Abstract
In the area of production planning and control, the aggregate production planning (APP) problem represents a great challenge for decision makers in production-inventory systems. Tradeoff between inventory-capacity is known as the APP problem. To address it, static and dynamic models have been proposed, which in general have several shortcomings. It is the premise of this paper that the main drawback of these proposals is, that they do not take into account the dynamic nature of the APP. For this reason, we propose the use of an Optimal Control (OC) formulation via the approach of energy-based and Hamiltonian-present value. The main contribution of this paper is the mathematical model which integrates a second order dynamical system coupled with a first order system, incorporating production rate, inventory level, and capacity as well with the associated cost by work force in the same formulation. Also, a novel result in relation with the Hamiltonian-present value in the OC formulation is that it reduces the inventory level compared with the pure energy based approach for APP. A set of simulations are provided which verifies the theoretical contribution of this work.
Highlights
Nowadays one of the most important challenges faced by business is the adjustment of firm resources in order to satisfy market requirements subjected to fluctuations over time, namely costs, prices, existences, demands, etc. [1]
By converting monthly sales forecasts, inventory levels, labor inputs, and production rates—of a single entity with characteristics representative of an entire product group—to a convenient aggregate load/capacity format, a production plan is generated [10]: this involves a tradeoff between penalties for carrying inventory and varying the capacity level incurs the minimum total marginal cost over a calendar year
In [34] the author presents a series of reasons for using control engineering techniques in production/inventory control, i.e., the use of standard forms, the block diagram format, standard techniques that enable important performance metrics to be calculated without recourse to simulation, there are a number of techniques for transferring problems from one domain into another, etc
Summary
Nowadays one of the most important challenges faced by business is the adjustment of firm resources in order to satisfy market requirements subjected to fluctuations over time, namely costs, prices, existences, demands, etc. [1]. ‚ Use of inventories (excess of SKUs, backlog of orders, or lost sales); this is known as the level plan: maintain a steady production rate over the entire year, using finished goods (smoothing/anticipation) stocks to absorb ongoing differences between output and sales. The aggregate planning process has an economic importance due to the decisions involved (regarding the capacity and inventory levels necessary to meet anticipated demand over the planning period), as they impact the company’s performance, i.e., profit maximization This in turn requires complete and accurate information about: machine capacity, labor utilization, levels (inventory, safety stock, manpower adjustment, subcontract, storage), time (regular/overtime), costs (production, inventory, overtime/idle time, subcontracts, shortage, lost sales, break down, backorder, hiring/firing/training).
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