Question

The manager at GetFit notices that the suppliers have different levels of service. The levels of service of the companies are listed in Table 2a. The costs per % level of service depends on the SKU, and are listed in Table 2b. The costs and maximum total number of units that can be supplied by each supplier remain the same as in Part 1.

Please normalize the costs to Supplier A's level of service (92%) to get the answer.

Table 2a. Level of service (%)

Supplier A	Supplier B	Supplier C	Supplier D
92	98	95	97

Table 2b. Cost per % level of service

Parts	Cost per %
W32A	10
Y33A	2
W32B	1
X33B	3
Z32A	8

Considering the levels of service of the suppliers, what is the minimum total procurement cost for GetFit?

Answer 1

Using the reference of the previous subpart-

GetFit is a company that makes high-end exercise machines and the machine Pilates Power is their most popular product. For each production cycle of the Pilates Power machines, GetFit purchases 5 SKUs: W32A, Y33A, W32B, X33B, and Z32A. There are four suppliers: Supplier A, B, C, and D. The number of units needed in each production cycle and the prices for each unit offered by the suppliers are listed in Table 1a. The maximum total number of units that each company can supply are listed in Table 1b. For example, if Supplier C supplies 24800 pieces of SKU Z32A, it cannot supply anything else.

Table 1a. Number of units needed and unit prices (in dollars) offered by the suppliers.

Parts	Number of units needed	Supplier A	Supplier B	Supplier C	Supplier D
W32A	9000	500	538	570	566
Y33A	16000	109	108	116	117
W32B	5000	27	28	30	29
X33B	31000	230	225	207	245
Z32A	33000	324	354	352	378

Table 1b. The maximum total number of parts that each company can supply

Supplier A	Supplier B	Supplier C	Supplier D
25200	11200	24800	35800

Answer-

Let i =1,2,3,4,5 represent the parts W32A, Y33A, W32B, X33B, Z32A

Let j= A,B,C,D,E represent the supplier A, B,C,D,E

Let Pij be the integer variable representing the number of parts of part type i being supplied from j supplier

Let Cij be the cost of obtaining i part from j supplier

The Supplier B has 6% improvement, Supplier C has 3% improvement and Supplier D has 5% improvement in service level compared to Supplier A.

Therefore the part cost for any supplier = Cost of that part in Supplier A+(%improvement in Service Level*Cost per % level of service)

The Cost Matrix would thus be-

	Supplier A	Supplier B	Supplier C	Supplier D
W32A	500	560	530	550
Y33A	109	121	115	119
W32B	27	33	30	32
X33B	230	248	239	245
Z32A	324	372	348	364

Our objective is to obtain our required level of parts inventory at the minimum cost. Thus our objective function is-

Min((Xij*Cij)

The constraints are-

From number of parts needed-

X1A + X1B + X1C + X1D = 6000

X2A+X2B+X2C+X2D = 32000

X3A+X3B+X3C+X3D=22000

X4A+X4B+X4C+X4D=6000

X5A+X5B+X5C+X5D= 27000

From the maximum capability of each supplier-

X1A+X2A+X3A+X4A+X5A <= 26400

X1B+X2B+X3B+X4B+X5B <= 25600

X1C+X2C+X3C+X4C+X5C <= 3000

X1D+X2D+X3D+X4D+X5D <= 41000

As the number of parts can't be negative, Xij >= 0

The solver screenshots are-

Considering the levels of service of the suppliers, what is the minimum total procurement cost for GetFit? = 25407800 (from Objective cell J1)

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