprehensive heuristics are proposed based on these mathematical models to solve the CLSP-PCSC. The performance of the proposed models and heuristics are evaluated using problem instances of various sizes. This book also covers mathematical models developed for the Capacitated Lot Sizing Problem with Production Carryover and Setup Crossover across periods, and with Sequence-Dependent Setup Times and Setup Costs (CLSP-SD-PCSC). These models allow the presence of backorders and also address real-life situations present in process industries such as production of a product starting immediately after its setup and its uninterrupted production carryover across periods, along with the presence of short/long setup times. Heuristics proposed for the CLSP-PCSC can be extended to address the CLSP problem with sequence dependent setup costs and setup times. All the models and heuristics proposed in this book address some real-life considerations present in process industries.