Question

Ram? Roy's firm has developed the following? supply, demand,? cost, and inventory data.

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Supply Available
Period	Regular Time	Overtime	Subcontract	Demand Forecast
1	30	15	10	50
2	35	15	10	50
3	40	15	10	55

Initial inventory	30 units
?Regular-time cost per unit	?$100
Overtime cost per unit	?$160
Subcontract cost per unit	?$250
Carrying cost per unit per month	?$2

Assume that the initial inventory has no holding cost in the first period and backorders are not permitted.

Allocating production capacity to meet demand at a minimum cost using the transportation? method, the total cost is

?$

?(enter your response as a whole? number).

Answer 1

Decision variable: as shown in fig1 in green

regular production: X1,X2,X3 for period 1,2,3

overtime: Y1,Y2,Y3 for period 1,2,3

subcontract: Z1,Z2,Z3 for period 1,2,3

objective function: as shown in fig1 in yellow

minimize cost:

regular production cost: 100*(X1+X2+X3)

overtime production cost: 160*(Y1+Y2+Y3)

Subcontract cost: 250*(Z1+Z2+Z3)

Inventory for 1st month: X1+Y1+Z1 + 30 - 50 (30 is initial inventory, 50 is demand)

in excel initial inventory: -C8+B5+SUM(C2:C4)

inventory cost = (X1+Y1+Z1 + 30 - 50)*2

total cost = 100*(X1+X2+X3) + 160*(Y1+Y2+Y3) + 200*(Z1+Z2+Z3) + (X1+Y1+Z1 + 30 - 50)*2

in excel: C16 =SUM(C11:E14)

1. regular time:

period 1: X1 30, in excel: C2 H2

period 2: X2 35, in excel: D2 I2

period 3: X3 40, in excel: E2 J2

2.

2. overtime:

all periods: Y1,Y2.Y3 15, in excel: C3:E3 H3

3. subcontract:

all periods: Z1,Z2.Z3 10, in excel: C4:E4 H4

4. All decision variables 0

solving as shown in fig1&2

fig1

fig2

the total cost is 13720