Determine the ordering policy is recommended by the silver-Meal heuristic. Concept Introduction: Silver-Meal heuristic mainly focused on the manufacture planning in the production companies. It determines that within the minimum cost level, the quantities of the products will be produced by the company.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 8, Problem 49AP

a)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the silver-Meal heuristic.

Concept Introduction: Silver-Meal heuristic mainly focused on the manufacture planning in the production companies. It determines that within the minimum cost level, the quantities of the products will be produced by the company.

a)

Expert Solution

Answer to Problem 49AP

The order policy according to silver meal heuristic method is (56,0,52,0,0,114,0,0,106,0)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy of the inventory under silver meal method can be calculated as follows:

According to silver meal method the average cost per period C (T) is a function of the average holding and set up cost per period for T number of Periods. The production in period 1 is equal to the demand in that period 1 to incur the order cost K.

Hence C(1)=K

And C(2)=(K+hr2)/2

C(3)=(K+hr2+2hr3)/3

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/j

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

Now, calculate the order policy using the above formula as follows:

Starting in period 1:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200

C(2)=(200+(3.24)(34))/2=155.25

C(3)=[200+(3.24)(34)+(2)(3.24)(32)]3=172.8

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200

C(2)=[200+(3.25)(12)]2=119.5

C(3)=[200+(3.25)(12)+(2)(3.25)(8)]3=97

C(4)=[200+(3.25)(12)+(2)(3.25)(8)+(3)(3.25)(44)]4=180

Stop the process since C(4)≻C(3),

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

C(1)=200

C(2)=[200+(3.25)(54)]2=187.75

C(3)=[200+(3.25)(54)+(2)(3.25)(16)]3=159.8

C(4)=[200+(3.25)(54)+(2)(3.25)(16)+(3)(3.25)(76)]4=305.12

Stop the process since C(4)≻C(3),

y6=r6+r7+r8

y6=44+54+16=114

Starting in period 9:

y9=r9+r10

y9=76+30=106

b)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the part period balancing heuristic.

Concept Introduction: one of the lot-sizing technique is to implementing the lowest-cost with the interconnection between costs of order and carrying cost for the inventory is generally known as Part period balancing.it is more effective for the product whose demand is unstable.

b)

Expert Solution

Answer to Problem 49AP

The order policy according to the part period balancing heuristic method will be

is (56,0,52,0,0,98,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to part period balancing method can be calculated as follows:

In this method the order horizon that equates holding and setup cost over that period has to be calculated as follows:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1:

Period	Holding Cost
2	110.5
3	318.5

Since the setup cost $200 is closer at period 4, stop and equate

y1=r1+r2

y1=22+34=56

Starting in period 3:

Period	Holding Cost
2	25
3	65
4	520

Since the setup cost $200 is closer to 4 than 3, stop and equate

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

Period	Holding Cost
2	175.5
3	279.5

Since the setup cost $200 is closer to 3, stop and equate

y6=r6+r7

y6=44+54=98

Starting in period 8:

Period	Holding Cost
2	247

Since the setup cost $200 is closer to 2, stop and equate

y8=r8+r9

y8=16+76=92

c)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the least unit cost heuristic.

Concept Introduction: Least unit cost heuristic technique is one of the time-varying demand pattern technique.one of the dynamic lot-sizing concept is that interrelated between the order cost and carrying cost of the inventory for the every lot size is defined as

Least Unit Cost (LUC).

c)

Expert Solution

Answer to Problem 49AP

The order policy according to the least unit cost heuristic method will be

is (56,0,44,0,106,0,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to lease unit cost(LUC) method can be calculated as follows:

LUC divides the average cost per period C (T) by the total number of units demanded. Hence C(1)=K/r1

And C(2)=(K+hr2)+(r1+r2),

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/(r1+r2...+rj)

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200/22=0.09

C(2)=(200+(3.25)(34))/(22+34)=5.54

C(3)=[200+(3.25)(34)+(2)(32)]22+34+32=5.89

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200/32=6.25

C(2)=[200+(3.25)(12)](32+12)=5.43

C(3)=[200+(3.25)(12)+(2)(3.25)(8)](32+12+8)=5.6

Stop the process since C(3)≻C(2),

y3=r3+r4

y3=32+12=44

Starting in period 5:

C(1)=200/8=25

C(2)=[200+(3.25)(44)](8+44)=6.60

C(3)=[200+(3.25)(44)+(2)(3.25)(54)](8+44+54)=6.54

C(4)=[200+(3.25)(44)+(2)(3.25)(54)+(3)(3.25)(16)](8+44+54+16)=7.97

Stop the process since C(4)≻C(3),

y5=r5+r6+r7

y5=8+44+54=106

Starting in period 8:

C(1)=200/16=12.5

C(2)=[200+(3.25)(76)](16+76)=4.85

C(3)=[200+(3.25)(76)+(2)(3.25)(30)](16+76+30)=5.2

Stop the process since C(3)≻C(2),

y8=r8+r9

y8=16+76=92

y10=r10=30

d)

Summary Introduction

Interpretation: Determine the method resulted in the lowest-cost policy for the given problem.

Concept Introduction: Least unit cost method makes the present period of the demands and evaluates the period of the future. Adding the carrying cost for the setup and the period of the inventory cost, the least unit cost will be occur.

d)

Expert Solution

Answer to Problem 49AP

The least expensive method is the least unit cost method with a total cost of $1351

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

Comparison of the three methods can be calculated as follows:

Calculate the total cost of the inventory for the three months. The method which yields less cost is the lowest cost policy.

The total cost under silver meal method can be calculated as follows:

The method required is 4 set ups

The total set up cost is 4×200=800

The total holding cost is (3.25)(22+32+44+76)=565.5

The total cost 800+565.5=1365.5

The total cost under silver-meal heuristic is $1365.5

The total cost under least unit cost method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+8+16+30)=351

The total cost 1000+351=1351

The total cost under least unit cost method is $1351

The total cost under part period balancing method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+44+16+30)=468

The total cost 1000+468=1468

The total cost under part period balancing method is $1468

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Please provide detailed solutions to the following problems/exercises (4 problems/exercises x 9 points each): 1) View the video ON Unveils ‘Lightspray’ Technology (4.55 mins, Ctrl+Click in the link), and The Secret of Lightspray (8.27 mins, Ctrl+Click in the link), answer the following questions: https://www.youtube.com/watch?v=wjmeaC-wlZs a) What is new about the design of ON’s shoes? b) How will ON’s new manufacturing technique affect location planning for footwear firms? c) How does ON focus on it sustainability strategy? Note: As a rough guideline, please try to keep the written submission to one or two paragraphs for each of the questions. 2) Unimed Hospital currently processes patient admissions through three admitting clerks who are set up to work in series, with respective reliabilities of 0.96, 0.95, and 0.90 (see figure below). a) Find the reliability of the current admission process. Due to rising patient complaints, the hospital administrator, Chimeg…

3) A startup firm, Pocket International, has come up with a tiny programmable computer, NerdCom Mini Air, that sells for $49.99. The firm estimates that the programmable computers have an expected life that is exponential, with a mean of 24 months. The firm wants to estimate the probability that the NerdCom Mini Air will have a life that ends: a) after the initial 24 months of service. b) before the 24 months of service is completed. c) not before 48 months of service. Note: You could work out the problem by hand or use excel; in chapter 4S, section 4S.2 of the Stevenson text, reliability (finding the probability of functioning for a specified length of time) is covered with examples; chapters 4 & 4S Stevenson lecture power point slides 33 to 38 (chapters 4 & 4S lecture: 32.30 mins to 38.56 mins) cover reliability over time with examples.

Discuss how training and development programs can be best presented to ultimately change the behavior of employees, often without their knowledge or awareness.

Answer 2

Question

Chapter 8, Problem 49AP

a)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the silver-Meal heuristic.

Concept Introduction: Silver-Meal heuristic mainly focused on the manufacture planning in the production companies. It determines that within the minimum cost level, the quantities of the products will be produced by the company.

a)

Expert Solution

Answer to Problem 49AP

The order policy according to silver meal heuristic method is (56,0,52,0,0,114,0,0,106,0)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy of the inventory under silver meal method can be calculated as follows:

According to silver meal method the average cost per period C (T) is a function of the average holding and set up cost per period for T number of Periods. The production in period 1 is equal to the demand in that period 1 to incur the order cost K.

Hence C(1)=K

And C(2)=(K+hr2)/2

C(3)=(K+hr2+2hr3)/3

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/j

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

Now, calculate the order policy using the above formula as follows:

Starting in period 1:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200

C(2)=(200+(3.24)(34))/2=155.25

C(3)=[200+(3.24)(34)+(2)(3.24)(32)]3=172.8

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200

C(2)=[200+(3.25)(12)]2=119.5

C(3)=[200+(3.25)(12)+(2)(3.25)(8)]3=97

C(4)=[200+(3.25)(12)+(2)(3.25)(8)+(3)(3.25)(44)]4=180

Stop the process since C(4)≻C(3),

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

C(1)=200

C(2)=[200+(3.25)(54)]2=187.75

C(3)=[200+(3.25)(54)+(2)(3.25)(16)]3=159.8

C(4)=[200+(3.25)(54)+(2)(3.25)(16)+(3)(3.25)(76)]4=305.12

Stop the process since C(4)≻C(3),

y6=r6+r7+r8

y6=44+54+16=114

Starting in period 9:

y9=r9+r10

y9=76+30=106

b)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the part period balancing heuristic.

Concept Introduction: one of the lot-sizing technique is to implementing the lowest-cost with the interconnection between costs of order and carrying cost for the inventory is generally known as Part period balancing.it is more effective for the product whose demand is unstable.

b)

Expert Solution

Answer to Problem 49AP

The order policy according to the part period balancing heuristic method will be

is (56,0,52,0,0,98,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to part period balancing method can be calculated as follows:

In this method the order horizon that equates holding and setup cost over that period has to be calculated as follows:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1:

Period	Holding Cost
2	110.5
3	318.5

Since the setup cost $200 is closer at period 4, stop and equate

y1=r1+r2

y1=22+34=56

Starting in period 3:

Period	Holding Cost
2	25
3	65
4	520

Since the setup cost $200 is closer to 4 than 3, stop and equate

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

Period	Holding Cost
2	175.5
3	279.5

Since the setup cost $200 is closer to 3, stop and equate

y6=r6+r7

y6=44+54=98

Starting in period 8:

Period	Holding Cost
2	247

Since the setup cost $200 is closer to 2, stop and equate

y8=r8+r9

y8=16+76=92

c)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the least unit cost heuristic.

Concept Introduction: Least unit cost heuristic technique is one of the time-varying demand pattern technique.one of the dynamic lot-sizing concept is that interrelated between the order cost and carrying cost of the inventory for the every lot size is defined as

Least Unit Cost (LUC).

c)

Expert Solution

Answer to Problem 49AP

The order policy according to the least unit cost heuristic method will be

is (56,0,44,0,106,0,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to lease unit cost(LUC) method can be calculated as follows:

LUC divides the average cost per period C (T) by the total number of units demanded. Hence C(1)=K/r1

And C(2)=(K+hr2)+(r1+r2),

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/(r1+r2...+rj)

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200/22=0.09

C(2)=(200+(3.25)(34))/(22+34)=5.54

C(3)=[200+(3.25)(34)+(2)(32)]22+34+32=5.89

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200/32=6.25

C(2)=[200+(3.25)(12)](32+12)=5.43

C(3)=[200+(3.25)(12)+(2)(3.25)(8)](32+12+8)=5.6

Stop the process since C(3)≻C(2),

y3=r3+r4

y3=32+12=44

Starting in period 5:

C(1)=200/8=25

C(2)=[200+(3.25)(44)](8+44)=6.60

C(3)=[200+(3.25)(44)+(2)(3.25)(54)](8+44+54)=6.54

C(4)=[200+(3.25)(44)+(2)(3.25)(54)+(3)(3.25)(16)](8+44+54+16)=7.97

Stop the process since C(4)≻C(3),

y5=r5+r6+r7

y5=8+44+54=106

Starting in period 8:

C(1)=200/16=12.5

C(2)=[200+(3.25)(76)](16+76)=4.85

C(3)=[200+(3.25)(76)+(2)(3.25)(30)](16+76+30)=5.2

Stop the process since C(3)≻C(2),

y8=r8+r9

y8=16+76=92

y10=r10=30

d)

Summary Introduction

Interpretation: Determine the method resulted in the lowest-cost policy for the given problem.

Concept Introduction: Least unit cost method makes the present period of the demands and evaluates the period of the future. Adding the carrying cost for the setup and the period of the inventory cost, the least unit cost will be occur.

d)

Expert Solution

Answer to Problem 49AP

The least expensive method is the least unit cost method with a total cost of $1351

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

Comparison of the three methods can be calculated as follows:

Calculate the total cost of the inventory for the three months. The method which yields less cost is the lowest cost policy.

The total cost under silver meal method can be calculated as follows:

The method required is 4 set ups

The total set up cost is 4×200=800

The total holding cost is (3.25)(22+32+44+76)=565.5

The total cost 800+565.5=1365.5

The total cost under silver-meal heuristic is $1365.5

The total cost under least unit cost method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+8+16+30)=351

The total cost 1000+351=1351

The total cost under least unit cost method is $1351

The total cost under part period balancing method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+44+16+30)=468

The total cost 1000+468=1468

The total cost under part period balancing method is $1468

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 8, Problem 49AP

a)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the silver-Meal heuristic.

Concept Introduction: Silver-Meal heuristic mainly focused on the manufacture planning in the production companies. It determines that within the minimum cost level, the quantities of the products will be produced by the company.

a)

Expert Solution

Answer to Problem 49AP

The order policy according to silver meal heuristic method is (56,0,52,0,0,114,0,0,106,0)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy of the inventory under silver meal method can be calculated as follows:

According to silver meal method the average cost per period C (T) is a function of the average holding and set up cost per period for T number of Periods. The production in period 1 is equal to the demand in that period 1 to incur the order cost K.

Hence C(1)=K

And C(2)=(K+hr2)/2

C(3)=(K+hr2+2hr3)/3

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/j

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

Now, calculate the order policy using the above formula as follows:

Starting in period 1:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200

C(2)=(200+(3.24)(34))/2=155.25

C(3)=[200+(3.24)(34)+(2)(3.24)(32)]3=172.8

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200

C(2)=[200+(3.25)(12)]2=119.5

C(3)=[200+(3.25)(12)+(2)(3.25)(8)]3=97

C(4)=[200+(3.25)(12)+(2)(3.25)(8)+(3)(3.25)(44)]4=180

Stop the process since C(4)≻C(3),

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

C(1)=200

C(2)=[200+(3.25)(54)]2=187.75

C(3)=[200+(3.25)(54)+(2)(3.25)(16)]3=159.8

C(4)=[200+(3.25)(54)+(2)(3.25)(16)+(3)(3.25)(76)]4=305.12

Stop the process since C(4)≻C(3),

y6=r6+r7+r8

y6=44+54+16=114

Starting in period 9:

y9=r9+r10

y9=76+30=106

b)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the part period balancing heuristic.

Concept Introduction: one of the lot-sizing technique is to implementing the lowest-cost with the interconnection between costs of order and carrying cost for the inventory is generally known as Part period balancing.it is more effective for the product whose demand is unstable.

b)

Expert Solution

Answer to Problem 49AP

The order policy according to the part period balancing heuristic method will be

is (56,0,52,0,0,98,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to part period balancing method can be calculated as follows:

In this method the order horizon that equates holding and setup cost over that period has to be calculated as follows:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1:

Period	Holding Cost
2	110.5
3	318.5

Since the setup cost $200 is closer at period 4, stop and equate

y1=r1+r2

y1=22+34=56

Starting in period 3:

Period	Holding Cost
2	25
3	65
4	520

Since the setup cost $200 is closer to 4 than 3, stop and equate

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

Period	Holding Cost
2	175.5
3	279.5

Since the setup cost $200 is closer to 3, stop and equate

y6=r6+r7

y6=44+54=98

Starting in period 8:

Period	Holding Cost
2	247

Since the setup cost $200 is closer to 2, stop and equate

y8=r8+r9

y8=16+76=92

c)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the least unit cost heuristic.

Concept Introduction: Least unit cost heuristic technique is one of the time-varying demand pattern technique.one of the dynamic lot-sizing concept is that interrelated between the order cost and carrying cost of the inventory for the every lot size is defined as

Least Unit Cost (LUC).

c)

Expert Solution

Answer to Problem 49AP

The order policy according to the least unit cost heuristic method will be

is (56,0,44,0,106,0,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to lease unit cost(LUC) method can be calculated as follows:

LUC divides the average cost per period C (T) by the total number of units demanded. Hence C(1)=K/r1

And C(2)=(K+hr2)+(r1+r2),

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/(r1+r2...+rj)

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200/22=0.09

C(2)=(200+(3.25)(34))/(22+34)=5.54

C(3)=[200+(3.25)(34)+(2)(32)]22+34+32=5.89

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200/32=6.25

C(2)=[200+(3.25)(12)](32+12)=5.43

C(3)=[200+(3.25)(12)+(2)(3.25)(8)](32+12+8)=5.6

Stop the process since C(3)≻C(2),

y3=r3+r4

y3=32+12=44

Starting in period 5:

C(1)=200/8=25

C(2)=[200+(3.25)(44)](8+44)=6.60

C(3)=[200+(3.25)(44)+(2)(3.25)(54)](8+44+54)=6.54

C(4)=[200+(3.25)(44)+(2)(3.25)(54)+(3)(3.25)(16)](8+44+54+16)=7.97

Stop the process since C(4)≻C(3),

y5=r5+r6+r7

y5=8+44+54=106

Starting in period 8:

C(1)=200/16=12.5

C(2)=[200+(3.25)(76)](16+76)=4.85

C(3)=[200+(3.25)(76)+(2)(3.25)(30)](16+76+30)=5.2

Stop the process since C(3)≻C(2),

y8=r8+r9

y8=16+76=92

y10=r10=30

d)

Summary Introduction

Interpretation: Determine the method resulted in the lowest-cost policy for the given problem.

Concept Introduction: Least unit cost method makes the present period of the demands and evaluates the period of the future. Adding the carrying cost for the setup and the period of the inventory cost, the least unit cost will be occur.

d)

Expert Solution

Answer to Problem 49AP

The least expensive method is the least unit cost method with a total cost of $1351

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

Comparison of the three methods can be calculated as follows:

Calculate the total cost of the inventory for the three months. The method which yields less cost is the lowest cost policy.

The total cost under silver meal method can be calculated as follows:

The method required is 4 set ups

The total set up cost is 4×200=800

The total holding cost is (3.25)(22+32+44+76)=565.5

The total cost 800+565.5=1365.5

The total cost under silver-meal heuristic is $1365.5

The total cost under least unit cost method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+8+16+30)=351

The total cost 1000+351=1351

The total cost under least unit cost method is $1351

The total cost under part period balancing method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+44+16+30)=468

The total cost 1000+468=1468

The total cost under part period balancing method is $1468

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 8, Problem 49AP

a)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the silver-Meal heuristic.

Concept Introduction: Silver-Meal heuristic mainly focused on the manufacture planning in the production companies. It determines that within the minimum cost level, the quantities of the products will be produced by the company.

a)

Expert Solution

Answer to Problem 49AP

The order policy according to silver meal heuristic method is (56,0,52,0,0,114,0,0,106,0)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy of the inventory under silver meal method can be calculated as follows:

According to silver meal method the average cost per period C (T) is a function of the average holding and set up cost per period for T number of Periods. The production in period 1 is equal to the demand in that period 1 to incur the order cost K.

Hence C(1)=K

And C(2)=(K+hr2)/2

C(3)=(K+hr2+2hr3)/3

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/j

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

Now, calculate the order policy using the above formula as follows:

Starting in period 1:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200

C(2)=(200+(3.24)(34))/2=155.25

C(3)=[200+(3.24)(34)+(2)(3.24)(32)]3=172.8

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200

C(2)=[200+(3.25)(12)]2=119.5

C(3)=[200+(3.25)(12)+(2)(3.25)(8)]3=97

C(4)=[200+(3.25)(12)+(2)(3.25)(8)+(3)(3.25)(44)]4=180

Stop the process since C(4)≻C(3),

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

C(1)=200

C(2)=[200+(3.25)(54)]2=187.75

C(3)=[200+(3.25)(54)+(2)(3.25)(16)]3=159.8

C(4)=[200+(3.25)(54)+(2)(3.25)(16)+(3)(3.25)(76)]4=305.12

Stop the process since C(4)≻C(3),

y6=r6+r7+r8

y6=44+54+16=114

Starting in period 9:

y9=r9+r10

y9=76+30=106

b)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the part period balancing heuristic.

Concept Introduction: one of the lot-sizing technique is to implementing the lowest-cost with the interconnection between costs of order and carrying cost for the inventory is generally known as Part period balancing.it is more effective for the product whose demand is unstable.

b)

Expert Solution

Answer to Problem 49AP

The order policy according to the part period balancing heuristic method will be

is (56,0,52,0,0,98,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to part period balancing method can be calculated as follows:

In this method the order horizon that equates holding and setup cost over that period has to be calculated as follows:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1:

Period	Holding Cost
2	110.5
3	318.5

Since the setup cost $200 is closer at period 4, stop and equate

y1=r1+r2

y1=22+34=56

Starting in period 3:

Period	Holding Cost
2	25
3	65
4	520

Since the setup cost $200 is closer to 4 than 3, stop and equate

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

Period	Holding Cost
2	175.5
3	279.5

Since the setup cost $200 is closer to 3, stop and equate

y6=r6+r7

y6=44+54=98

Starting in period 8:

Period	Holding Cost
2	247

Since the setup cost $200 is closer to 2, stop and equate

y8=r8+r9

y8=16+76=92

c)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the least unit cost heuristic.

Concept Introduction: Least unit cost heuristic technique is one of the time-varying demand pattern technique.one of the dynamic lot-sizing concept is that interrelated between the order cost and carrying cost of the inventory for the every lot size is defined as

Least Unit Cost (LUC).

c)

Expert Solution

Answer to Problem 49AP

The order policy according to the least unit cost heuristic method will be

is (56,0,44,0,106,0,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to lease unit cost(LUC) method can be calculated as follows:

LUC divides the average cost per period C (T) by the total number of units demanded. Hence C(1)=K/r1

And C(2)=(K+hr2)+(r1+r2),

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/(r1+r2...+rj)

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200/22=0.09

C(2)=(200+(3.25)(34))/(22+34)=5.54

C(3)=[200+(3.25)(34)+(2)(32)]22+34+32=5.89

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200/32=6.25

C(2)=[200+(3.25)(12)](32+12)=5.43

C(3)=[200+(3.25)(12)+(2)(3.25)(8)](32+12+8)=5.6

Stop the process since C(3)≻C(2),

y3=r3+r4

y3=32+12=44

Starting in period 5:

C(1)=200/8=25

C(2)=[200+(3.25)(44)](8+44)=6.60

C(3)=[200+(3.25)(44)+(2)(3.25)(54)](8+44+54)=6.54

C(4)=[200+(3.25)(44)+(2)(3.25)(54)+(3)(3.25)(16)](8+44+54+16)=7.97

Stop the process since C(4)≻C(3),

y5=r5+r6+r7

y5=8+44+54=106

Starting in period 8:

C(1)=200/16=12.5

C(2)=[200+(3.25)(76)](16+76)=4.85

C(3)=[200+(3.25)(76)+(2)(3.25)(30)](16+76+30)=5.2

Stop the process since C(3)≻C(2),

y8=r8+r9

y8=16+76=92

y10=r10=30

d)

Summary Introduction

Interpretation: Determine the method resulted in the lowest-cost policy for the given problem.

Concept Introduction: Least unit cost method makes the present period of the demands and evaluates the period of the future. Adding the carrying cost for the setup and the period of the inventory cost, the least unit cost will be occur.

d)

Expert Solution

Answer to Problem 49AP

The least expensive method is the least unit cost method with a total cost of $1351

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

Comparison of the three methods can be calculated as follows:

Calculate the total cost of the inventory for the three months. The method which yields less cost is the lowest cost policy.

The total cost under silver meal method can be calculated as follows:

The method required is 4 set ups

The total set up cost is 4×200=800

The total holding cost is (3.25)(22+32+44+76)=565.5

The total cost 800+565.5=1365.5

The total cost under silver-meal heuristic is $1365.5

The total cost under least unit cost method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+8+16+30)=351

The total cost 1000+351=1351

The total cost under least unit cost method is $1351

The total cost under part period balancing method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+44+16+30)=468

The total cost 1000+468=1468

The total cost under part period balancing method is $1468

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 8, Problem 49AP

a)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the silver-Meal heuristic.

Concept Introduction: Silver-Meal heuristic mainly focused on the manufacture planning in the production companies. It determines that within the minimum cost level, the quantities of the products will be produced by the company.

a)

Expert Solution

Answer to Problem 49AP

The order policy according to silver meal heuristic method is (56,0,52,0,0,114,0,0,106,0)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy of the inventory under silver meal method can be calculated as follows:

According to silver meal method the average cost per period C (T) is a function of the average holding and set up cost per period for T number of Periods. The production in period 1 is equal to the demand in that period 1 to incur the order cost K.

Hence C(1)=K

And C(2)=(K+hr2)/2

C(3)=(K+hr2+2hr3)/3

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/j

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

Now, calculate the order policy using the above formula as follows:

Starting in period 1:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200

C(2)=(200+(3.24)(34))/2=155.25

C(3)=[200+(3.24)(34)+(2)(3.24)(32)]3=172.8

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200

C(2)=[200+(3.25)(12)]2=119.5

C(3)=[200+(3.25)(12)+(2)(3.25)(8)]3=97

C(4)=[200+(3.25)(12)+(2)(3.25)(8)+(3)(3.25)(44)]4=180

Stop the process since C(4)≻C(3),

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

C(1)=200

C(2)=[200+(3.25)(54)]2=187.75

C(3)=[200+(3.25)(54)+(2)(3.25)(16)]3=159.8

C(4)=[200+(3.25)(54)+(2)(3.25)(16)+(3)(3.25)(76)]4=305.12

Stop the process since C(4)≻C(3),

y6=r6+r7+r8

y6=44+54+16=114

Starting in period 9:

y9=r9+r10

y9=76+30=106

b)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the part period balancing heuristic.

Concept Introduction: one of the lot-sizing technique is to implementing the lowest-cost with the interconnection between costs of order and carrying cost for the inventory is generally known as Part period balancing.it is more effective for the product whose demand is unstable.

b)

Expert Solution

Answer to Problem 49AP

The order policy according to the part period balancing heuristic method will be

is (56,0,52,0,0,98,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to part period balancing method can be calculated as follows:

In this method the order horizon that equates holding and setup cost over that period has to be calculated as follows:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1:

Period	Holding Cost
2	110.5
3	318.5

Since the setup cost $200 is closer at period 4, stop and equate

y1=r1+r2

y1=22+34=56

Starting in period 3:

Period	Holding Cost
2	25
3	65
4	520

Since the setup cost $200 is closer to 4 than 3, stop and equate

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

Period	Holding Cost
2	175.5
3	279.5

Since the setup cost $200 is closer to 3, stop and equate

y6=r6+r7

y6=44+54=98

Starting in period 8:

Period	Holding Cost
2	247

Since the setup cost $200 is closer to 2, stop and equate

y8=r8+r9

y8=16+76=92

c)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the least unit cost heuristic.

Concept Introduction: Least unit cost heuristic technique is one of the time-varying demand pattern technique.one of the dynamic lot-sizing concept is that interrelated between the order cost and carrying cost of the inventory for the every lot size is defined as

Least Unit Cost (LUC).

c)

Expert Solution

Answer to Problem 49AP

The order policy according to the least unit cost heuristic method will be

is (56,0,44,0,106,0,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to lease unit cost(LUC) method can be calculated as follows:

LUC divides the average cost per period C (T) by the total number of units demanded. Hence C(1)=K/r1

And C(2)=(K+hr2)+(r1+r2),

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/(r1+r2...+rj)

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200/22=0.09

C(2)=(200+(3.25)(34))/(22+34)=5.54

C(3)=[200+(3.25)(34)+(2)(32)]22+34+32=5.89

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200/32=6.25

C(2)=[200+(3.25)(12)](32+12)=5.43

C(3)=[200+(3.25)(12)+(2)(3.25)(8)](32+12+8)=5.6

Stop the process since C(3)≻C(2),

y3=r3+r4

y3=32+12=44

Starting in period 5:

C(1)=200/8=25

C(2)=[200+(3.25)(44)](8+44)=6.60

C(3)=[200+(3.25)(44)+(2)(3.25)(54)](8+44+54)=6.54

C(4)=[200+(3.25)(44)+(2)(3.25)(54)+(3)(3.25)(16)](8+44+54+16)=7.97

Stop the process since C(4)≻C(3),

y5=r5+r6+r7

y5=8+44+54=106

Starting in period 8:

C(1)=200/16=12.5

C(2)=[200+(3.25)(76)](16+76)=4.85

C(3)=[200+(3.25)(76)+(2)(3.25)(30)](16+76+30)=5.2

Stop the process since C(3)≻C(2),

y8=r8+r9

y8=16+76=92

y10=r10=30

d)

Summary Introduction

Interpretation: Determine the method resulted in the lowest-cost policy for the given problem.

Concept Introduction: Least unit cost method makes the present period of the demands and evaluates the period of the future. Adding the carrying cost for the setup and the period of the inventory cost, the least unit cost will be occur.

d)

Expert Solution

Answer to Problem 49AP

The least expensive method is the least unit cost method with a total cost of $1351

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

Comparison of the three methods can be calculated as follows:

Calculate the total cost of the inventory for the three months. The method which yields less cost is the lowest cost policy.

The total cost under silver meal method can be calculated as follows:

The method required is 4 set ups

The total set up cost is 4×200=800

The total holding cost is (3.25)(22+32+44+76)=565.5

The total cost 800+565.5=1365.5

The total cost under silver-meal heuristic is $1365.5

The total cost under least unit cost method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+8+16+30)=351

The total cost 1000+351=1351

The total cost under least unit cost method is $1351

The total cost under part period balancing method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+44+16+30)=468

The total cost 1000+468=1468

The total cost under part period balancing method is $1468

Answer 6

Chapter 8, Problem 49AP

a)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the silver-Meal heuristic.

Concept Introduction: Silver-Meal heuristic mainly focused on the manufacture planning in the production companies. It determines that within the minimum cost level, the quantities of the products will be produced by the company.

a)

Expert Solution

Answer to Problem 49AP

The order policy according to silver meal heuristic method is (56,0,52,0,0,114,0,0,106,0)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy of the inventory under silver meal method can be calculated as follows:

According to silver meal method the average cost per period C (T) is a function of the average holding and set up cost per period for T number of Periods. The production in period 1 is equal to the demand in that period 1 to incur the order cost K.

Hence C(1)=K

And C(2)=(K+hr2)/2

C(3)=(K+hr2+2hr3)/3

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/j

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

Now, calculate the order policy using the above formula as follows:

Starting in period 1:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200

C(2)=(200+(3.24)(34))/2=155.25

C(3)=[200+(3.24)(34)+(2)(3.24)(32)]3=172.8

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200

C(2)=[200+(3.25)(12)]2=119.5

C(3)=[200+(3.25)(12)+(2)(3.25)(8)]3=97

C(4)=[200+(3.25)(12)+(2)(3.25)(8)+(3)(3.25)(44)]4=180

Stop the process since C(4)≻C(3),

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

C(1)=200

C(2)=[200+(3.25)(54)]2=187.75

C(3)=[200+(3.25)(54)+(2)(3.25)(16)]3=159.8

C(4)=[200+(3.25)(54)+(2)(3.25)(16)+(3)(3.25)(76)]4=305.12

Stop the process since C(4)≻C(3),

y6=r6+r7+r8

y6=44+54+16=114

Starting in period 9:

y9=r9+r10

y9=76+30=106

Answer 7

Chapter 8, Problem 49AP

a)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the silver-Meal heuristic.

Concept Introduction: Silver-Meal heuristic mainly focused on the manufacture planning in the production companies. It determines that within the minimum cost level, the quantities of the products will be produced by the company.

Answer 8

a)

Expert Solution

Answer to Problem 49AP

The order policy according to silver meal heuristic method is (56,0,52,0,0,114,0,0,106,0)

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy of the inventory under silver meal method can be calculated as follows:

According to silver meal method the average cost per period C (T) is a function of the average holding and set up cost per period for T number of Periods. The production in period 1 is equal to the demand in that period 1 to incur the order cost K.

Hence C(1)=K

And C(2)=(K+hr2)/2

C(3)=(K+hr2+2hr3)/3

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/j

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

Now, calculate the order policy using the above formula as follows:

Starting in period 1:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200

C(2)=(200+(3.24)(34))/2=155.25

C(3)=[200+(3.24)(34)+(2)(3.24)(32)]3=172.8

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200

C(2)=[200+(3.25)(12)]2=119.5

C(3)=[200+(3.25)(12)+(2)(3.25)(8)]3=97

C(4)=[200+(3.25)(12)+(2)(3.25)(8)+(3)(3.25)(44)]4=180

Stop the process since C(4)≻C(3),

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

C(1)=200

C(2)=[200+(3.25)(54)]2=187.75

C(3)=[200+(3.25)(54)+(2)(3.25)(16)]3=159.8

C(4)=[200+(3.25)(54)+(2)(3.25)(16)+(3)(3.25)(76)]4=305.12

Stop the process since C(4)≻C(3),

y6=r6+r7+r8

y6=44+54+16=114

Starting in period 9:

y9=r9+r10

y9=76+30=106

Answer 13

b)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the part period balancing heuristic.

Concept Introduction: one of the lot-sizing technique is to implementing the lowest-cost with the interconnection between costs of order and carrying cost for the inventory is generally known as Part period balancing.it is more effective for the product whose demand is unstable.

b)

Expert Solution

Answer to Problem 49AP

The order policy according to the part period balancing heuristic method will be

is (56,0,52,0,0,98,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to part period balancing method can be calculated as follows:

In this method the order horizon that equates holding and setup cost over that period has to be calculated as follows:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1:

Period	Holding Cost
2	110.5
3	318.5

Since the setup cost $200 is closer at period 4, stop and equate

y1=r1+r2

y1=22+34=56

Starting in period 3:

Period	Holding Cost
2	25
3	65
4	520

Since the setup cost $200 is closer to 4 than 3, stop and equate

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

Period	Holding Cost
2	175.5
3	279.5

Since the setup cost $200 is closer to 3, stop and equate

y6=r6+r7

y6=44+54=98

Starting in period 8:

Period	Holding Cost
2	247

Since the setup cost $200 is closer to 2, stop and equate

y8=r8+r9

y8=16+76=92

Answer 14

b)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the part period balancing heuristic.

Concept Introduction: one of the lot-sizing technique is to implementing the lowest-cost with the interconnection between costs of order and carrying cost for the inventory is generally known as Part period balancing.it is more effective for the product whose demand is unstable.

Answer 15

b)

Expert Solution

Answer to Problem 49AP

The order policy according to the part period balancing heuristic method will be

is (56,0,52,0,0,98,0,92,0,30)

Answer 16

b)

Expert Solution

Answer 17

b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to part period balancing method can be calculated as follows:

In this method the order horizon that equates holding and setup cost over that period has to be calculated as follows:

K=$200

h=(0.005)(0.65)

(Since h is calculated on 0.5% annual interest rate with each unit cost at 65cents)

h=3.25 Per thousand

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1:

Period	Holding Cost
2	110.5
3	318.5

Since the setup cost $200 is closer at period 4, stop and equate

y1=r1+r2

y1=22+34=56

Starting in period 3:

Period	Holding Cost
2	25
3	65
4	520

Since the setup cost $200 is closer to 4 than 3, stop and equate

y3=r3+r4+r5

y3=32+12+8=52

Starting in period 6:

Period	Holding Cost
2	175.5
3	279.5

Since the setup cost $200 is closer to 3, stop and equate

y6=r6+r7

y6=44+54=98

Starting in period 8:

Period	Holding Cost
2	247

Since the setup cost $200 is closer to 2, stop and equate

y8=r8+r9

y8=16+76=92

Answer 20

c)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the least unit cost heuristic.

Concept Introduction: Least unit cost heuristic technique is one of the time-varying demand pattern technique.one of the dynamic lot-sizing concept is that interrelated between the order cost and carrying cost of the inventory for the every lot size is defined as

Least Unit Cost (LUC).

c)

Expert Solution

Answer to Problem 49AP

The order policy according to the least unit cost heuristic method will be

is (56,0,44,0,106,0,0,92,0,30)

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to lease unit cost(LUC) method can be calculated as follows:

LUC divides the average cost per period C (T) by the total number of units demanded. Hence C(1)=K/r1

And C(2)=(K+hr2)+(r1+r2),

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/(r1+r2...+rj)

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200/22=0.09

C(2)=(200+(3.25)(34))/(22+34)=5.54

C(3)=[200+(3.25)(34)+(2)(32)]22+34+32=5.89

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200/32=6.25

C(2)=[200+(3.25)(12)](32+12)=5.43

C(3)=[200+(3.25)(12)+(2)(3.25)(8)](32+12+8)=5.6

Stop the process since C(3)≻C(2),

y3=r3+r4

y3=32+12=44

Starting in period 5:

C(1)=200/8=25

C(2)=[200+(3.25)(44)](8+44)=6.60

C(3)=[200+(3.25)(44)+(2)(3.25)(54)](8+44+54)=6.54

C(4)=[200+(3.25)(44)+(2)(3.25)(54)+(3)(3.25)(16)](8+44+54+16)=7.97

Stop the process since C(4)≻C(3),

y5=r5+r6+r7

y5=8+44+54=106

Starting in period 8:

C(1)=200/16=12.5

C(2)=[200+(3.25)(76)](16+76)=4.85

C(3)=[200+(3.25)(76)+(2)(3.25)(30)](16+76+30)=5.2

Stop the process since C(3)≻C(2),

y8=r8+r9

y8=16+76=92

y10=r10=30

Answer 21

c)

Summary Introduction

Interpretation: Determine the ordering policy is recommended by the least unit cost heuristic.

Concept Introduction: Least unit cost heuristic technique is one of the time-varying demand pattern technique.one of the dynamic lot-sizing concept is that interrelated between the order cost and carrying cost of the inventory for the every lot size is defined as

Least Unit Cost (LUC).

Answer 22

c)

Expert Solution

Answer to Problem 49AP

The order policy according to the least unit cost heuristic method will be

is (56,0,44,0,106,0,0,92,0,30)

Answer 23

c)

Expert Solution

Answer 24

c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

The order policy according to lease unit cost(LUC) method can be calculated as follows:

LUC divides the average cost per period C (T) by the total number of units demanded. Hence C(1)=K/r1

And C(2)=(K+hr2)+(r1+r2),

And general equation is C(j)=(K+hr2+2hr3+...+(j−1)hrj)/(r1+r2...+rj)

Once C(j)≻C(j−1), stop the function and set y=r1+r2+r3+....rj−1

r=(22,34,32,12,8,44,54,16,76,30)

Starting from period 1

C(1)=200/22=0.09

C(2)=(200+(3.25)(34))/(22+34)=5.54

C(3)=[200+(3.25)(34)+(2)(32)]22+34+32=5.89

Stop the process since C(3)≻C(2),

y1=r1+r2

y1=22+34=56

Starting in period 3:

C(1)=200/32=6.25

C(2)=[200+(3.25)(12)](32+12)=5.43

C(3)=[200+(3.25)(12)+(2)(3.25)(8)](32+12+8)=5.6

Stop the process since C(3)≻C(2),

y3=r3+r4

y3=32+12=44

Starting in period 5:

C(1)=200/8=25

C(2)=[200+(3.25)(44)](8+44)=6.60

C(3)=[200+(3.25)(44)+(2)(3.25)(54)](8+44+54)=6.54

C(4)=[200+(3.25)(44)+(2)(3.25)(54)+(3)(3.25)(16)](8+44+54+16)=7.97

Stop the process since C(4)≻C(3),

y5=r5+r6+r7

y5=8+44+54=106

Starting in period 8:

C(1)=200/16=12.5

C(2)=[200+(3.25)(76)](16+76)=4.85

C(3)=[200+(3.25)(76)+(2)(3.25)(30)](16+76+30)=5.2

Stop the process since C(3)≻C(2),

y8=r8+r9

y8=16+76=92

y10=r10=30

Answer 27

d)

Summary Introduction

Interpretation: Determine the method resulted in the lowest-cost policy for the given problem.

Concept Introduction: Least unit cost method makes the present period of the demands and evaluates the period of the future. Adding the carrying cost for the setup and the period of the inventory cost, the least unit cost will be occur.

d)

Expert Solution

Answer to Problem 49AP

The least expensive method is the least unit cost method with a total cost of $1351

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

Comparison of the three methods can be calculated as follows:

Calculate the total cost of the inventory for the three months. The method which yields less cost is the lowest cost policy.

The total cost under silver meal method can be calculated as follows:

The method required is 4 set ups

The total set up cost is 4×200=800

The total holding cost is (3.25)(22+32+44+76)=565.5

The total cost 800+565.5=1365.5

The total cost under silver-meal heuristic is $1365.5

The total cost under least unit cost method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+8+16+30)=351

The total cost 1000+351=1351

The total cost under least unit cost method is $1351

The total cost under part period balancing method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+44+16+30)=468

The total cost 1000+468=1468

The total cost under part period balancing method is $1468

Answer 28

d)

Summary Introduction

Interpretation: Determine the method resulted in the lowest-cost policy for the given problem.

Concept Introduction: Least unit cost method makes the present period of the demands and evaluates the period of the future. Adding the carrying cost for the setup and the period of the inventory cost, the least unit cost will be occur.

Answer 29

d)

Expert Solution

Answer to Problem 49AP

The least expensive method is the least unit cost method with a total cost of $1351

Answer 30

d)

Expert Solution

Answer 31

d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given information: The anticipated demand for an inventory is as follows:

Week	1	2	3	4	5	6	7	8	9	10
Demand	22	34	32	12	8	44	54	16	76	30

The inventory costs 65 cents each and holding cost (h) is calculated on annual interest rate at 0.5% per week. The set up cost (K) is $200.

Comparison of the three methods can be calculated as follows:

Calculate the total cost of the inventory for the three months. The method which yields less cost is the lowest cost policy.

The total cost under silver meal method can be calculated as follows:

The method required is 4 set ups

The total set up cost is 4×200=800

The total holding cost is (3.25)(22+32+44+76)=565.5

The total cost 800+565.5=1365.5

The total cost under silver-meal heuristic is $1365.5

The total cost under least unit cost method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+8+16+30)=351

The total cost 1000+351=1351

The total cost under least unit cost method is $1351

The total cost under part period balancing method can be calculated as follows:

The method required is 5 set ups

The total set up cost is 5×200=1000

The total holding cost is (3.25)(22+32+44+16+30)=468

The total cost 1000+468=1468

The total cost under part period balancing method is $1468

Answer 34

Ch. 8.1 - Prob. 1P Ch. 8.1 - Prob. 2P Ch. 8.1 - Prob. 3P Ch. 8.1 - Prob. 4P Ch. 8.1 - Prob. 5P Ch. 8.1 - Prob. 6P Ch. 8.1 - Prob. 7P Ch. 8.1 - Prob. 8P Ch. 8.1 - Prob. 9P Ch. 8.2 - Prob. 10P

Concept explainers

Videos

Answer to Problem 49AP

Explanation of Solution

Answer to Problem 49AP

Explanation of Solution

Answer to Problem 49AP

Explanation of Solution

Answer to Problem 49AP

Explanation of Solution

Want to see more full solutions like this?

Chapter 8 Solutions