حداکثر سازی سود در مشکل تعیین اندازه دسته تولید و برنامه ریزی همزمان

This paper extends the simultaneous lot-sizing and scheduling problem, to include demand choice flexibility. The basic assumption in most research about lot-sizing and scheduling problems is that all the demands should be satisfied. However, in a business with a goal of maximizing profit, meeting all demands may not be an optimum decision. In the profit maximization simultaneous lot-sizing and scheduling problem with demand choice flexibility, the accepted demand in each period, lot-sizing and scheduling are three problems which are considered simultaneously. In other words the decisions pertaining to mid-term planning and short-term planning are considered as one problem and not hierarchically. According to this assumption, the objective function of traditional models changes from minimizing costs to maximizing profits. In this paper, two mathematical models are developed for the problem, and the efficiency of them is evaluated in different problem sets. These two models are different in the method of lot-sizing.

Lot-sizing and scheduling are important problems in the field of production planning. Most of the time, decisions about these two problems are made hierarchically. In this method, the lot-sizing problem is solved at first and then the result is used for the sequencing and scheduling problem [1]. The problem which was named the general lot-sizing and scheduling problem (GLSP) [2] considers lot-sizing and scheduling problems simultaneously due to their dependency. In most of the models for production planning and especially in lot-sizing and scheduling problems, the objective function is minimizing costs. In these models, the assumption is that all the customers’ demands should be met. However, in a business with a goal of maximizing profit, satisfying all potential demands may not always be an optimal solution [3]. In this situation, the appropriate selection of demand (to be met) is an effective step for demand management. In this paper, the profit maximization in simultaneous lot-sizing and scheduling problem with demand choice flexibility is studied. The accepted demand in each period can vary between its upper and lower bounds. The upper bound could be the forecasted demand and the lower bound could be the organization commitments towards customers or the minimum production level according to the production policy. In other words, the amounts of accepted demands, lot-sizing and scheduling are problems which are considered simultaneously. According to these assumptions the objective function of the problem is maximizing the revenue of sales minus the production, inventory holding, and setup costs. The result of this model is the amount of accepted demand for each product in each period, the size of production lots, and the sequence of them. In this problem, the mix product problem which pertains to mid-term planning and lot-sizing and scheduling problems, which relate to short-term scheduling, are considered in one problem. Because the basic problem was first named GLSP, we use PGLSP as a name for our problem, but it is wise to say that if we wanted to name the model by considering its basic model rather than the concept of GLSP we should name it PCLSPSD. The proposed problem will result in better decisions especially when mix of products is decided in mid-term planning while short term decision is about scheduling of different machines. This model is presented based on the characteristics of industries like the moquette weaving industry. In this type of industry setup times and costs are considerable so it is wise to use the simultaneous lot-sizing and scheduling models. Besides that selecting the demand without considering back order costs is also possible, and predicting the exact amount of demand is impossible, so it is more reliable to define upper and lower bounds for demand. Wholesalers accept this policy, so sometimes the amount of products they deliver is less than their orders. For preserving the percentage of products and enhancing the service level, the lower bounds are greater than zero. We have a few products in this company in different models and colors. The planning period of two weeks and the planning horizon of 8 weeks are suitable for the company.

In this paper profit maximization general lot-sizing and scheduling problem with demand choice flexibility is studied. In this problem decisions about lot-sizing, scheduling and demand selection are made in order to maximize the total revenue minus production, holding, and setup costs. This new problem which is an extension of GLSP by adding the assumption of flexibility in choosing demands, integrates two different levels of production planning, short-term planning and mid-term scheduling. The result of this model is the accepted demand in each period for each product, the quantity of production lots, and the sequence of them. In this paper, two mathematical models developed for PGLSP and comprised using different data sets. These models are different in the way of lot-sizing. Although models’ preferences vary in different data sets, to sum up all results the second model with tighter production constraints has a better performance. Representing exact methods which try to find an optimal solution based on the model structure like branch and bound algorithm is a good aspect for future research. Efficient heuristic and meta-heuristic algorithms are also appropriate methods to solve PGLSP. Considering the effect of transportation costs in choosing demands, obtaining the delivery time of each product as one of the output of the model and extension of the problem environment to more complex one like flow shop and job shop are suggested for future researches.