Advanced production scheduling for batch plants in process industries

An Advanced Planning System (APS) offers support at all planning levels along the supply chain while observing limited resources. We consider an APS for process industries (e.g. chemical and pharmaceutical industries) consisting of the modules network design (for long–term decisions), supply network planning (for medium–term decisions), and detailed production scheduling (for short–term decisions). For each module, we outline the decision problem, discuss the specifi cs of process industries, and review state–of–the–art solution approaches. For the module detailed production scheduling, a new solution approach is proposed in the case of batch production, which can solve much larger practical problems than the methods known thus far. The new approach decomposes detailed production scheduling for batch production into batching and batch scheduling. The batching problem converts the primary requirements for products into individual batches, where the work load is to be minimized. We formulate the batching problem as a nonlinear mixed–integer program and transform it into a linear mixed–binary program of moderate size, which can be solved by standard software. The batch scheduling problem allocates the batches to scarce resources such as processing units, workers, and intermediate storage facilities, where some regular objective function like the makespan is to be minimized. The batch scheduling problem is modelled as a resource–constrained project scheduling problem, which can be solved by an efficient truncated branch–and–bound algorithm developed recently. The performance of the new solution procedures for batching and batch scheduling is demonstrated by solving several instances of a case study from process industries.

Batch scheduling in process industries: an application of resource-constrained project scheduling

The paper deals with batch scheduling problems in process industries where final products arise from several successive chemical or physical transformations of raw materials using multi–purpose equipment. In batch production mode, the total requirements of intermediate and final products are partitioned into batches. The production start of a batch at a given level requires the availability of all input products. We consider the problem of scheduling the production of given batches such that the makespan is minimized. Constraints like minimum and maximum time lags between successive production levels, sequence–dependent facility setup times, finite intermediate storages, production breaks, and time–varying manpower contribute to the complexity of this problem. We propose a new solution approach using models and methods of resource–constrained project scheduling, which (approximately) solves problems of industrial size within a reasonable amount of time.

Storage problems in batch scheduling

This paper is concerned with the modelling of storage configurations for intermediate products in process industries. Those models form the basis of algorithms for scheduling chemical production plants. Different storage capacity settings (unlimited, finite, and no intermediate storage), storage homogeneity settings (dedicated and shared storage), and storage time settings (unlimited, finite, and no wait) are considered. We discuss a classification of storage constraints in batch scheduling and show how those constraints can be integrated into a general production scheduling model that is based on the concept of cumulative resources.

Feather-pecking response of laying hens to feather and cellulose-based rations fed during rearing.

Recent studies in laying hens have shown that feather peckers eat more feathers than nonpeckers. We hypothesized that food pellets containing feathers would decrease the birds' appetite for feathers and thereby also decrease feather pecking. To separate the effect of feathers from that of insoluble fiber per se, additional control groups were fed pellets containing similar amounts of cellulose. Sixty (experiment 1) and 180 (experiment 2) 1-d-old Lohmann-Selected Leghorn birds were divided into 12 groups of 5 (experiment 1) and 15 (experiment 2) birds, respectively, and kept on slatted floors. During the rearing period, 4 groups each had ad libitum access to either a commercial pelleted diet, a pelleted diet containing 5% (experiment 1) or 10% (experiment 2) of chopped feathers, respectively, or a pelleted diet containing 5% (experiment 1) or 10% (experiment 2) of cellulose, respectively. In the consecutive laying period, all groups received a commercial pelleted diet. In experiment 1, feather pecking was recorded weekly from wk 5 to wk 16. In the laying period, observations were made in wk 18, 20, 22, 23, 24, 25, 26, 27, 28, and 30. In experiment 2, feather pecking was recorded weekly from wk 5 to 11, in wk 16 to wk 18, and in wk 20 and 21. At the end of the rearing period, plumage condition per individual hen was scored. Scores from 1 (denuded) to 4 (intact) were given for each of 6 body parts. The addition of 10% of feathers to the diet reduced the number of severe feather-pecking bouts (P < 0.0129) and improved plumage condition of the back area (P < 0.001) significantly compared with control diets. The relationship between feather pecking/eating and the gastrointestinal consequences thereof, which alter feather pecking-behavior, are unclear. Understanding this relationship might be crucial for understanding the causation of feather pecking in laying hens.

Transient Fanconi syndrome with severe polyuria and polydipsia in a 4-year old Shih Tzu fed chicken jerky treats.

Acquired Fanconi syndrome is characterized by inappropriate urinary loss of amino acids, bicarbonate, electrolytes, and water. It has recently been described in dogs fed chicken jerky treats from China, a new differential diagnosis to the classical inciting infectious diseases (e.g. leptospirosis, pyelonephritis) and toxins. A dog fed exclusively chicken jerky treats purchased in Switzerland was presented to our clinic with severe polyuria, polydipsia and profound electrolyte and acid base disturbances. Other inciting causes of Fanconi syndrome were ruled out. The requirement of a very intensive supportive treatment in this dog stands in contrast to treatment of chronic forms of Fanconi syndrome as described in the Basenji. This intensive therapy and the associated monitoring can be a real challenge and a limiting factor for the prognosis of acquired Fanconi syndrome. Veterinarians should be aware of the risk of excessive feeding of chicken jerky treats.

Differentiating the Multipoint Expected Improvement for Optimal Batch Design

This work deals with parallel optimization of expensive objective functions which are modelled as sample realizations of Gaussian processes. The study is formalized as a Bayesian optimization problem, or continuous multi-armed bandit problem, where a batch of q > 0 arms is pulled in parallel at each iteration. Several algorithms have been developed for choosing batches by trading off exploitation and exploration. As of today, the maximum Expected Improvement (EI) and Upper Confidence Bound (UCB) selection rules appear as the most prominent approaches for batch selection. Here, we build upon recent work on the multipoint Expected Improvement criterion, for which an analytic expansion relying on Tallis’ formula was recently established. The computational burden of this selection rule being still an issue in application, we derive a closed-form expression for the gradient of the multipoint Expected Improvement, which aims at facilitating its maximization using gradient-based ascent algorithms. Substantial computational savings are shown in application. In addition, our algorithms are tested numerically and compared to state-of-the-art UCB-based batchsequential algorithms. Combining starting designs relying on UCB with gradient-based EI local optimization finally appears as a sound option for batch design in distributed Gaussian Process optimization.