Efficient method for designing slabs for production from an...

Details Efficient method for designing slabs for production from an... Efficient method for designing slabs for production from an...

1998-08-05

2001-11-20

Sheikh, Ayaz (Department: 2155)

Data processing: generic control systems or specific application

Specific application, apparatus or process

Product assembly or manufacturing

C705S028000, C705S029000

Reexamination Certificate

active

06321132

ABSTRACT:

DESCRIPTION
BACKGROUND OF TIE INVENTION
1. Field of the Invention
The present invention generally relates to operations planning in a process industry and, more particularly, to a method of designing a set of slabs from target orders in a near-optimal manner while satisfying design restrictions.
2. Background Description
General background information may be had by reference to the following two books:
1. Ahuja, R. K., Magnanti, T. L. and Orlin, J. B. (1993),
Network Flows
, Prentice Hall, N.J.
2. Horowitz, E. and Sahni, S. (1978),
Fundamentals of Data Structures
, Computer Science Press, Inc.
Operations planning in a process industry typically begins with a order book which contains a list of orders that need to be satisfied. The initial two steps in an operations planning exercise involves (1) first trying to satisfy orders from the order book using leftover stock from the inventory and (2) subsequently designing productions units for manufacture from the remaining orders. Two important characteristics of a process industry are that the products are all manufactured based on the orders instead of being based on a forecast of the expected demand (as in retail or semiconductor manufacturing) and, as a consequence, the inventory is merely the stock of previously produced units which for reasons of quality could not be shipped to the customer.
The subject invention is a novel and fast computer-implemented method for the second of these problems from an optimization perspective. The second problem, i.e., designing production units, involves using the order book to design the size and number of production units that need to be manufactured. The goal of this design is to minimize the number of units that need to be manufactured, which for a given order book is equivalent to maximizing the average size of the production unit. This problem has a strong flavor of a grouping exercise where different orders are grouped together to form a slab (the manufacturing unit in a steel industry)—we call this the slab design problem. There are, once again, several constraints regarding which orders can be grouped together, based on grade and surface quality and weight considerations, which give rise to integrality constraints. The maximum allowable size of a slab for a potential group of orders is constrained based on manufacturing considerations. Additionally, each designed slab needs to be of a minimum size, and any group of orders weighing less than this minimum introduces a designed slab with some partial surplus. The partial surplus is clearly undesirable and needs to be minimized. This problem can be formulated as a variation of the variable size bin packaging problem.
Characteristics of Orders and Slabs
In application Ser. No. 09/047,275, we introduced the inventory matching problem in terms of an order book which contains a list of orders and their specifications, and an inventory of existing slabs. Here, we provide a description of the order book which is similar to the one described in Ser. No. 09/047,275. We will also describe constraints that arise in designing virtual slabs. The specification of orders and the use of inventory (or slabs) has some unique attributes which are important in understanding the integer formulations that arise while modeling these problems.
The order book contains a list of orders from various customers. Each order has a target weight (O
t
) that needs to be delivered. However, there are allowances with respect to this target weight which specify the minimum (O
min
) and maximum weight (O
max
) that are accepted at delivery. Over and above the total weight (per order) that needs to be delivered, there are additional restrictions regarding the size and number of units into which this order can be factorized at delivery. For example, with each order is associated a range for the weight of units which are delivered. We call the units to be delivered “Deliverable Production Units” or DPUs. Let us assume that the minimum weight for the deliverable production unit is DPU
min
and the maximum is DPU
max
. Then, for each order we need to deliver an integral number of deliverable production units (DPU
mumber
) of size in the interval [DPU
min
, DPU
max
] so that the total order weight delivered is in the range [O
min
, O
max
]. In order to fulfill an order, we need to choose a size for the deliverable production unit (DPU
size
) and the number of deliverable production units (DPU
number
) to be produced such that
 
O
min
≦DPU
size
×DPU
number
≦O
max
DPU
min
≦DPU
size
≦DPU
max
DPU
number
∈{0,1,2, . . . }  (1)
Notice that the DPU
number
is a general integer variable. Additionally, the constraint represented by Equation (1) is a bilinear constraint.
In addition to the weight requirements, each order has four other classes of attributes, wherein (1) the first pertains to the quality requirements such as grade, surface anti internal properties of the material to be delivered; (2) the second set are physical attributes such as the width and thickness of the product delivered; and (3) the third set of attributes refer to the finishing process that needs to be applied to the deliverable production units. For example, car manufacturers often require the steel sheets to be galvanized. Finally, (4), the fourth set of attributes provides the maximum and the minimum slab size that can be used to produce this order. At first this may appear undesirable since the decision of how to manufacture slabs to fulfill an order should, in general, be left to a manufacturer. It turns out, however, that the maximum and minimum allowable slab size is in fact determined by the manufacturer based on the current technological limitations of process technologies. For example, in a steel mill, all slabs need to be hot rolled to produce units of desired physical dimensions. However, based on the width and thickness required and the quality requirements, the maximum size of the slab that can be hot rolled is constrained, and this determines the allowable maximum allowable slab size. Similar considerations are used to prescribe the minimum allowable slab size.
For the slab design problem, the dimensions of the slab are unknown. The objective of the slab design problem is to optimally design the dimensions of the slab, subject to various processing constraints which are described below.
The Slab Design Problem
The slab design problem requires that we design a minimal number of slabs to satisfy the order book, subject to constraints on the maximum allowable size for each of the designed slabs. It is possible to group multiple orders on the same designed slab. There are two considerations that arise in grouping multiple orders to the same slab:
1. Orders need to compatible in terms of physical dimensions in order to be grouped together. Orders that have similar width and thickness requirements can be packed together. As we had mentioned before for inventory matching according to Ser. No. 09/047,275, it is possible to alter the thickness and width (within a range) by rolling. Therefore, orders with thickness and width close to each other can be grouped on the same slab.
2. The second set of grouping constraints arise from process considerations in the hot/cold mill and the finishing line. These constraints can be represented using color constraints. More explicitly, we can associate with each order a color which represents the finishing operations that are required. As before, we can specify color constraints which limit the number of colors that can be grouped on each designed slab.
Orders that are grouped on the same slab might have different maximum allowable slab weights. However, when grouped as such, the allowable maximum slab weight is actually determined by the largest of all the allowable slab weights.
We therefore have a representation of the slab design problem in terms of multiple groups of orders, where each group can be packed on the same slab of a maximum allowable size. The maximum allowable slab size for each group ca

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