Determining the optimum replacement policy for Holstein dairy herds in Iran

An integer linear programming model was developed to establish the optimal replacement strategy for a commercial dairy herd. Monthly revenues and costs for cows were computed based on factors such as milk production, calf and carcass values, feed expenses, replacement heifer costs, insemination charges, and veterinary expenses. The model characterized cows using five parity numbers, two decision options (retain or replace), a 5-year planning horizon, and ten cow categories. It accounted for variations in milk yield, milk prices, calf and carcass values, feed costs, and replacement expenses. The parameters and prices used were tailored to reflect the Holstein-Friesian population in a commercial dairy herd in Egypt. The optimal annual replacement rate was determined to be approximately 30%, with an average productive life of 3.33 years. The maximum annual net revenue, expressed as a yearly annuity over the 5-year planning horizon, was estimated at 1,055 LE per cow. Sensitivity analyses were conducted to assess the impact of variations in average milk yield and the prices of milk, calves, carcasses, feed, and replacement heifers on the optimal replacement decisions. Profitability declined as the replacement rate increased from 10 to 50%. Productive life, replacement rate, and annual net present value were most influenced by changes in average milk yield and the prices of milk, feed, and replacement heifers. In contrast, variations in calf and carcass prices had relatively minor effects on the optimal replacement policy.

The conception rate in dairy cows is dependent on a number of cow factors such as days in milk and insemination number. Unfortunately, some of these factors were not accounted for in optimal insemination and replacement decision models. By using wrong estimates of the conception rate, the calculated optimal insemination and replacement policy might differ from the real optimal insemination and replacement policy. The objective of this study was to evaluate different sets of conception rates with an increasing level of accuracy to determine the insemination policy. An existing dynamic program for optimal insemination and replacement was used to compare three different scenarios in the estimation of conception rates, based on the reproductive performance of Dutch dairy cattle: (i) constant conception rate throughout lactation, (ii) conception rate dependent on parity and months in milk, and (iii) conception rate dependent on parity, months in milk and insemination number. The time step of the model was 30.4 days (1 month). The discounted future cash flow of culling a cow at each time step (replace a heifer immediately) was compared with keeping that cow under optimal future decisions. The difference between immediate culling and optimal decisions is defined as the retention pay-off. The insemination value was calculated as the difference between the future cash flow between immediate insemination of a cow and waiting one time-step. The results show that the difference in the insemination values and the optimal time to stop insemination depend on parity, lactation stage and the relative milk yield. In older cows with equal milk yields and at the same months in milk, the insemination value was lower than in younger cows. Within a parity, the insemination value was higher for cows with a higher milk yield. On individual cow level, using more accurate conception rate as input in the optimal insemination and replacement model might reduce miscalculation of the economic consequences for at least of €20-€38 per cow per year. Basing insemination decisions on less accurate input of the probabilities of conception, however, did not have an economic consequence at the herd level. In conclusion, using the appropriate conception rate as input in the optimal insemination and replacement model would increase the precise decision for the optimal time to stop insemination and hence improve the reproductive management efficacy.

This paper investigates the optimal state-dependent replacement policy for semi-Markovian deteriorating systems. It is assumed that the replacement time, replacement cost, operating cost rate and sojourn time distributions are all state-dependent. The optimization criterion is to minimize the expected long-run cost per unit time. Under some sufficient conditions on the cost and time parameters, we show that the optimal policy is of control limit type and has monotonic properties which facilitate the derivation of the optimal policy. Finally, a numerical example is given to illustrate the structure of the optimal policy.

A large Markovian linear program to optimize replacement policies and dairy herd net income for diets and nitrogen excretion

A simple formulation and solution to the replacement problem: A practical tool to assess the economic cow value, the value of a new pregnancy, and the cost of a pregnancy loss

Condition-based maintenance using the inverse Gaussian degradation model

Optimizing Model: Insemination, Replacement, Seasonal Production, and Cash Flow

In the manufacturing of fattening pigs, pig marketing refers to a sequence of culling decisions until the production unit is empty. The profit of a production unit is highly dependent on the price of pork, the cost of feeding and the cost of buying piglets. Price fluctuations in the market consequently influence the profit, and the optimal marketing decisions may change under different price conditions. Most studies have considered pig marketing under constant price conditions. However, because price fluctuations have an influence on profit and optimal marketing decisions it is relevant to consider pig marketing under price fluctuations. In this paper we formulate a hierarchical Markov decision process with two levels which model sequential marketing decisions under price fluctuations in a pig pen. The state of the system is based on information about pork, piglet and feed prices. Moreover, the information is updated using a Bayesian approach and embedded into the hierarchical Markov decision process. The optimal policy is analyzed under different patterns of price fluctuations. We also assess the value of including price information into the model.

It is well-known in the standard age replacement policy that a finite preventive replacement time does not exist when the failure time is exponential and the optimal preventive replacement time is nonrandom. It is shown that when the failure time is exponential, a finite time exists by introducing the shortage and excess costs. In addition, the random age replacement is proposed and similar discussions are made. Furthermore, the periodic and random inspection policies are taken up, and their optimal policies are shown to correspond theoretically to those of the age replacement ones. It is shown finally that when the random inspection cost is the half of the periodic one, two expected costs are almost the same.

Optimal replacement policy for a deteriorating system with increasing repair times

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. When failures occur, the repair of both component 1 and component 2 are not ‘as good as new’. The consecutive operating times of component 1 after repair constitute a decreasing geometric process, while the repair times of component 1 are independent and identically distributed. For component 2, its failure is rectified by minimal repair, and the repair time is negligible. Component 1 has priority in use when both components are good. The replacement policy N is based on the failure number of component 1. Under policy N, we derive the explicit expression of the long-run average cost rate C(N) as well as the average number of repairs of component 2 before the system replaced. The optimal replacement policy N*, which minimises the long-run average cost rate C(N), is obtained theoretically. If the failure rate r(t) of component 2 is increasing, the existence and uniqueness of the optimal policy N* is also proved. Finally, a numerical example is given to validate the developed theoretical model. Some sensitivity analyses are provided to show the influence of some parameters, such as the costs for replacement and repair, and the parameters of the lifetime and repair time distributions of both components, to the optimal replacement policy N* and corresponding average cost rate C(N*).

We formulate and analyze a Markov decision process (dynamic programming) model for airline seat allocation (yield management) on a single-leg flight with multiple fare classes. Unlike previous models, we allow cancellation, no-shows, and overbooking. Additionally, we make no assumptions on the arrival patterns for the various fare classes. Our model is also applicable to other problems of revenue management with perishable commodities, such as arise in the hotel and cruise industries. We show how to solve the problem exactly using dynamic programming. Under realistic conditions, we demonstrate that an optimal booking policy is characterized by state- and time-dependent booking limits for each fare class. Our approach exploits the equivalence to a problem in the optimal control of admission to a queueing system, which has been well studied in the queueing-control literature. Techniques for efficient implementation of the optimal policy and numerical examples are also given. In contrast to previous models, we show that 1) the booking limits need not be monotonic in the time remaining until departure; 2) it may be optimal to accept a lower-fare class and simultaneously reject a higher-fare class because of differing cancellation refunds, so that the optimal booking limits may not always be nested according to fare class; and 3) with the possibility of cancellations, an optimal policy depends on both the total capacity and the capacity remaining. Our numerical examples show that revenue gains of up to 9% are possible with our model, compared with an equivalent model omitting the effects of cancellations and no-shows. We also demonstrate the computational feasibility of our approach using data from a real-life airline application.

In this paper, a cold standby repairable system consisting of two identical components and one repairman is studied. Assume that each component after repair is not “as good as new”, by using a geometric process, we consider two kinds of repair replacement policy, one based on the working age T of component 1 under which the system is replaced when the working age of component 1 reaches T, and the other based on the failure number N of component 1 under which the system is replaced when the failure number of component 1 reaches N. Our problem is to choose optimal replacement policies T* and N* respectively such that the long-run average cost per unit time of the system is minimized. And we can prove under some mild conditions that the optimal policy N* is better than the optimal policy T*. Finally, a numerical example for policy N is given.

Optimal replacement policy for the case where the damage process is a one-sided Lévy process

One most common problem in reinforcement learning systems (e.g. Q-learning) is to reduce the number of trials to converge to an optimal policy. As one of the solution to the problem, k-certainty exploration method was proposed. Miyazaki reported that this method could determine an optimal policy faster than Q-learning in Markov decision processes (MDPs). This method is very efficient learning method. But, we propose an improvement plan that makes this method more efficient. In k-certainty exploration method, in case there is no k-uncertainty rule (rules which aren’t selected more than k times) in current state, an agent sometimes walks randomly until it finds a state where it can select a k-uncertainty rule. We think that this behavior is not efficient. To reduce this useless behavior, we propose combining k-certainty exploration method with Dynamic programming (DP). Miyazaki’s system uses DP after all rules are executed at least k times. But, our method uses k-certainty exploration method along with DP during learning. Our method, takes two pattern actions. In case an agent can select k-uncertainty rules, one of these rules is selected at random as k-certainty exploration method. In another case there is no k-uncertainty rule, behavior of agent is different from the behavior of k-certainty exploration method. In that case, our method uses DP to compute an optimal policy for moving from a current state to a state in which some k-uncertainty rules remain. The model for DP is constructed by using only known states. The outline will be described below. First, an agent makes a map constructed by using only known states. In the map, goals are states in which there are k-uncertainty rules and arbitrary state values are set in these states. Point to which attention should be paid is that the map is not given from outside. It is made from only experience. Next, each state values of states in which there are only k-certainty rules in the map are computed by DP (we used Policy Iteration). Finally, an agent continues to select greedy action until it arrives at a state in which it can select a k-uncertainty rule. By this improvement, we expect it can determine an optimal policy faster than k-certainty exploration method. And we have verified that our exploration method can determine an optimal policy faster than k-certainty exploration method by computer simulation.