00Production Planning Models 10

00Production Planning Models 10 - Production Planning...

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1 Production Planning Models ISEN 615 Summer 2010 Homework D u e D a y D a t e Points Number Problem Type {20} (1) Numerical instance Wednesday 7/7 {20} (2) Capacitated facility location Thursday 7/8 {20} (3) Setup and change over cost Thursday 7/8 {20} (4) Production smoothing Friday 7/9 {20} (5) Assembly Monday 7/12 {20} (6) Multi-product, multi-stage, Monday 7/12 multi-period model
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2 {20} (1) Numerical Instance. Formulate the following problem as a numerical instance for solution by linear programming. See separate pdf file in classes directory entitled 00Production Planning Models Homework Problem 1 09.pdf
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3 {20} (2) Capacitated Facility Location . A facility can be opened at each of a set J of potential locations to supply a set I of customers. Facility jJ provides capacity j U and requires a fixed investment cost (in $) of j f . Customer i demands i b units. The (variable) cost of supplying a unit to customer i from facility j is ij c (in $ per unit). Formulate a model to minimize cost for this capacitated facility location problem. {20} (3) Setup and changeover cost. Consider setup as well as changeover costs in a single- machine, multi-product, multi-period case. Time for changeover, setup and production must be accommodated by the machine capacity each period. At most one product can be produced in any time period. The machine must be setup for the product p that is produced in period t . If the machine is setup to produce product p in period 1 t and that product is produced again in period t , no change over is needed. Otherwise (i.e., if product p is not produced in period 1 t but is in period t ), a changeover is required (in addition to the setup for product p ). Furthermore, management has decided that at most one changeover and at most one setup can be made in each time period. State any assumptions, define any additional notation needed, and formulate a model to minimize total cost. Indices p products p P t time periods 1,. .., tT Parameters p a time (i.e., hours) required to produce each unit of product p pt c cost to produce one unit of product p in period t pt d demand for product p in period t C pt f cost to setup for product p in period t H pt f time (i.e., hours) required to setup for product p in period t C pt F cost to changeover to product p in period t H pt F time (i.e., hours) required to changeover to product p in period t pt h cost to hold over each product p at the end of period t t K capacity (i.e., total number of hours available to produce) of the machine in period t p n total demand for product p T number of time periods in the planning horizon Sets P products {20} (4) Product Smoothing. Extend the single product production planning (lot sizing) model to include both on-hand inventories and backorders (and their respective costs) and production smoothing, which penalizes either a positive or negative change in the quantity produced in period t in comparison with the quantity produced in period 1 t .
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4 {20} (5)Assembly.
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This note was uploaded on 10/12/2010 for the course ISEN 615 taught by Professor Staff during the Spring '08 term at Texas A&M.

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00Production Planning Models 10 - Production Planning...

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