Production and Operation Managements Scheduling in Supply Chain Management Prof.JAING Zhibin Dr GeNG Na Department of Industrial Engineering Management Shanghai Jiao Tong University
Production and Operation Managements Prof. JAING Zhibin Dr GENG Na Department of Industrial Engineering & Management Shanghai Jiao Tong University Scheduling in Supply Chain Management
Scheduling in Supply Chain Management Contents Introduction Transportation Problem Generalizations of the Transportation; More General Network Formulations Distribution Resources Planning; Determining Delivery Routes in Supply Chain The Role of information in the SCM Multilevel Distribution Systems Designing the Supply Chain in a Global Environment
Scheduling in Supply Chain Management Contents • Introduction • Transportation Problem • Generalizations of the Transportation; • More General Network Formulations • Distribution Resources Planning; • Determining Delivery Routes in Supply Chain • The Role of information in the SCM • Multilevel Distribution Systems • Designing the Supply Chain in a Global Environment
Generalizations of the Transportation ·Infeasible Routes Eliminate routes from some sources to some sinks-Set the costs of these routes very high; Traditionally M is used to denote the very high cost.However,in practice,costs of these routes are assigned numbers much larger than the costs of other feasible routes,so that optimal solution will never assign flow to these routes
Generalizations of the Transportation • Infeasible Routes Eliminate routes from some sources to some sinks=Set the costs of these routes very high; Traditionally M is used to denote the very high cost. However, in practice, costs of these routes are assigned numbers much larger than the costs of other feasible routes, so that optimal solution will never assign flow to these routes
Generalizations of the Transportation ·Unbalanced Problems The total amount shipped from the sources is not equal to the total amount required at the sinks. Occurs when the demand exceeds the supply or vice versa. √Two measures either add a dummy row or a dummy column to absorb the excess supply or demand: "Alter the appropriate set of constraints to either or form
Generalizations of the Transportation • Unbalanced Problems The total amount shipped from the sources is not equal to the total amount required at the sinks. Occurs when the demand exceeds the supply or vice versa. Two measures either add a dummy row or a dummy column to absorb the excess supply or demand; Alter the appropriate set of constraints to either or form
Generalizations of the Transportation Suppose that the demand for the drives was higher than anticipated. The anticipated demand for the four sinks: 80784755 (the anticipated total demand is 260) √The actual demands: 90 78 5555 (the actual total demand is 278) Treatments to turn into balanced problem in Greedy Heuristic >Add an additional fictitious factory to account for this 18-unit shortfall:add a dummy row in the transportation tableau and all entries for this row are assigned an arbitrarily large unit cost
• Suppose that the demand for the drives was higher than anticipated. The anticipated demand for the four sinks: 80 78 47 55 (the anticipated total demand is 260) The actual demands: 90 78 55 55 (the actual total demand is 278) • Treatments to turn into balanced problem in Greedy Heuristic Add an additional fictitious factory to account for this 18-unit shortfall: add a dummy row in the transportation tableau and all entries for this row are assigned an arbitrarily large unit cost. Generalizations of the Transportation
Demand 278>supply 260 Warehouse Factories Amarillo Teaneck Chicago Sioux Falls 250 420 380 280 Sunnyvale 45 1,280 990 1,440 1,520 Dublin 120 1,550 1,420 1,660 1,730 Bangkok 95 M M M M A 18 90 78 55 55
Demand 278>supply 260 Amarillo Teaneck Chicago Sioux Falls Warehouse Factories Sunnyvale Dublin Bangkok 250 420 380 280 1,280 990 1,440 1,520 1,550 1,420 1,660 1,730 45 120 95 90 78 55 55 A 18 M M M M
Generalizations of the Transportation Example 6.1 Variables x11 x12x13 x14 x21 X22 x23 x24 x31x32 x33 x34 x41 x42 x43 x44 Oper ator Value Values 0 00 45 42 78 0 0 48 0 47 0 0 0 8 10 Objective 155142 1E+01E+01E+0 Coeff 250 420380280 1280 990 1440 1520 00 16601730 1E+06 Min 1.8E+07 66 6 st LHS RHS Constraint 1 45 45 Constraint 2 1 1 1 1 = 120 120 Constraint 3 11 1 1 = 95 95 Constraint 4 18 18 Constraint 5 1 1 1 1 90 90 Constraint 6 1 1 1 1 = 78 78 Constraint 7 55 55 Constraint 8 1 1 1 1 = 55 55
Generalizations of the Transportation Example 6.1 Variables x11 x12 x13 x14 x21 x22 x23 x24 x31 x32 x33 x34 x41 x42 x43 x44 Oper ator Value Values 0 0 0 45 42 78 0 0 48 0 47 0 0 0 8 10 Objective Coeff 250 420 380 280 1280 990 1440 1520 155 0 142 0 1660 1730 1E+0 6 1E+0 6 1E+0 6 1E+06 Min 1.8E+07 st LHS RHS Constraint 1 1 1 1 1 = 45 45 Constraint 2 1 1 1 1 = 120 120 Constraint 3 1 1 1 1 = 95 95 Constraint 4 1 1 1 1 = 18 18 Constraint 5 1 1 1 1 = 90 90 Constraint 6 1 1 1 1 = 78 78 Constraint 7 1 1 1 1 = 55 55 Constraint 8 1 1 1 1 = 55 55
Treatment for LP Unbalanced transportation problem can be formulated as LP by inequality (demand or supply )constraints. When the demand exceeds the anticipated,use equality supply constraint(first three)to make sure of complete shipment;and use less than or equal demand constraint
Treatment for LP • Unbalanced transportation problem can be formulated as LP by inequality (demand or supply )constraints. • When the demand exceeds the anticipated, use equality supply constraint (first three) to make sure of complete shipment; and use less than or equal demand constraint
Unbalanced TP:Demand Supply Solve TP by LP Let m be the number of sources and n be the number of sinks; ·a,the supply from the source i,.l≤ism b,=the demand of sink j,1sjsn; C-the cost of shipping one unit from source i to sink j; X-the flow from the source i to sink j for 1s ism and 1sj<n; n m Min ∑x Min ∑x 目 St. St. ∑y=aarl≤i≤r → sa frisisn n ∑为，=bor1≤j≤m ，=br1sj≤m i= 出≥0 for1≤i≤nand1≤j≤m x≥0 for1≤i≤nand1≤j≤m
1 1 1 1 . . 1 ; 1 ; 01 1 n m ij ij i j m ij i j n ij j i ij Min c x St x a for i n x b for j m x for i n and j m 1 1 1 1 . . 1 ; 1 ; 01 1 n m ij ij i j m ij i j n ij j i ij Min c x St x a for i n x b for j m x for i n and j m Unbalanced TP： Demand > Supply Solve TP by LP • Let m be the number of sources and n be the number of sinks; • ai= the supply from the source i, 1 im • bj =the demand of sink j, 1jn; • cij =the cost of shipping one unit from source i to sink j; • xij=the flow from the source i to sink j for 1 im and 1jn;
Scheduling in Supply Chain Management Contents Introduction Transportation Problem 。 Generalizations of the Transportation More General Network Formulations Distribution Resources Planning; Determining Delivery Routes in Supply Chain The Role of information in the SCM Multilevel Distribution Systems Designing the Supply Chain in a Global Environment
Scheduling in Supply Chain Management Contents • Introduction • Transportation Problem • Generalizations of the Transportation • More General Network Formulations • Distribution Resources Planning; • Determining Delivery Routes in Supply Chain • The Role of information in the SCM • Multilevel Distribution Systems • Designing the Supply Chain in a Global Environment
