1. What are all necessary changes to the below model so that constraint set (1) becomes...

 

 

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1. What are all necessary changes to the below model so that constraint set (1) becomes soft Give the new full model. a;, are parameters. Original OF refers to an already existing function of the decision variables that is being maximized. max Original OF m aijXij = 10 Vj = 1,...,n (1) i=1 Xij 20 Vi= 1,..,m;Vj = 1,...,n What will change if the problem becomes a minimization problem? 2. Consider the following multiperiod, multiproduct production-inventory problem. Suppose that we are examining T periods t=1,..,T, and some N products i=1,...N. There is an initial inventory of y;0 that is available at hand for each product i=1,...,N. We need to principally determine the level of production for each product i=1,...,N during each of the periods t=1,..,T, so as to meet the forecasted demand d; for each product i during each period t when it occurs, at a minimal total cost. To take advantage of varying demands and costs, we are permitted to produce excess quantities to be stored for later use. However, each unit of product i consumes a storage space s, and incurs a storage cost c, during period t, for i-1,...,N, t=1,...,T. The total storage space anticipated to be available for these N products during period t is S, t=1,...,T. Furthermore, each unit of product i requires h; hours of labor to produce, where the labor cost per hour when producing a unit of product i during period tis given by l for i=1,...,N, t=1,...,T. The total number of labor hours available to manufacture these N products during period t is given by H. Formulate a linear program to solve this production- inventory control system problem. Clearly specify and explain your decision variables. 1. What are all necessary changes to the below model so that constraint set (1) becomes soft Give the new full model. a;, are parameters. Original OF refers to an already existing function of the decision variables that is being maximized. max Original OF m aijXij = 10 Vj = 1,...,n (1) i=1 Xij 20 Vi= 1,..,m;Vj = 1,...,n What will change if the problem becomes a minimization problem? 2. Consider the following multiperiod, multiproduct production-inventory problem. Suppose that we are examining T periods t=1,..,T, and some N products i=1,...N. There is an initial inventory of y;0 that is available at hand for each product i=1,...,N. We need to principally determine the level of production for each product i=1,...,N during each of the periods t=1,..,T, so as to meet the forecasted demand d; for each product i during each period t when it occurs, at a minimal total cost. To take advantage of varying demands and costs, we are permitted to produce excess quantities to be stored for later use. However, each unit of product i consumes a storage space s, and incurs a storage cost c, during period t, for i-1,...,N, t=1,...,T. The total storage space anticipated to be available for these N products during period t is S, t=1,...,T. Furthermore, each unit of product i requires h; hours of labor to produce, where the labor cost per hour when producing a unit of product i during period tis given by l for i=1,...,N, t=1,...,T. The total number of labor hours available to manufacture these N products during period t is given by H. Formulate a linear program to solve this production- inventory control system problem. Clearly specify and explain your decision variables.

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