{"text_format":"1","workbook":"xlsx","n_sheets":24,"sheets":["Welcome","Descrip","Demand","AvailRes","ResNeeded","HoldingCost","ProductionCost","Model","ShippingCost","InitialInv","Report","Results","NumProd","NumProdC","NumShip","NumShipC","ShipCost","ShipCostC","HoldCost","HoldCostC","ProdCost","ProdCostC","ResProd","ResFac"],"not_rendered":{"charts":10,"images":4,"macros":1,"external_links":0,"defined_names":266,"comments":0,"pivot_tables":5},"unopened":[{"sheet":"NumProdC","index":13,"reason":"not_a_worksheet"},{"sheet":"NumShipC","index":15,"reason":"not_a_worksheet"},{"sheet":"ShipCostC","index":17,"reason":"not_a_worksheet"},{"sheet":"HoldCostC","index":19,"reason":"not_a_worksheet"},{"sheet":"ProdCostC","index":21,"reason":"not_a_worksheet"}],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Welcome","index":0,"n_rows":1,"n_cols":1,"rows_kept":1,"cut":false,"hidden":false,"merged":[]}
["©2005 Seref, Ahuja, Winston"]

{"sheet":"Descrip","index":1,"n_rows":70,"n_cols":6,"rows_kept":70,"cut":false,"hidden":true,"merged":[]}
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Decision variables:"]
[null,1,"Number to produce of each product (in each factory for each period) = x(ijt)"]
[null,2,"Number to ship of each product (from each factory to each customer for each period) = y(ijkt)"]
[]
[null,"Constraints:"]
[null,1,"Amount shipped of each product (per factory in each period) must be less than or equal to the amount produced of each product (at each factory in each period). "]
[null,null,"Remember that the amount shipped is also per customer, therefore we must sum these values over"]
[null,null," all customers for each product, factory, and period to compare it to the production amount."]
[]
[null,null,null,"∑(k) y(ijkt) ≤ x(ijt)",null,"for all i, j, t"]
[]
[null,2,"Resources used (per factory per period) must be less than or equal to available resources (per factory per period). "]
[null,null,"Here, resources used are equal to the resources needed per product (given, N(ri)) times the amount produced of each product, "]
[null,null,"and the available resources are given (per factory per period, A(rjt))."]
[]
[null,null,null,"∑(i) N(ri) * x(ijt) ≤ A(rjt)",null,"for all r, j, t"]
[]
[null,3,"Ending inventory (per product per factory per period, V(ijt)) must be greater than 0 for each period. "]
[null,null,"Here, we define the ending inventory of period t+1 to be equal to the ending inventory in "]
[null,null,"period t plus the amount produced in period t+1 minus the amount shipped in period t+1."]
[]
[null,null,null,"V(ij(t+1)) = V(ijt) + x(ij(t+1)) -- y(ij(t+1))"]
[]
[null,null,null,"V(ijt) ≥ 0",null,"for all i, j, t"]
[]
[null,4,"Amount shipped (of each product from each factory to each customer) must meet demand per customer. "]
[null,null,"Here, demand has been given per product per customer per period, D(ikt). Remember that the amount shipped is also per factory, "]
[null,null,"therefore we must sum these values over all factories for each product, customer, and period to compare it to the demand values."]
[]
[null,null,null,"∑(j) y(ijkt) ≥ D(ikt)"]
[]
[null,5,"All decision variables should be greater than or equal to 0."]
[]
[null,null,null,"y(ijkt) ≥ 0, x(ijt) ≥ 0"]
[]
[]
[null,"Objective function: Minimize total costs = total shipping costs + total holding costs + total production costs."]
[null,1,"Total shipping costs = amount shipped * shipping costs per product from each factory to each customer. "]
[null,null,"Here, shipping costs have been given per product per factory per customer, s(ijk). Remember that the amount shipped is also per period, "]
[null,null,"therefore we must sum these values over all periods for each product, customer, and factory to multiply with the shipping costs."]
[]
[null,null,null,"∑(t) y(ijkt) * s(ijk)"]
[]
[null,2,"Total holding costs = ending inventory * holding cost per product per factory per period. Here, holding costs have been given per product per period, h(it). "]
[null,null,"Remember that ending inventory is also in terms of factories, therefore we must sum these values over all factories to multiply with holding costs."]
[]
[null,null,null,"∑(j) V(ijt) * h(it)"]
[]
[null,3,"Total production costs = amount produced * production cost per product per factory per period. "]
[null,null,"Here, production costs are given per product per factory per period, p(ijt). "]
[]
[null,null,null,"x(ijt) * p(ijt)"]
[]
[null,4,"Total costs:"]
[]
[null,null,null,"z = ∑(i) ∑(j) ∑(k) (∑(t) y(ijkt) * s(ijk)) + ∑(i) ∑(t) (∑(j) V(ijt) * h(it)) +∑(i) ∑(j) ∑(t) (x(ijt) * p(ijt))"]

{"sheet":"Demand","index":2,"n_rows":23,"n_cols":5,"rows_kept":23,"cut":false,"hidden":true,"merged":[]}
[]
[]
[]
[]
[null,"Product","Customer","Period","Demand"]
[null,1,1,1,1333]
[null,null,null,2,2000]
[null,null,2,1,1333]
[null,null,null,2,2000]
[null,null,3,1,1333]
[null,null,null,2,2000]
[null,2,1,1,1333]
[null,null,null,2,2000]
[null,null,2,1,1333]
[null,null,null,2,2000]
[null,null,3,1,2000]
[null,null,null,2,2133]
[null,3,1,1,2266]
[null,null,null,2,2400]
[null,null,2,1,2533]
[null,null,null,2,2666]
[null,null,3,1,2800]
[null,null,null,2,2933]

{"sheet":"AvailRes","index":3,"n_rows":23,"n_cols":5,"rows_kept":23,"cut":false,"hidden":true,"merged":[[2,6,2,7]]}
[]
[]
[]
[]
[null,"Resource","Factory","Period","Amount Available"]
[null,1,1,1,100000]
[null,null,null,2,100000]
[null,null,2,1,100000]
[null,null,null,2,100000]
[null,null,3,1,100000]
[null,null,null,2,100000]
[null,2,1,1,100000]
[null,null,null,2,100000]
[null,null,2,1,100000]
[null,null,null,2,100000]
[null,null,3,1,100000]
[null,null,null,2,100000]
[null,3,1,1,100000]
[null,null,null,2,100000]
[null,null,2,1,100000]
[null,null,null,2,100000]
[null,null,3,1,100000]
[null,null,null,2,100000]

{"sheet":"ResNeeded","index":4,"n_rows":14,"n_cols":4,"rows_kept":14,"cut":false,"hidden":true,"merged":[[2,6,2,7]]}
[]
[]
[]
[]
[null,"Resource","Product","Amount Needed"]
[null,1,1,10]
[null,null,2,10]
[null,null,3,10]
[null,2,1,10]
[null,null,2,10]
[null,null,3,10]
[null,3,1,10]
[null,null,2,10]
[null,null,3,10]

{"sheet":"HoldingCost","index":5,"n_rows":11,"n_cols":4,"rows_kept":11,"cut":false,"hidden":true,"merged":[[2,6,2,7]]}
[]
[]
[]
[]
[null,"Product","Period","Holding Cost"]
[null,1,1,0.5]
[null,null,2,0.5]
[null,2,1,0.5]
[null,null,2,0.5]
[null,3,1,0.5]
[null,null,2,0.5]

{"sheet":"ProductionCost","index":6,"n_rows":23,"n_cols":5,"rows_kept":23,"cut":false,"hidden":true,"merged":[[2,6,2,7]]}
[]
[]
[]
[]
[null,"Product","Factory","Period","Production Cost"]
[null,1,1,1,0.25]
[null,null,null,2,0.25]
[null,null,2,1,0.25]
[null,null,null,2,0.25]
[null,null,3,1,0.25]
[null,null,null,2,0.25]
[null,2,1,1,0.25]
[null,null,null,2,0.25]
[null,null,2,1,0.25]
[null,null,null,2,0.25]
[null,null,3,1,0.25]
[null,null,null,2,0.25]
[null,3,1,1,0.25]
[null,null,null,2,0.25]
[null,null,2,1,0.25]
[null,null,null,2,0.25]
[null,null,3,1,0.25]
[null,null,null,2,0.25]

{"sheet":"Model","index":7,"n_rows":60,"n_cols":56,"rows_kept":60,"cut":false,"hidden":true,"merged":[[2,6,2,7]]}
[]
[]
[]
[null,"Decision Variables",null,null,null,null,null,null,null,null,null,null,"Constraints",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Objective Function"]
[null,"Number of products to produce at each factory per period",null,null,null,null,"Number of products to ship to each customer",null,null,null,null,null,"Amount shipped per factory must be less than or equal to amount produced",null,null,null,null,null,null,"Resources used must be less than or equal to Available Resources",null,null,null,null,null,null,"Ending inventory must be greater than 0 for each period",null,null,null,null,null,null,"Amount shipped must meet Demand per customer",null,null,null,null,null,null,"Minimize total costs = shipping costs*amount shipped + holding cost * ending inventory + production cost * amount produced"]
[null,"Product","Factory","Period","Number to Produce",null,"Product","Factory","Customer","Period","Number to Ship",null,"Product","Factory","Period","Number Shipped",null,"Number Produced",null,"Resource","Factory","Period","Amount Needed",null,"Amount Available",null,"Product","Factory","Period","Inventory",null,null,null,"Product","Customer","Period","Amount Shipped",null,"Demand",null,"Product","Factory","Customer","Total Shipping Cost",null,"Product","Factory","Period","Total Holding Cost",null,"Product","Factory","Period","Total Production Cost",null,"Total Cost"]
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{"sheet":"HoldCost","index":18,"n_rows":21,"n_cols":6,"rows_kept":21,"cut":false,"hidden":true,"merged":[]}
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{"sheet":"ProdCost","index":20,"n_rows":21,"n_cols":6,"rows_kept":21,"cut":false,"hidden":true,"merged":[]}
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[]
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