Edgar Possani

Lot streaming multiple jobs in a flow shop

In this article we consider the advantages of applying lot streaming in a multiple job flow-shop context. The lot streaming process of splitting jobs into sublots to allow overlapping between successive operations has been shown to reduce makespan and thus increase customer satisfaction. Efficient algorithms are available in the literature for solving the problem for a single job. However, for multiple jobs, job sequencing, as well as lot sizing, is involved, and the problem is therefore NP-hard. We consider two special cases for which we provide polynomial time solutions. In one case, we eliminate diversity of the jobs, and hence the job sequencing decision, and in the other we restrict the number of machines. We show that for jobs with identical processing times and number of sublots, no advantage is obtained by allowing inconsistency in sublot sizing of consecutive jobs. For the two-machine case, we also explain why the sequencing and sublot size decision can be approached independently, and supply a polynomial time algorithm for minimising makespan, taking account of attached set-ups on the first machine and transportation times.

Keep or return? Managing ordering and return policies in start-up companies

Abstract Start-up companies are considered an important factor in the success of a nation’s economy. We are interested in the decisions for long-term survival of these firms when they have considerable cash restrictions. In this paper we analyse several inventory control models to manage inventory purchasing and return policies. The Markov decision models are formulated for both established companies that look at maximising average profit and start-up companies that look at maximising their long-term survival probability. We contrast both objectives, and present properties of the policies and the survival probabilities. We find that start-up companies may need to be riskier if the return price is very low, but there is a period where a start-up firm becomes more cautious than an established company and there is a point, as it accumulates capital, where it starts behaving as an established firm. We compare the various models and give conditions under which their policies are equivalent.

Split-merge

We address the problem of scheduling a single batching machine to minimize the maximum lateness with a constraint restricting the batch size. A solution for this NP-hard problem is defined by a selection of jobs for each batch and an ordering of those batches. As an alternative, we choose to represent a solution as a sequence of jobs. This approach is justified by our development of a dynamic program to find a schedule that minimizes the maximum lateness while preserving the underlying job order. Given this solution representation, we are able to define and evaluate various job-insert and job-swap neighborhood searches. Furthermore we introduce a new neighborhood, named split-merge, that allows multiple job inserts in a single move. The split-merge neighborhood is of exponential size, but can be searched in polynomial time by dynamic programming. Computational results with an iterated descent algorithm that employs the split-merge neighborhood show that it compares favorably with corresponding iterated descent algorithms based on the job-insert and job-swap neighborhoods. HighlightsWe study the scheduling of a single batching machine with restricted batch size.We develop an exponential neighborhood that can be explored in polynomial time.Dynamic programing formulations are developed for optimal batching.We evaluate and compare different local search heuristics.

Loans, ordering and shortage costs in start-ups: a dynamic stochastic decision approach

Start-up companies are a vital ingredient in the success of a globalised networked world economy. We believe that such companies are interested in maximising the chance of surviving in the long term. We present a Markov decision model to analyse survival probabilities of start-up manufacturing companies. Our model examines the implications of their operating decisions, in particular how their inventory strategy is influenced by purchasing, shortage, transportation and ordering costs, as well as loans to the firm. It is shown that although the start-up company should be more conservative in its component purchasing strategy than if it were a well-established company it should not be too conservative. Nor is its strategy monotone in the amount of capital available.

Managing Inventory and Production Capacity in Start-Up Firms

We consider the problem of managing inventory and production capacity in a start-up manufacturing firm with the objective of maximising the probability of the firm surviving as well as the more common objective of maximising profit. Using Markov decision process models, we characterise and compare the form of optimal policies under the two objectives. This analysis shows the importance of coordination in the management of inventory and production capacity. The analysis also reveals that a start-up firm seeking to maximise its chance of survival will often choose to keep production capacity significantly below the profit-maximising level for a considerable time. This insight helps us to explain the seemingly cautious policies adopted by a real start-up manufacturing firm.

Bi-objective scheduling on a restricted batching machine

Abstract In this work, we consider a batching machine that can process several jobs at the same time. Batches have a restricted batch size, and the processing time of a batch is equal to the largest processing time among all jobs within the batch. We solve the bi-objective problem of minimizing the maximum lateness and number of batches. This function is relevant as we are interested in meeting due dates and minimizing the cost of handling each batch. Our aim is to find the Pareto-optimal solutions by using an epsilon-constraint method on a new mathematical model that is enhanced with a family of valid inequalities and constraints that avoid symmetric solutions. Additionally, we present a biased random-key genetic algorithm to approximate the optimal Pareto points of larger instances in reasonable time. Experimental results show the efficiency of our methodologies.

A Circulation Network Model for the Exchange Rate Arbitrage Problem

In this article we present a circulation network model for the detection of arbitrage opportunities in the currencies and securities markets. As an illustration we present its application to the interest rate of the Mexican and American bond market, the interbank loan rate of both countries, as well as to the deposits rate of US and Canada reported in Bloomberg. Deviations of covered interest rate parity imply that there exist a series of transactions that can be carried out to obtain riskless profits by exploiting arbitrage opportunities. The problem of finding arbitrage opportunities is modeled via a generalized maximum flow problem. The maximum flow over the generalized circulation network represents profits from arbitrage, and it’s obtained through the application of a minimum cost flow algorithm.

Heuristic Approaches for Experimentation in Catalyst Optimization

In this paper we give an overview of algorithms developed to aid catalyst optimization at the Mexican Institute of Petroleum. We present a methodology that uses an evolutionary approach and ideas from tabu search and simulated annealing to guide the search for optimum catalytic materialsbased on previous experimentation. We give results on butane isomerization in ZrO2/Al2O3, and compare the approach with other theoretical models. The method leads to higher efficiency and reduction in the number of tested materials.